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color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3309" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3741" to=3D"624,37= 41" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3310" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3939" to=3D"624,39= 39" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3311" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3918" to=3D"624,39= 18" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3312" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3510" to=3D"624,35= 10" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3313" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3546" to=3D"624,35= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3314" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3579" to=3D"624,35= 79" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3315" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3420" to=3D"624,34= 20" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3316" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3372" to=3D"624,33= 72" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3317" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3465" to=3D"624,34= 65" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3318" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2973" to=3D"624,29= 73" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3319" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2946" to=3D"624,29= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3320" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3327" to=3D"624,33= 27" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3321" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3201" to=3D"624,32= 01" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3322" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3120" to=3D"624,31= 20" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3323" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3306" to=3D"624,33= 06" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3324" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2994" to=3D"624,29= 94" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3325" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3048" to=3D"624,30= 48" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3326" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3246" to=3D"624,32= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3327" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3225" to=3D"624,32= 25" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3328" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2831" to=3D"624,28= 31" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3329" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2750" to=3D"624,27= 50" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3330" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2678" to=3D"624,26= 78" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3331" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2876" to=3D"624,28= 76" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3332" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2855" to=3D"624,28= 55" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3333" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2554" to=3D"624,25= 54" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3334" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2590" to=3D"624,25= 90" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3335" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2623" to=3D"624,26= 23" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3336" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2464" to=3D"624,24= 64" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3337" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2416" to=3D"624,24= 16" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3338" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2509" to=3D"624,25= 09" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3339" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2371" to=3D"624,23= 71" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3340" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2245" to=3D"624,22= 45" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3341" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2350" to=3D"624,23= 50" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3342" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2290" to=3D"624,22= 90" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3343" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2269" to=3D"624,22= 69" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3344" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2130" to=3D"624,21= 30" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3345" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2166" to=3D"624,21= 66" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3346" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2199" to=3D"624,21= 99" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3347" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2040" to=3D"624,20= 40" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3348" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1992" to=3D"624,19= 92" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3349" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2085" to=3D"624,20= 85" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3350" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1593" to=3D"624,15= 93" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3351" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1566" to=3D"624,15= 66" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3352" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1947" to=3D"624,19= 47" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3353" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1821" to=3D"624,18= 21" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3354" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1740" to=3D"624,17= 40" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" 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Functional Forms</span> </div> <div v:shape=3D"_x0000_s32771"> <div class=3DB><span style=3D'position:absolute;top:33.5%;left:13.67%;widt= h:85.2%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-4.39%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>The crux of the dual appr= oach is then to </span></span><span style=3D'position:absolute;top:40.5%;left:1= 3.67%; width:87.26%;height:6.75%'><span style=3D'mso-bidi-font-family:"Times New = Roman"'>estimate a manifestation of behavior that </span></span><span style=3D'position:abs= olute; top:47.5%;left:13.67%;width:81.46%;height:6.75%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>economist know something about.</span> </span></div> <div class=3DB1><span style=3D'position:absolute;top:56.0%;left:17.97%;wid= th:90.63%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Thus, instead of estimati= ng production functions </span></span><span style=3D'position:absolute;top:62= .25%; left:17.97%;width:84.26%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>that are purely physical forms that economist </span></span><span style=3D'posi= tion: absolute;top:68.5%;left:17.97%;width:82.58%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>have little expertise in developing, we could </span></span><span style=3D'position:absolute;top:74= .5%; left:17.97%;width:84.83%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>estimate the cost function that represents cost </span></span><span style=3D'positi= on: absolute;top:80.75%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>minimizing behavior.</spa= n> </span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/master03_image004.gif 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style=3D'position:absolute;top:39.5%;left:17.97%;width:88.38%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>properties of these cost functions are consistent </span></span><span style=3D'position:absolute; top:45.75%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>with our hypotheses about technology.</span> </spa= n></div> <div class=3DB1><span style=3D'position:absolute;top:53.25%;left:17.97%; width:91.94%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-3.46%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= However, it is often the direct implications of the </span></span><span style=3D'position:absolute;top:59.5%;left:17.97%;width:88.76%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>cost minimizing behavior = that we are interested </span></span><span style=3D'position:absolute;top:65.75= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>in:</span> </span></div> <div class=3DB2><span style=3D'position:absolute;top:73.0%;left:21.72%;wid= th:78.65%; height:5.25%'><span class=3DB2B style=3D'position:absolute;left:-3.09%;top= :.49em'>l</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>How will farmers react to changes in agricultural </span></span><span style=3D'position:absolute; top:78.25%;left:21.72%;width:73.4%;height:5.25%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>prices through commodity programs?</span> </span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum 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height:100.0%'><span style=3D'visibility:hidden'><span class=3DB2B style=3D'position:absolute;left:-3.31%'>l</span></span> </span></div> <div class=3DB2 style=3D'position:absolute;top:51.5%;left:19.28%;width:75.= 84%; height:5.25%'><span style=3D'position:absolute;top:0%;left:3.2%;width:96.7= 9%; height:100.0%'><span style=3D'visibility:hidden'><span class=3DB2B style=3D'position:absolute;left:-3.31%'>l</span></span> </span></div> <div class=3DB1><span style=3D'position:absolute;top:57.99%;left:17.97%; width:86.89%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-3.66%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Thus, the dual cost function results are usually </span></span><span style=3D'position:absolute;top:64.25%;left:17.97%;width:87.07%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman"'>sufficient for most quest= ion facing agricultural </span></span><span style=3D'position:absolute;top:70.= 5%; 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position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s35843"> <div class=3DB><span style=3D'position:absolute;top:33.5%;left:13.67%;widt= h:97.0%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-3.86%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Given that we are interes= ted in estimating the </span></span><span style=3D'position:absolute;top:40.5%; left:13.67%;width:84.64%;height:6.75%'><span style=3D'mso-bidi-font-family= :"Times New Roman"'>cost function directly, the next question </span></span><span style=3D'position= :absolute; top:47.5%;left:13.67%;width:90.26%;height:6.75%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>involves how to specify the cost function?</span> = </span></div> <div class=3DB1><span style=3D'position:absolute;top:56.0%;left:17.97%;wid= th:90.63%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>One approach to the estim= ation of cost functions </span></span><span style=3D'position:absolute;top:62.25= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>would then be to hypothesize a primal </span></span><span style=3D'position:abso= lute; top:68.5%;left:17.97%;width:89.13%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>production function and derive the theoretically </span= ></span><span style=3D'position:absolute;top:74.5%;left:17.97%;width:82.58%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>consistent specification = for the cost function </span></span><span style=3D'position:absolute;top:80.75= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>based on this primal. </span></span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0006.htm 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o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s36867"> <div class=3DB1><span style=3D'position:absolute;top:33.25%;left:17.97%; width:78.08%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-4.07%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= However, this approach would appear too </span></span><span style=3D'position:absol= ute; top:39.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>restrictive. </span></span></div> <div class=3DB1><span style=3D'position:absolute;top:47.0%;left:17.97%;wid= th:78.08%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-4.07%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Thus, economists have typ= ically turned to </span></span><span style=3D'position:absolute;top:53.25%;left:1= 7.97%; width:86.32%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New R= oman"'>flexible functional forms that allow for a wide </span></span><span style=3D'positi= on: absolute;top:59.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>variety of technologies. = </span></span></div> <div class=3DB style=3D'position:absolute;top:67.25%;left:9.92%;width:85.2= %; height:6.75%'><span style=3D'position:absolute;top:0%;left:4.39%;width:95.= 6%; height:100.0%'><span style=3D'visibility:hidden'><span class=3DBB style=3D'position:absolute;left:-4.59%'>w</span></span><span style=3D'mso-= bidi-font-family: "Times New Roman";mso-special-format:lastCR;display:none'> </span></sp= an></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: 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color2=3D"white [0]"/> <v:shadow color=3D"#e3e2c7 [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> </v:rect> <div v:shape=3D"_x0000_s40963" class=3DB1> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:32.75%;left:17.97%;width:91.94%;height:6.0%'><span style=3D'mso-specia= l-format: bullet;position:absolute;left:-3.46%;top:.74em;font-family:Wingdings; font-size:55%'>n</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>The real problem is that we don’t know the value </span></span><span style=3D'position:absolute;top:38.5%;left:17.97%;width:91.57%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>of </span><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>x</i></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:67%;position:rel= ative; top:-.45em;mso-text-raise:30%'>*</span><span style=3D'mso-bidi-font-family= :"Times New Roman"'>.<span style=3D'mso-spacerun:yes'> </span>As a result, we approximate this = term with </span></span><span style=3D'position:absolute;top:44.0%;left:17.97%; width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New R= oman"'>a residual:</span> </span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:51.0%;left:= 14.79%; width:80.14%;height:6.0%'><span style=3D'position:absolute;top:0%;left:3.9= 7%; width:96.26%;height:100.0%'><span style=3D'visibility:hidden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:57.75%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:64.5%;left:17.97%;width:80.52%;height:6.0%'><span style=3D'mso-special= -format: bullet;position:absolute;left:-3.95%;top:.74em;font-family:Wingdings; font-size:55%'>n</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>Given this approach, we can conjecture the </span></span><span style=3D'position= :absolute; top:70.25%;left:17.97%;width:90.63%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>relative size of the approximation error based on </spa= n></span><span style=3D'position:absolute;top:75.75%;left:17.97%;width:91.76%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman"'>the relative size of the = third derivative of the cost </span></span><span style=3D'position:absolute; top:81.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>function.</span> </span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" 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<title>Cost Functions and the Estimation of Flexible Functional Forms </tit= le> <![if IE]> <base href=3D"file:///C:\B2E9C635\Lecture18-2005_files\slide0010.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"11/14/2005"> <link rel=3DStylesheet href=3D"master03_stylesheet.css"> <![if !ppt]> <style media=3Dprint>  </style> <script src=3Dscript.js></script><script></script><![endif]><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"41"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#ffffff,#003366,#e3e2c7,#003366,#cccc99,#003366,#003366,#800000" masterhref=3D"master03.xml"> <p:shaperange href=3D"master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange href=3D"master03.xml#_x0000_s1249"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s1249,_x0000_s1146,_x0000_s1147,_x0000_s1148,_x0000_s11= 49,_x0000_s1150,_x0000_s1151,_x0000_s1152,_x0000_s1153,_x0000_s1154,_x0000_= s1155,_x0000_s1156,_x0000_s1157,_x0000_s1158,_x0000_s1159,_x0000_s1160,_x00= 00_s1161,_x0000_s1162,_x0000_s1163,_x0000_s1164,_x0000_s1165,_x0000_s1166,_= x0000_s1167,_x0000_s1168,_x0000_s1169,_x0000_s1170,_x0000_s1171,_x0000_s117= 2,_x0000_s1173,_x0000_s1174,_x0000_s1175,_x0000_s1176,_x0000_s1177,_x0000_s= 1178,_x0000_s1179,_x0000_s1180,_x0000_s1181,_x0000_s1182,_x0000_s1183,_x000= 0_s1184,_x0000_s1185,_x0000_s1186,_x0000_s1187,_x0000_s1188,_x0000_s1189,_x= 0000_s1190,_x0000_s1191,_x0000_s1192,_x0000_s1193,_x0000_s1194,_x0000_s1195= ,_x0000_s1196,_x0000_s1197,_x0000_s1198,_x0000_s1199,_x0000_s1200,_x0000_s1= 201,_x0000_s1202,_x0000_s1203,_x0000_s1204,_x0000_s1205,_x0000_s1206,_x0000= 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</span><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>w</i></span><span style=3D'mso-bidi-font-family:"Times New Roman"'> and output levels </span= ><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>y</i></span><span style=3D'mso-bidi-font-family:"Times New Roman"'>, we could then stack </s= pan></span><span style=3D'position:absolute;top:44.0%;left:17.97%;width:78.27%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>the two into a single vec= tor and derive the </span></span><span style=3D'position:absolute;top:49.75%; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>flexible functional form:</span> </span></div> <div class=3DB1 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:= 56.49%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div class=3DB1 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:= 63.24%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div class=3DB2 style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positi= on:absolute; top:70.0%;left:21.72%;width:85.95%;height:5.25%'><span style=3D'mso-specia= l-format: bullet;position:absolute;left:-2.83%;top:.49em;font-family:Wingdings; font-size:65%'>l</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>This form is typically referred to as the quadratic cost </span></span><span style=3D'position:absolute;top:74.75%;left:21.72%;width:86.14%;height:5.25= %'><span 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class=3DB1B style=3D'position:absolute;left:-4.12%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Why have I imposed symmetry?</span> </span></div> <div class=3DB1 style=3D'position:absolute;top:40.75%;left:14.79%;width:93= .82%; height:6.0%'><span style=3D'position:absolute;top:0%;left:3.39%;width:96.6= %; height:100.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Why am I only estimating three demand curves?</span> </span></div> <div class=3DB><span style=3D'position:absolute;top:48.5%;left:13.67%;widt= h:83.33%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-4.49%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>One generalization of the Taylor series </span></span><span style=3D'position:absolute;top:55.75%; left:13.67%;width:81.46%;height:6.75%'><span style=3D'mso-bidi-font-family= :"Times New Roman"'>approach involves a 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style=3D'position:absolute;top:0%;left:3.97%;width:96.26%;height:100.0%'><= span style=3D'visibility:hidden'><span class=3DB1B style=3D'position:absolute;l= eft:-4.12%'>n</span></span> </span></div> <span style=3D'position:absolute;top:70.75%;left:17.97%;width:84.08%;heigh= t: 6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.78%;top:.74em'>= n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>This formulation complica= tes the Shephard’s </span></span><span style=3D'position:absolute;top:77= .0%; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>lemma results slightly:</span> </span></div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f 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position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s60419" class=3DB><span style=3D'position:absolute; top:33.25%;left:13.67%;width:93.07%;height:6.0%'><span style=3D'font-size:= 88%'><span class=3DBB style=3D'position:absolute;left:-4.02%'>w</span></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>This representation minimizes the Sobolev Norm, </span></span><span style=3D'position:absolute;top:39.5%;left:13.67%;width:92.88%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>which says = that it does a better job approximating </span></span><span style=3D'position:a= bsolute; top:45.75%;left:13.67%;width:96.62%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman";font-size:88%'>the derivatives of the function.<span style=3D'mso-spacerun:yes'> </span>In fact, it represents </span></s= pan><span style=3D'position:absolute;top:52.0%;left:13.67%;width:81.46%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>up to the <= /span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'><i>k</i></s= pan><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:58%;position:rel= ative; top:-.45em;mso-text-raise:30%'>th</span><span style=3D'mso-bidi-font-famil= y: "Times New Roman";font-size:88%'><span style=3D'mso-spacerun:yes'> </span>derivative of the function.</span>= <span style=3D'font-size:88%'> </span></span><span style=3D'position:absolu= te; top:59.5%;left:13.67%;width:84.26%;height:6.0%'><span style=3D'font-size:8= 8%'><span class=3DBB style=3D'position:absolute;left:-4.44%'>w</span></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>Note that i= f the cost function is specified as a </span></span><span style=3D'position:abso= lute; top:65.75%;left:13.67%;width:84.83%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman";font-size:88%'>multivariate Fourier expansion, the syste= m of </span></span><span style=3D'position:absolute;top:72.0%;left:13.67%;width= :90.26%; height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman";font-si= ze: 88%'>demand equations can be defined by Shephard’s </span></span><sp= an style=3D'position:absolute;top:78.25%;left:13.67%;width:81.46%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>lemma.</spa= n><span style=3D'font-size:88%'> </span></span></div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> 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c2l0ZWQNCgl7Y29sb3I6bWFyb29uICFpbXBvcnRhbnQ7fQ0K ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="us-ascii" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) 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return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii<collSeq.length;ii++) { if( collSeq[ii].getAttribute( "p:nodeType" ) =3D=3D "mainSeq" ) { g_animMainSequence =3D collSeq[ii]; break; } } } =09 if( g_animItemsToHide && document.body.playAnimations !=3D false ) { for(jj =3D 0; jj < g_animItemsToHide.length; jj++) { if( hideObj =3D GetObj(g_animItemsToHide[jj]) ) hideObj.runtimeStyle.visibility=3D"hidden"; } } if( g_animInteractiveItems ){ for(jj =3D 0; jj < g_animInteractiveItems.length; jj++) { if( triggerObj =3D GetObj(g_animInteractiveItems[jj]) ) triggerObj.runtimeStyle.cursor=3D"hand"; } } =09 if( gUseSldTimings && ''+g_animSlideTime !=3D 'undefined' ) { adjustedTime =3D document.body.calculateAutoAdvanceTimes( g_animSlideTim= e, g_animEffectTimings ); if( IsWin("PPTSld") && adjustedTime !=3D g_animSlideTime ) { var sld =3D GetCurSld(); sld.mAdvDelay =3D adjustedTime * 1000; } } } return g_animUseRuntime; } gSldJump =3D 0, gSldJumpTrack =3D 0, gSldJumpIdx =3D ""; function _KPH() {=20 if( IsNts() ) return; if( !parent.IsFramesMode() && event.keyCode =3D=3D 27 && !HideMenu() ) parent.window.close( self ); else if( event.keyCode =3D=3D 32 ) { if( window.name =3D=3D "PPTSld" ) parent.PPTSld.DocumentOnClick(); else parent.GoToNextSld(); } CatchNumKeys( parent, event ); } function CatchNumKeys( win, event ) { if( win.IsFullScrMode() && (48<=3Devent.keyCode) && (event.keyCode<=3D57) = ) { gSldJump =3D 1; gSldJumpIdx +=3D (event.keyCode-48).toString(); } if( win.IsFullScrMode() && gSldJump && event.keyCode =3D=3D 13 ) { var numSlds =3D parent.GetSldList().mList.length if ( gSldJumpIdx > numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D26, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("= slide0004.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("s= lide0006.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("sl= ide0008.htm",1,-1,1),new hrefList("slide0009.htm",1,-1,1),new hrefList("sli= de0010.htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("slid= e0012.htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("slide= 0014.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("slide0= 016.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slide00= 18.htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide002= 0.htm",1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0022= .htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0024.= htm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0026.h= tm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii<GetSldList().mList.length; ii++) { if ( GetSldList().mList[ii].mSldHref =3D=3D href ) return ii+1 } return 1 } function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] } function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) } function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) } function GoToNextSld() { ii=3DgCurSld + 1 if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) { if( ii<=3DGetSldList().mList.length ) { obj=3DGetHrefObj(ii) obj.mVis=3D1 GoToSldNum(ii) return } } else { obj=3DGetHrefObj( ii ) while ( obj && ( obj.mOrigVis =3D=3D 0 ) ) obj=3DGetHrefObj(++ii) if( obj && obj.mOrigVis ) { GoToSldNum(ii) return } } if( gSldStack.length > 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('<html><body dir=3D' + dir + ' bgcolor=3Dblack onload=3Dparent= .SetupEndShow() onunload=3Dparent.Unload()><center><p><font face=3DTahoma c= olor=3Dwhite size=3D2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></= body></html>') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii<arr.length;ii++) { this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[= ii].mAdvDelay, arr[ii].mAdvOnClk ); if( arr[ii].mOrigVis ) this.mList[ii].mSldIdx =3D idx++; } this.mNumVisSlds =3D idx-1; this.fEndShow =3D fEnd; } function GetSldList() { return gSldStack[gSldStack.length-1] } function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1]= } gSldStack =3D new Array(); gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1) function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } /********************************************* Custom Shows implementation When ViewCustomShow() is called, we create a new array that is a subset of the slides in=20 the main doc. This list pushed on a stack so we can return after the end of the custom show. *********************************************/ function ViewCustomShow(idx,fEnd) { if( !IsFullScrMode() ) return; var sldList =3D new Array(); var custShow =3D custShowList[idx-1]; var jj =3D 0; for( ii=3D0;ii<custShow.length;ii++ ) { if( custShow[ii] <=3D gMainDoc.length ) sldList[jj++] =3D gMainDoc[custShow[ii]-1]; } if (sldList.length > 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; 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style=3D'font-family:Arial;font-size:9pt'> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>1</font></div> </td> <td width=3D"100%"> <div id=3DPPTP1 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0001.htm');" id=3DPPTL1>Cost Functions a= nd the Estimation of Flexible Functional Forms</a></font></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Lecture XVIII</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>2</font></div> </td> <td> <div id=3DPPTP2 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0002.htm');" id=3DPPTL2>Flexible Functio= nal Forms</a></font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The crux of the dual approach is then to estimate a manifestation of behavior that economist know something about.</li> <ul> <li>Thus, instead of estimating production functions that are purely physical forms that economist have little expertise in developing, = we could estimate the cost function that represents cost minimizing behavior.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>3</font></div> </td> <td> <div id=3DPPTP3 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0003.htm');" id=3DPPTL3>"We then wo= uld be able..."</a></font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>We then would be able to determine whether the properties of these = cost functions are consistent with our hypotheses about technology.</li> <li>However, it is often the direct implications of the cost minimizing behavior that we are interested in:</li> <ul> <li>How will farmers react to changes in agricultural prices through commodity programs?</li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>4</font></div> </td> <td> <div id=3DPPTP4 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0004.htm');" id=3DPPTL4>"What is th= e impact of..."</a></font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <ul> <li>What is the impact of a change in input prices (say in an increase= in fuel prices) on agricultural output?</li> <br> <br> <br> </ul> <li>Thus, the dual cost function results are usually sufficient for most question facing agricultural economists.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>5</font></div> </td> <td> <div id=3DPPTP5 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0005.htm');" id=3DPPTL5>"Given that= we are interested..."</a></font></div> <div id=3DPPTC5 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Given that we are interested in estimating the cost function directl= y, the next question involves how to specify the cost function?</li> <ul> <li>One approach to the estimation of cost functions would then be to hypothesize a primal production function and derive the theoretical= ly consistent specification for the cost function based on this primal= .</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>6</font></div> </td> <td> <div id=3DPPTP6 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0006.htm');" id=3DPPTL6>"However&qu= ot;</a></font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>However, this approach would appear too restrictive.</li> <li>Thus, economists have typically turned to flexible functional forms that allow for a wide variety of technologies.</li> </ul> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>7</font></div> </td> <td> <div id=3DPPTP7 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0007.htm');" id=3DPPTL7>"A basic ap= proach to the..."</a></font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A basic approach to the specification of a cost function is to assume that an unspecified function exists, and then derive a closed form approximation of the function.</li> <ul> <li>One typical approach from optimization theory involves the Taylor series expansion:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>8</font></div> </td> <td> <div id=3DPPTP8 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0008.htm');" id=3DPPTL8>General Form of Univariate Taylor Expansion</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>9</font></div> </td> <td> <div id=3DPPTP9 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0009.htm');" id=3DPPTL9>"The real p= roblem is that..."</a></font></div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>The real problem is that we don’t know the value of x<sup>*</= sup>.<span style=3D'mso-spacerun:yes'> </span>As a result, we approximat= e this term with a residual:</li> <br> <br> <br> <li>Given this approach, we can conjecture the relative size of the approximation error based on the relative size of the third derivat= ive of the cost function.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>10</font></div> </td> <td> <div id=3DPPTP10 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0010.htm');" id=3DPPTL10>"Extending= this result to vector..."</a></font></div> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Extending this result to vector space, we have:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>11</font></div> </td> <td> <div id=3DPPTP11 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0011.htm');" id=3DPPTL11>"Given tha= t the cost function..."</a></font></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Given that the cost function is a function of input prices w and ou= tput levels y, we could then stack the two into a single vector and deri= ve the flexible functional form:</li> <br> <br> <br> <ul> <li>This form is typically referred to as the quadratic cost function.<span style=3D'mso-spacerun:yes'> </span>It is a second-order Taylor series expansion to an unknown cost function.<= /li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>12</font></div> </td> <td> <div id=3DPPTP12 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0012.htm');" id=3DPPTL12>"Following= the general concept (..."</a></font></div> <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <ul> <li>Following the general concept (and ignoring for the moment the err= or of approximation), Shephard’s lemma can be applied to this c= ost specification:</li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>13</font></div> </td> <td> <div id=3DPPTP13 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0013.htm');" id=3DPPTL13>Flexible Cost S= ystem</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>14</font></div> </td> <td> <div id=3DPPTP14 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0014.htm');" id=3DPPTL14>"Why have I imposed symmetry"</a></font></div> <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Why have I imposed symmetry?</li> <li>Why am I only estimating three demand curves?</li> </ul> <li>One generalization of the Taylor series approach involves a transformation of variables.<span style=3D'mso-spacerun:yes'> </span>Specifically, if we assume:</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0015.htm');" id=3DPPTL15>"The cost = function can be..."</a></font></div> <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>The cost function can be expressed as:</li> <br> <br> <br> <br> <br> <li>This formulation complicates the Shephard’s lemma results slightly:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>16</font></div> </td> <td> <div id=3DPPTP16 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0016.htm');" id=3DPPTL16><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>17</font></div> </td> <td> <div id=3DPPTP17 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0017.htm');" id=3DPPTL17>"Note that= letting l go..."</a></font></div> <div id=3DPPTC17 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Note that letting l go to zero implies</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>18</font></div> </td> <td> <div id=3DPPTP18 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0018.htm');" id=3DPPTL18><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>19</font></div> </td> <td> <div id=3DPPTP19 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0019.htm');" id=3DPPTL19>Fourier Expansi= on</a></font></div> <div id=3DPPTC19 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>In a univariate sense, any function can be approximated by a series = of sine and cosine curves:</li> <br> <br> <br> <li> where the l<sub>I</sub> are different periodicities.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>20</font></div> </td> <td> <div id=3DPPTP20 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0020.htm');" id=3DPPTL20>"Extending= this representation to a..."</a></font></div> <div id=3DPPTC20 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Extending this representation to a multivariate formulation:</li> <br> <br> <br> <li> where l<sub>i</sub> is a constant for periodicity and k<sub>a</sub>= is referred to as an Elementary Multi-Index:</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>21</font></div> </td> <td> <div id=3DPPTP21 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0021.htm');" id=3DPPTL21><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>22</font></div> </td> <td> <div id=3DPPTP22 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0022.htm');" id=3DPPTL22>K=3D1</a></font= ></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>23</font></div> </td> <td> <div id=3DPPTP23 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0023.htm');" id=3DPPTL23>K=3D2</a></font= ></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>24</font></div> </td> <td> <div id=3DPPTP24 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0024.htm');" id=3DPPTL24>"This representation minimizes the Sobolev..."</a></font></div> <div id=3DPPTC24 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>This representation minimizes the Sobolev Norm, which says that it d= oes a better job approximating the derivatives of the function.<span style=3D'mso-spacerun:yes'> </span>In fact, it represents up t= o the k<sup>th</sup> derivative of the function.</li> <li>Note that if the cost function is specified as a multivariate Fourier expansion, the system of demand equations can be defined by Shephard’s lemma.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>25</font></div> </td> <td> <div id=3DPPTP25 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0025.htm');" id=3DPPTL25>Estimation of C= ost Systems</a></font></div> <div id=3DPPTC25 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Regardless of the function form, cost functions are typically estima= ted as systems of equations using Seemingly Unrelated Regression, Iterat= ed Seemingly Unrelated Regression, or Maximum Likelihood.</li> <li>I prefer the use of Maximum Likelihood based on a concentrated likelihood function.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>26</font></div> </td> <td> <div id=3DPPTP26 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0026.htm');" id=3DPPTL26><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> </table> </div> <div style=3D'display:none'><a href=3D"../Lecture18-2005.htm"></a><a 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color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3309" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3741" to=3D"624,37= 41" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3310" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3939" to=3D"624,39= 39" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3311" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3918" to=3D"624,39= 18" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3312" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3510" to=3D"624,35= 10" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3313" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3546" to=3D"624,35= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3314" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3579" to=3D"624,35= 79" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3315" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3420" to=3D"624,34= 20" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3316" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3372" to=3D"624,33= 72" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3317" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3465" to=3D"624,34= 65" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3318" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2973" to=3D"624,29= 73" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3319" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2946" to=3D"624,29= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3320" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3327" to=3D"624,33= 27" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3321" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3201" to=3D"624,32= 01" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3322" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3120" to=3D"624,31= 20" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3323" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3306" to=3D"624,33= 06" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3324" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2994" to=3D"624,29= 94" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3325" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3048" to=3D"624,30= 48" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3326" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3246" to=3D"624,32= 46" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3327" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,3225" to=3D"624,32= 25" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3328" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2831" to=3D"624,28= 31" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3329" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2750" to=3D"624,27= 50" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3330" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2678" to=3D"624,26= 78" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3331" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2876" to=3D"624,28= 76" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3332" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2855" to=3D"624,28= 55" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3333" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2554" to=3D"624,25= 54" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3334" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2590" to=3D"624,25= 90" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3335" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2623" to=3D"624,26= 23" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3336" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2464" to=3D"624,24= 64" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3337" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2416" to=3D"624,24= 16" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3338" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2509" to=3D"624,25= 09" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3339" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2371" to=3D"624,23= 71" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3340" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2245" to=3D"624,22= 45" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3341" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2350" to=3D"624,23= 50" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3342" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2290" to=3D"624,22= 90" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3343" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2269" to=3D"624,22= 69" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3344" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2130" to=3D"624,21= 30" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3345" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2166" to=3D"624,21= 66" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3346" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2199" to=3D"624,21= 99" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3347" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2040" to=3D"624,20= 40" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3348" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1992" to=3D"624,19= 92" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3349" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,2085" to=3D"624,20= 85" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3350" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1593" to=3D"624,15= 93" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3351" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1566" to=3D"624,15= 66" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"3pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3352" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1947" to=3D"624,19= 47" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"1.5pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3353" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1821" to=3D"624,18= 21" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" stroke= weight=3D"2.25pt"> <v:shadow color=3D"#e3e2c7 [2]"/> </v:line><v:line id=3D"_x0000_s3354" style=3D'position:absolute; mso-wrap-style:none;v-text-anchor:middle' from=3D"0,1740" to=3D"624,17= 40" o:regroupid=3D"5" o:userdrawn=3D"t" strokecolor=3D"#e3e2c7 [2]" 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Functional Forms</span> </div> <div v:shape=3D"_x0000_s32771"> <div class=3DB><span style=3D'position:absolute;top:33.5%;left:13.67%;widt= h:85.2%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-4.39%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>The crux of the dual appr= oach is then to </span></span><span style=3D'position:absolute;top:40.5%;left:1= 3.67%; width:87.26%;height:6.75%'><span style=3D'mso-bidi-font-family:"Times New = Roman"'>estimate a manifestation of behavior that </span></span><span style=3D'position:abs= olute; top:47.5%;left:13.67%;width:81.46%;height:6.75%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>economist know something about.</span> </span></div> <div class=3DB1><span style=3D'position:absolute;top:56.0%;left:17.97%;wid= th:90.63%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Thus, instead of estimati= ng production functions </span></span><span style=3D'position:absolute;top:62= .25%; left:17.97%;width:84.26%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>that are purely physical forms that economist </span></span><span style=3D'posi= tion: absolute;top:68.5%;left:17.97%;width:82.58%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>have little expertise in developing, we could </span></span><span style=3D'position:absolute;top:74= .5%; left:17.97%;width:84.83%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>estimate the cost function that represents cost </span></span><span style=3D'positi= on: absolute;top:80.75%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>minimizing behavior.</spa= n> </span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/master03_image004.gif 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style=3D'position:absolute;top:39.5%;left:17.97%;width:88.38%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>properties of these cost functions are consistent </span></span><span style=3D'position:absolute; top:45.75%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>with our hypotheses about technology.</span> </spa= n></div> <div class=3DB1><span style=3D'position:absolute;top:53.25%;left:17.97%; width:91.94%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-3.46%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= However, it is often the direct implications of the </span></span><span style=3D'position:absolute;top:59.5%;left:17.97%;width:88.76%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>cost minimizing behavior = that we are interested </span></span><span style=3D'position:absolute;top:65.75= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>in:</span> </span></div> <div class=3DB2><span style=3D'position:absolute;top:73.0%;left:21.72%;wid= th:78.65%; height:5.25%'><span class=3DB2B style=3D'position:absolute;left:-3.09%;top= :.49em'>l</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>How will farmers react to changes in agricultural </span></span><span style=3D'position:absolute; top:78.25%;left:21.72%;width:73.4%;height:5.25%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>prices through commodity programs?</span> </span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f eqn=3D"prod @3 21600 pixelWidth"/> <v:f eqn=3D"prod @3 21600 pixelHeight"/> <v:f eqn=3D"sum 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height:100.0%'><span style=3D'visibility:hidden'><span class=3DB2B style=3D'position:absolute;left:-3.31%'>l</span></span> </span></div> <div class=3DB2 style=3D'position:absolute;top:51.5%;left:19.28%;width:75.= 84%; height:5.25%'><span style=3D'position:absolute;top:0%;left:3.2%;width:96.7= 9%; height:100.0%'><span style=3D'visibility:hidden'><span class=3DB2B style=3D'position:absolute;left:-3.31%'>l</span></span> </span></div> <div class=3DB1><span style=3D'position:absolute;top:57.99%;left:17.97%; width:86.89%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-3.66%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Thus, the dual cost function results are usually </span></span><span style=3D'position:absolute;top:64.25%;left:17.97%;width:87.07%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman"'>sufficient for most quest= ion facing agricultural </span></span><span style=3D'position:absolute;top:70.= 5%; 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position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s35843"> <div class=3DB><span style=3D'position:absolute;top:33.5%;left:13.67%;widt= h:97.0%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-3.86%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Given that we are interes= ted in estimating the </span></span><span style=3D'position:absolute;top:40.5%; left:13.67%;width:84.64%;height:6.75%'><span style=3D'mso-bidi-font-family= :"Times New Roman"'>cost function directly, the next question </span></span><span style=3D'position= :absolute; top:47.5%;left:13.67%;width:90.26%;height:6.75%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>involves how to specify the cost function?</span> = </span></div> <div class=3DB1><span style=3D'position:absolute;top:56.0%;left:17.97%;wid= th:90.63%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>One approach to the estim= ation of cost functions </span></span><span style=3D'position:absolute;top:62.25= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>would then be to hypothesize a primal </span></span><span style=3D'position:abso= lute; top:68.5%;left:17.97%;width:89.13%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>production function and derive the theoretically </span= ></span><span style=3D'position:absolute;top:74.5%;left:17.97%;width:82.58%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>consistent specification = for the cost function </span></span><span style=3D'position:absolute;top:80.75= %; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>based on this primal. </span></span></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0006.htm 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o:userdrawn=3D"f"> <v:fill o:detectmouseclick=3D"f"/> <v:stroke o:forcedash=3D"f"/> <o:lock v:ext=3D"edit" text=3D"f"/> <p:placeholder type=3D"body" position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s36867"> <div class=3DB1><span style=3D'position:absolute;top:33.25%;left:17.97%; width:78.08%;height:6.0%'><span class=3DB1B style=3D'position:absolute;lef= t:-4.07%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= However, this approach would appear too </span></span><span style=3D'position:absol= ute; top:39.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>restrictive. </span></span></div> <div class=3DB1><span style=3D'position:absolute;top:47.0%;left:17.97%;wid= th:78.08%; height:6.0%'><span class=3DB1B style=3D'position:absolute;left:-4.07%;top:= .74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>Thus, economists have typ= ically turned to </span></span><span style=3D'position:absolute;top:53.25%;left:1= 7.97%; width:86.32%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New R= oman"'>flexible functional forms that allow for a wide </span></span><span style=3D'positi= on: absolute;top:59.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman"'>variety of technologies. = </span></span></div> <div class=3DB style=3D'position:absolute;top:67.25%;left:9.92%;width:85.2= %; height:6.75%'><span style=3D'position:absolute;top:0%;left:4.39%;width:95.= 6%; height:100.0%'><span style=3D'visibility:hidden'><span class=3DBB style=3D'position:absolute;left:-4.59%'>w</span></span><span style=3D'mso-= bidi-font-family: "Times New Roman";mso-special-format:lastCR;display:none'> </span></sp= an></div> </div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0007.htm Content-Transfer-Encoding: quoted-printable Content-Type: 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color2=3D"white [0]"/> <v:shadow color=3D"#e3e2c7 [2]"/> <v:textbox style=3D'mso-fit-shape-to-text:t'/> </v:rect> <div v:shape=3D"_x0000_s40963" class=3DB1> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:32.75%;left:17.97%;width:91.94%;height:6.0%'><span style=3D'mso-specia= l-format: bullet;position:absolute;left:-3.46%;top:.74em;font-family:Wingdings; font-size:55%'>n</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>The real problem is that we don’t know the value </span></span><span style=3D'position:absolute;top:38.5%;left:17.97%;width:91.57%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>of </span><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>x</i></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:67%;position:rel= ative; top:-.45em;mso-text-raise:30%'>*</span><span style=3D'mso-bidi-font-family= :"Times New Roman"'>.<span style=3D'mso-spacerun:yes'> </span>As a result, we approximate this = term with </span></span><span style=3D'position:absolute;top:44.0%;left:17.97%; width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:"Times New R= oman"'>a residual:</span> </span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:51.0%;left:= 14.79%; width:80.14%;height:6.0%'><span style=3D'position:absolute;top:0%;left:3.9= 7%; width:96.26%;height:100.0%'><span style=3D'visibility:hidden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div style=3D'mso-line-spacing:"90 20 0";position:absolute;top:57.75%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div style=3D'mso-line-spacing:"90 20 0"'><span style=3D'position:absolute; top:64.5%;left:17.97%;width:80.52%;height:6.0%'><span style=3D'mso-special= -format: bullet;position:absolute;left:-3.95%;top:.74em;font-family:Wingdings; font-size:55%'>n</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>Given this approach, we can conjecture the </span></span><span style=3D'position= :absolute; top:70.25%;left:17.97%;width:90.63%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman"'>relative size of the approximation error based on </spa= n></span><span style=3D'position:absolute;top:75.75%;left:17.97%;width:91.76%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman"'>the relative size of the = third derivative of the cost </span></span><span style=3D'position:absolute; top:81.5%;left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-fo= nt-family: "Times New Roman"'>function.</span> </span></div> </div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" 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<title>Cost Functions and the Estimation of Flexible Functional Forms </tit= le> <![if IE]> <base href=3D"file:///C:\B2E9C635\Lecture18-2005_files\slide0010.htm" id=3D"webarch_temp_base_tag"> <![endif]> <meta name=3DDescription content=3D"11/14/2005"> <link rel=3DStylesheet href=3D"master03_stylesheet.css"> <![if !ppt]> <style media=3Dprint>  </style> <script src=3Dscript.js></script><script></script><![endif]><o:shapelayout v:ext=3D"edit"> <o:idmap v:ext=3D"edit" data=3D"41"/> </o:shapelayout> </head> <body lang=3DEN-US style=3D'margin:0px;background-color:black' onclick=3D"DocumentOnClick()" onresize=3D"_RSW()" onload=3D"LoadSld()" onkeypress=3D"_KPH()"> <div id=3DSlideObj class=3Dsld style=3D'position:absolute;top:0px;left:0px; width:534px;height:400px;font-size:16px;background-color:white;clip:rect(0%= , 101%, 101%, 0%); visibility:hidden'><p:slide coordsize=3D"720,540" colors=3D"#ffffff,#003366,#e3e2c7,#003366,#cccc99,#003366,#003366,#800000" masterhref=3D"master03.xml"> <p:shaperange href=3D"master03.xml#_x0000_s1025"/><![if !ppt]><p:shaperange href=3D"master03.xml#_x0000_s1249"/><![if !vml]><img border=3D0 v:shapes=3D"_x0000_s1249,_x0000_s1146,_x0000_s1147,_x0000_s1148,_x0000_s11= 49,_x0000_s1150,_x0000_s1151,_x0000_s1152,_x0000_s1153,_x0000_s1154,_x0000_= s1155,_x0000_s1156,_x0000_s1157,_x0000_s1158,_x0000_s1159,_x0000_s1160,_x00= 00_s1161,_x0000_s1162,_x0000_s1163,_x0000_s1164,_x0000_s1165,_x0000_s1166,_= x0000_s1167,_x0000_s1168,_x0000_s1169,_x0000_s1170,_x0000_s1171,_x0000_s117= 2,_x0000_s1173,_x0000_s1174,_x0000_s1175,_x0000_s1176,_x0000_s1177,_x0000_s= 1178,_x0000_s1179,_x0000_s1180,_x0000_s1181,_x0000_s1182,_x0000_s1183,_x000= 0_s1184,_x0000_s1185,_x0000_s1186,_x0000_s1187,_x0000_s1188,_x0000_s1189,_x= 0000_s1190,_x0000_s1191,_x0000_s1192,_x0000_s1193,_x0000_s1194,_x0000_s1195= ,_x0000_s1196,_x0000_s1197,_x0000_s1198,_x0000_s1199,_x0000_s1200,_x0000_s1= 201,_x0000_s1202,_x0000_s1203,_x0000_s1204,_x0000_s1205,_x0000_s1206,_x0000= 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</span><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>w</i></span><span style=3D'mso-bidi-font-family:"Times New Roman"'> and output levels </span= ><span style=3D'mso-bidi-font-family:"Times New Roman"'><i>y</i></span><span style=3D'mso-bidi-font-family:"Times New Roman"'>, we could then stack </s= pan></span><span style=3D'position:absolute;top:44.0%;left:17.97%;width:78.27%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman"'>the two into a single vec= tor and derive the </span></span><span style=3D'position:absolute;top:49.75%; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>flexible functional form:</span> </span></div> <div class=3DB1 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:= 56.49%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div class=3DB1 style=3D'mso-line-spacing:"90 20 0";position:absolute;top:= 63.24%; left:14.79%;width:80.14%;height:6.0%'><span style=3D'position:absolute; top:0%;left:3.97%;width:96.26%;height:100.0%'><span style=3D'visibility:hi= dden'><span style=3D'mso-special-format:bullet;position:absolute;left:-4.12%;font-fami= ly: Wingdings;font-size:55%'>n</span></span> </span></div> <div class=3DB2 style=3D'mso-line-spacing:"90 20 0"'><span style=3D'positi= on:absolute; top:70.0%;left:21.72%;width:85.95%;height:5.25%'><span style=3D'mso-specia= l-format: bullet;position:absolute;left:-2.83%;top:.49em;font-family:Wingdings; font-size:65%'>l</span><span style=3D'mso-bidi-font-family:"Times New Roma= n"'>This form is typically referred to as the quadratic cost </span></span><span style=3D'position:absolute;top:74.75%;left:21.72%;width:86.14%;height:5.25= %'><span 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class=3DB1B style=3D'position:absolute;left:-4.12%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Why have I imposed symmetry?</span> </span></div> <div class=3DB1 style=3D'position:absolute;top:40.75%;left:14.79%;width:93= .82%; height:6.0%'><span style=3D'position:absolute;top:0%;left:3.39%;width:96.6= %; height:100.0%'><span class=3DB1B style=3D'position:absolute;left:-3.51%; top:.74em'>n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>= Why am I only estimating three demand curves?</span> </span></div> <div class=3DB><span style=3D'position:absolute;top:48.5%;left:13.67%;widt= h:83.33%; height:6.75%'><span class=3DBB style=3D'position:absolute;left:-4.49%'>w</= span><span style=3D'mso-bidi-font-family:"Times New Roman"'>One generalization of the Taylor series </span></span><span style=3D'position:absolute;top:55.75%; left:13.67%;width:81.46%;height:6.75%'><span style=3D'mso-bidi-font-family= :"Times New Roman"'>approach involves a 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style=3D'position:absolute;top:0%;left:3.97%;width:96.26%;height:100.0%'><= span style=3D'visibility:hidden'><span class=3DB1B style=3D'position:absolute;l= eft:-4.12%'>n</span></span> </span></div> <span style=3D'position:absolute;top:70.75%;left:17.97%;width:84.08%;heigh= t: 6.0%'><span class=3DB1B style=3D'position:absolute;left:-3.78%;top:.74em'>= n</span><span style=3D'mso-bidi-font-family:"Times New Roman"'>This formulation complica= tes the Shephard’s </span></span><span style=3D'position:absolute;top:77= .0%; left:17.97%;width:77.15%;height:6.0%'><span style=3D'mso-bidi-font-family:= "Times New Roman"'>lemma results slightly:</span> </span></div> <v:shapetype id=3D"_x0000_t75" coordsize=3D"21600,21600" o:spt=3D"75" o:preferrelative=3D"t" path=3D"m@4@5l@4@11@9@11@9@5xe" filled=3D"f" strok= ed=3D"f"> <v:stroke joinstyle=3D"miter"/> <v:formulas> <v:f eqn=3D"if lineDrawn pixelLineWidth 0"/> <v:f eqn=3D"sum @0 1 0"/> <v:f eqn=3D"sum 0 0 @1"/> <v:f eqn=3D"prod @2 1 2"/> <v:f 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position=3D"1"/></v:shape> <div v:shape=3D"_x0000_s60419" class=3DB><span style=3D'position:absolute; top:33.25%;left:13.67%;width:93.07%;height:6.0%'><span style=3D'font-size:= 88%'><span class=3DBB style=3D'position:absolute;left:-4.02%'>w</span></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>This representation minimizes the Sobolev Norm, </span></span><span style=3D'position:absolute;top:39.5%;left:13.67%;width:92.88%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>which says = that it does a better job approximating </span></span><span style=3D'position:a= bsolute; top:45.75%;left:13.67%;width:96.62%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman";font-size:88%'>the derivatives of the function.<span style=3D'mso-spacerun:yes'> </span>In fact, it represents </span></s= pan><span style=3D'position:absolute;top:52.0%;left:13.67%;width:81.46%;height:6.0%'= ><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>up to the <= /span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'><i>k</i></s= pan><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:58%;position:rel= ative; top:-.45em;mso-text-raise:30%'>th</span><span style=3D'mso-bidi-font-famil= y: "Times New Roman";font-size:88%'><span style=3D'mso-spacerun:yes'> </span>derivative of the function.</span>= <span style=3D'font-size:88%'> </span></span><span style=3D'position:absolu= te; top:59.5%;left:13.67%;width:84.26%;height:6.0%'><span style=3D'font-size:8= 8%'><span class=3DBB style=3D'position:absolute;left:-4.44%'>w</span></span><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>Note that i= f the cost function is specified as a </span></span><span style=3D'position:abso= lute; top:65.75%;left:13.67%;width:84.83%;height:6.0%'><span style=3D'mso-bidi-f= ont-family: "Times New Roman";font-size:88%'>multivariate Fourier expansion, the syste= m of </span></span><span style=3D'position:absolute;top:72.0%;left:13.67%;width= :90.26%; height:6.0%'><span style=3D'mso-bidi-font-family:"Times New Roman";font-si= ze: 88%'>demand equations can be defined by Shephard’s </span></span><sp= an style=3D'position:absolute;top:78.25%;left:13.67%;width:81.46%;height:6.0%= '><span style=3D'mso-bidi-font-family:"Times New Roman";font-size:88%'>lemma.</spa= n><span style=3D'font-size:88%'> </span></span></div> </p:slide></div> </body> </html> ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/slide0025.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" <html xmlns:v=3D"urn:schemas-microsoft-com:vml" xmlns:o=3D"urn:schemas-microsoft-com:office:office" xmlns:p=3D"urn:schemas-microsoft-com:office:powerpoint" xmlns:oa=3D"urn:schemas-microsoft-com:office:activation" xmlns=3D"http://www.w3.org/TR/REC-html40"> <head> <meta http-equiv=3DContent-Type content=3D"text/html; charset=3Dus-ascii"> 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c2l0ZWQNCgl7Y29sb3I6bWFyb29uICFpbXBvcnRhbnQ7fQ0K ------=_NextPart_01C5E927.0CF86950 Content-Location: file:///C:/B2E9C635/Lecture18-2005_files/script.js Content-Transfer-Encoding: quoted-printable Content-Type: application/javascript; charset="us-ascii" function LoadSld() { var sld=3DGetObj("SlideObj") if( !g_supportsPPTHTML ) { =09 sld.style.visibility=3D"visible" return } if( MakeNotesVis() ) return runAnimations =3D _InitAnimations(); =09 if( IsWin("PPTSld") ) parent.SldUpdated(GetSldId()) g_origSz=3DparseInt(SlideObj.style.fontSize) g_origH=3Dsld.style.posHeight g_origW=3Dsld.style.posWidth g_scaleHyperlinks=3D(document.all.tags("AREA").length>0) if( g_scaleHyperlinks ) InitHLinkArray() if( g_scaleInFrame||(IsWin("PPTSld") && parent.IsFullScrMode() ) ) document.body.scroll=3D"no" _RSW() if( IsWin("PPTSld") && parent.IsFullScrMode() ) FullScrInit(); =09 MakeSldVis(); ChkAutoAdv() if( runAnimations ) { if( document.all("NSPlay") ) document.all("NSPlay").autoStart =3D false; if( sld.filters && sld.filters.revealtrans ) setTimeout( "document.body.start()", sld.filters.revealtrans.duration * = 1000 ); else document.body.start(); } } function MakeSldVis()=20 { var fTrans=3Dg_showAnimation && SldHasTrans() if( fTrans )=09 { if( g_bgSound ) { idx=3Dg_bgSound.indexOf(","); pptSound.src=3Dg_bgSound.substr( 0, idx ); pptSound.loop=3D -(parseInt(g_bgSound.substr(idx+1))); } SlideObj.filters.revealtrans.Apply()=09 } SlideObj.style.visibility=3D"visible" if( fTrans ) SlideObj.filters.revealtrans.Play() } function MakeNotesVis()=20 { if( !IsNts() ) return false=20 SlideObj.style.display=3D"none" nObj =3D document.all.item("NotesObj") parent.SetHasNts(0) if( nObj ) {=20 nObj.style.display=3D"" parent.SetHasNts(1) } return 1 } function ChkAutoAdv() { if(SldHasTrans()) SlideObj.onfilterchange=3DAutoAdv else AutoAdv() } function AutoAdv() { if(!IsWin("PPTSld") || !gUseSldTimings )return var sld=3DGetCurSld() if( (sld.mAdvDelay>0) && !parent.IsFramesMode() ) 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return false } function IsWin( name ) { return window.name =3D=3D name } function IsNts() { return IsWin("PPTNts") } function IsSldOrNts() { return( IsWin("PPTSld")||IsWin("PPTNts") ) } function SupportsPPTAnimation() { return( navigator.platform =3D=3D "Win32"= && navigator.appVersion.indexOf("Windows")>0 ) } function SupportsPPTHTML() { var appVer=3Dnavigator.appVersion, msie=3DappVer.indexOf("MSIE "), ver=3D0 if( msie >=3D 0 ) ver=3DparseFloat( appVer.substring( msie+5, appVer.indexOf(";",msie) ) ) else ver=3DparseInt(appVer) return( ver >=3D 4 && msie >=3D 0 ) } function _RSW() { if( !g_supportsPPTHTML || IsNts() || ( !g_scaleInFrame && (!IsWin("PPTSld") || !parent.IsFullScrMode()) ) ) return var padding=3D0; if( IsWin("PPTSld") && parent.IsFramesMode() ) padding=3D6 cltWidth=3Ddocument.body.clientWidth-padding cltHeight=3Ddocument.body.clientHeight-padding factor=3D(1.0*cltWidth)/g_origW if( cltHeight < g_origH*factor ) factor=3D(1.0*cltHeight)/g_origH newSize =3D g_origSz * factor if( newSize < 1 ) newSize=3D1 s=3DSlideObj.style s.fontSize=3DnewSize+"px" s.posWidth=3Dg_origW*factor s.posHeight=3Dg_origH*factor s.posLeft=3D(cltWidth-s.posWidth+padding)/2 s.posTop=3D(cltHeight-s.posHeight+padding)/2 if( g_scaleHyperlinks ) ScaleHyperlinks( factor ) } function _InitAnimations() { animRuntimeInstalled =3D ''+document.body.localTime !=3D 'undefined'; isFullScreen =3D (window.name =3D=3D "PPTSld") && !parent.IsFramesMode(); g_animUseRuntime =3D g_showAnimation && animRuntimeInstalled && !(isFullSc= reen && parent.IsSldVisited()); if( g_animUseRuntime ) { collSeq =3D document.all.tags("seq"); if( collSeq !=3D null ) { for(ii=3D0;ii<collSeq.length;ii++) { if( collSeq[ii].getAttribute( "p:nodeType" ) =3D=3D "mainSeq" ) { g_animMainSequence =3D collSeq[ii]; break; } } } =09 if( g_animItemsToHide && document.body.playAnimations !=3D false ) { for(jj =3D 0; jj < g_animItemsToHide.length; jj++) { if( hideObj =3D GetObj(g_animItemsToHide[jj]) ) hideObj.runtimeStyle.visibility=3D"hidden"; } } if( g_animInteractiveItems ){ for(jj =3D 0; jj < g_animInteractiveItems.length; jj++) { if( triggerObj =3D GetObj(g_animInteractiveItems[jj]) ) triggerObj.runtimeStyle.cursor=3D"hand"; } } =09 if( gUseSldTimings && ''+g_animSlideTime !=3D 'undefined' ) { adjustedTime =3D document.body.calculateAutoAdvanceTimes( g_animSlideTim= e, g_animEffectTimings ); if( IsWin("PPTSld") && adjustedTime !=3D g_animSlideTime ) { var sld =3D GetCurSld(); sld.mAdvDelay =3D adjustedTime * 1000; } } } return g_animUseRuntime; } gSldJump =3D 0, gSldJumpTrack =3D 0, gSldJumpIdx =3D ""; function _KPH() {=20 if( IsNts() ) return; if( !parent.IsFramesMode() && event.keyCode =3D=3D 27 && !HideMenu() ) parent.window.close( self ); else if( event.keyCode =3D=3D 32 ) { if( window.name =3D=3D "PPTSld" ) parent.PPTSld.DocumentOnClick(); else parent.GoToNextSld(); } CatchNumKeys( parent, event ); } function CatchNumKeys( win, event ) { if( win.IsFullScrMode() && (48<=3Devent.keyCode) && (event.keyCode<=3D57) = ) { gSldJump =3D 1; gSldJumpIdx +=3D (event.keyCode-48).toString(); } if( win.IsFullScrMode() && gSldJump && event.keyCode =3D=3D 13 ) { var numSlds =3D parent.GetSldList().mList.length if ( gSldJumpIdx > numSlds ) gSldJumpIdx =3D numSlds; if ( gSldJumpIdx >=3D 0 ) { if ( gSldJumpIdx =3D=3D 0 ) gSldJumpIdx =3D 1; var jumpTo =3D parseInt(gSldJumpIdx); gSldJump =3D 0; gSldJumpIdx =3D ""; win.GoToSld( parent.GetSldList().mList[jumpTo-1].mSldHref ) } } } function _KDH() { if( event.keyCode =3D=3D 8 ) { event.returnValue =3D 0; parent.GoToPrevSld(); } }function DocumentOnClick() { if( IsNts() || parent.HideMenu() ) return; if( ( g_allowAdvOnClick && (window.name=3D=3D"PPTSld") && !parent.IsFrames= Mode() ) || (event && event.keyCode=3D=3D32) ) { =09 if( g_animUseRuntime && g_animMainSequence && g_animMainSequence.cangonex= t ) return; parent.GoToNextSld(); } } var g_supportsPPTHTML =3D SupportsPPTHTML(), g_scaleInFrame =3D 1, gId=3D""= , g_bgSound=3D"", g_scaleHyperlinks =3D false, g_allowAdvOnClick =3D 1, g_showInBrowser = =3D 0, gLoopCont =3D 0, gUseSldTimings =3D 1; var g_showAnimation =3D g_supportsPPTHTML && SupportsPPTAnimation() && ( (w= indow.name=3D=3D"PPTSld" && !parent.IsFramesMode()) || g_showInBrowser );va= r g_animManager =3D null; var g_animUseRuntime =3D false; var g_animItemsToHide, g_animInteractiveItems, g_animSlideTime; var g_animMainSequence =3D null; var ENDSHOW_MESG=3D"End of slide show, click to exit.", SCREEN_MODE=3D"Fram= es", gIsEndShow=3D0, NUM_VIS_SLDS=3D26, SCRIPT_HREF=3D"script.js", FULLSCR_= HREF=3D"fullscreen.htm"; var gCurSld =3D gPrevSld =3D 1, g_offset =3D 0, gNtsOpen =3D gHasNts =3D gO= tlTxtExp =3D 0, gHasNarration =3D 0, gOtlOpen =3D true window.gPPTHTML=3DSupportsPPTHTML() var g_fBaseHyperlink =3D false; var gMainDoc=3Dnew Array(new hrefList("slide0001.htm",1,-1,1),new hrefList(= "slide0002.htm",1,-1,1),new hrefList("slide0003.htm",1,-1,1),new hrefList("= slide0004.htm",1,-1,1),new hrefList("slide0005.htm",1,-1,1),new hrefList("s= lide0006.htm",1,-1,1),new hrefList("slide0007.htm",1,-1,1),new hrefList("sl= ide0008.htm",1,-1,1),new hrefList("slide0009.htm",1,-1,1),new hrefList("sli= de0010.htm",1,-1,1),new hrefList("slide0011.htm",1,-1,1),new hrefList("slid= e0012.htm",1,-1,1),new hrefList("slide0013.htm",1,-1,1),new hrefList("slide= 0014.htm",1,-1,1),new hrefList("slide0015.htm",1,-1,1),new hrefList("slide0= 016.htm",1,-1,1),new hrefList("slide0017.htm",1,-1,1),new hrefList("slide00= 18.htm",1,-1,1),new hrefList("slide0019.htm",1,-1,1),new hrefList("slide002= 0.htm",1,-1,1),new hrefList("slide0021.htm",1,-1,1),new hrefList("slide0022= .htm",1,-1,1),new hrefList("slide0023.htm",1,-1,1),new hrefList("slide0024.= htm",1,-1,1),new hrefList("slide0025.htm",1,-1,1),new hrefList("slide0026.h= tm",1,-1,1)); /********************************************* Frameset functions These functions control slide navigation and state of the frameset. **********************************************/ function RemoveFilePrefixFromHref(href) { var regExp =3D /^file:\/\/\//i; return href.replace(regExp, "") } function FullScrInit() { g_allowAdvOnClick =3D GetCurSld().mAdvOnClk document.body.style.backgroundColor=3D"black" document.oncontextmenu=3Dparent._CM; document.onkeydown =3D _KDH; document.ondragstart=3DCancel document.onselectstart=3DCancel self.focus() } function Redirect( frmId ) {=09 var str=3Ddocument.location.hash,idx=3Dstr.indexOf('#'), sId=3DGetSldId() if(idx>=3D0) str=3Dstr.substr(1); if( window.name !=3D frmId && ( sId !=3D str) ) { obj =3D GetObj("Main-File") window.location.href=3Dobj.href+"#"+sId return 1 } return 0 } var MHTMLPrefix =3D CalculateMHTMLPrefix();=20 function CalculateMHTMLPrefix() { if ( document.location.protocol =3D=3D 'mhtml:') {=20 href=3Dnew String(document.location.href)=20 Start=3Dhref.indexOf('!')+1=20 End=3Dhref.lastIndexOf('/')+1=20 if (End < Start)=20 return href.substring(0, Start)=20 else=20 return href.substring(0, End)=20 } return ''; } function GetTags(base,tag) { if(g_supportsPPTHTML) return base.all.tags(tag); else return base.getElementsByTagName(tag); } function UpdNtsPane(){ if(frames["PPTNts"]) PPTNts.location.replace( MHTMLP= refix+GetHrefObj( gCurSld ).mNtsHref ) } function UpdNavPane( sldIndex ){ if(gNavLoaded) PPTNav.UpdNav() } function UpdOtNavPane(){ if(gOtlNavLoaded) PPTOtlNav.UpdOtlNav() } function UpdOtlPane(){ if(gOtlLoaded) PPTOtl.UpdOtl() } function SetHasNts( fVal ) { if( gHasNts !=3D fVal ) { gHasNts=3DfVal UpdNavPane() } } function ToggleOtlText() { gOtlTxtExp=3D!gOtlTxtExp UpdOtlPane() } function ClearMedia() { // Clear any sounds playing before launching another browser window. Other= wise, // in fullscreen mode, you'll continue to hear the sound in the frames mod= e. if (PPTSld.pptSound) PPTSld.pptSound.loop =3D 0; } function FullScreen() {=20 if ( PPTSld.g_animUseRuntime ) PPTSld.document.body.pause(); ClearMedia(); var href =3D ( document.location.protocol =3D=3D 'mhtml:') ? FULLSCR_HREF = : FULLSCR_HREF+"#"+GetHrefObj(gCurSld).mSldHref; if (MHTMLPrefix !=3D "") href =3D RemoveFilePrefixFromHref(href) if(PPTNav.event.ctrlKey) { var w =3D (window.screen.availWidth * 1.0) / 2.0 var h =3D w * (PPTSld.g_origH * 1.0) / PPTSld.g_origW win =3D window.open( MHTMLPrefix+href,null,"toolbar=3D0,resizable=3D1,top= =3D0,left=3D0," + "width=3D"+ w + ",height=3D" + h ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } else { win =3D window.open( MHTMLPrefix+href,null,"fullscreen=3Dyes" ); if( win.document.body && PPTSld.g_animUseRuntime ) win.document.body.PPTSldFrameset=3Dwindow; } } function ToggleVNarration() { rObj=3DPPTSld.document.all("NSPlay") if( rObj && !PPTSld.g_animUseRuntime ) { if( (rObj.playState =3D=3D 1)||(rObj.playState =3D=3D 0) ) rObj.Play() else if( rObj.playState =3D=3D 2 ) rObj.Pause() else return; } else if( PPTSld.g_animUseRuntime ) { narObj =3D PPTSld.document.all("narrationID") if( narObj ) narObj.togglePause() } } function GetCurSldNum() { =20 obj=3DGetHrefObj(gCurSld) if( obj.mOrigVis =3D=3D 1 ) return obj.mSldIdx else =20 return gCurSld } function GetNumSlds() { =20 if( GetHrefObj(gCurSld).mOrigVis =3D=3D 1 ) return GetSldList().mNumVisSlds; else return GetSldList().mList.length } function GetSldNum( href ) { for(ii=3D0; ii<GetSldList().mList.length; ii++) { if ( GetSldList().mList[ii].mSldHref =3D=3D href ) return ii+1 } return 1 } function GetHrefObj( sldIdx ){ return GetSldList().mList[sldIdx-1] } function IsFramesMode(){ return ( SCREEN_MODE =3D=3D "Frames" ) } function IsFullScrMode(){ return ( SCREEN_MODE =3D=3D "FullScreen" ) } function GoToNextSld() { ii=3DgCurSld + 1 if( GetHrefObj( ii-1 ).mOrigVis =3D=3D 0 ) { if( ii<=3DGetSldList().mList.length ) { obj=3DGetHrefObj(ii) obj.mVis=3D1 GoToSldNum(ii) return } } else { obj=3DGetHrefObj( ii ) while ( obj && ( obj.mOrigVis =3D=3D 0 ) ) obj=3DGetHrefObj(++ii) if( obj && obj.mOrigVis ) { GoToSldNum(ii) return } } if( gSldStack.length > 1 ) PopSldList(); else if( !IsFramesMode() ) { if( gLoopCont ) GoToFirst() else EndShow() } } function GoToPrevSld() { ii=3DgCurSld-1 if( ii > 0 ) { obj=3DGetHrefObj(ii) while ( obj && ( obj.mVis =3D=3D 0 ) && ( ii>0 ) ) obj=3DGetHrefObj(--ii) if( ii =3D=3D 0 ) ii=3D1 GoToSldNum(ii) } } function GoToFirst(){ GoToSld( GetHrefObj(1).mSldHref ) } function GoToLast() { ii=3DGetSldList().mList.length if( ii !=3D gCurSld ) GoToSld( GetHrefObj(ii).mSldHref ) } function GoToSldNum( num ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue obj =3D GetHrefObj( num ) obj.mVis=3D1 gPrevSld=3DgCurSld gCurSld =3D num; =09 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(obj.mSldHref= )) else PPTSld.location.replace(obj.mSldHref) =09 if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function GoToSld( href ) { if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue GetHrefObj( GetSldNum(href) ).mVis=3D1 if (MHTMLPrefix !=3D "") PPTSld.location.replace(MHTMLPrefix+RemoveFilePrefixFromHref(href)) else PPTSld.location.replace(href) } function SldUpdated( id ) { if( id =3D=3D GetHrefObj(gCurSld).mSldHref ) return gPrevSld=3DgCurSld gCurSld=3DGetSldNum(id) if( IsFramesMode() ) { UpdNavPane(); UpdOtlPane(); UpdNtsPane() } } function PrevSldViewed(){ GoToSld( GetHrefObj(gPrevSld).mSldHref ) } function HasPrevSld() { return ( gIsEndShow || ( gCurSld !=3D 1 && GetHrefO= bj( gCurSld-1 ).mVis =3D=3D 1 )||( GetCurSldNum() > 1 ) ) } function HasNextSld() { return (GetCurSldNum() !=3D GetNumSlds()) } function CloseWindow() { if( HideMenu() ) return; =09 var event =3D PPTSld.event; if( !IsFramesMode() && event && (event.keyCode=3D=3D27 || event.keyCode=3D= =3D32 || event.type=3D=3D"click" ) ) window.close( self ); CatchNumKeys( self, event ); } function Unload() { gIsEndShow=3D0; } function SetupEndShow() { gIsEndShow=3D1; PPTSld.document.body.scroll=3D"no"; PPTSld.document.onkeypress=3DCloseWindow; PPTSld.document.onclick=3DCloseWindow; PPTSld.document.oncontextmenu=3D_CM; } function EndShow() { if( IsFramesMode() ) return if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue doc=3DPPTSld.document var dir =3D doc.body.dir if( dir !=3D "rtl" ) dir =3D "ltr"; doc.open() doc.writeln('<html><body dir=3D' + dir + ' bgcolor=3Dblack onload=3Dparent= .SetupEndShow() onunload=3Dparent.Unload()><center><p><font face=3DTahoma c= olor=3Dwhite size=3D2><br><b>' + ENDSHOW_MESG + '</b></font></p></center></= body></html>') doc.close() } function SetSldVisited(){ GetSldList().mList[gCurSld-1].mVisited=3Dtrue } function IsSldVisited(){ return GetSldList().mList[gCurSld-1].mVisited } function hrefList( sldHref, visible, advDelay, advClk ) { this.mSldHref=3D this.mNtsHref =3D sldHref this.mOrigVis=3D this.mVis =3D visible this.mVisited=3D false this.mAdvDelay=3D advDelay this.mAdvOnClk=3D advClk } function SldList(arr,curSld,fEnd) { this.mCurSld =3D curSld; this.mList =3D new Array(); var idx =3D 1; for(ii=3D0;ii<arr.length;ii++) { this.mList[ii] =3D new hrefList( arr[ii].mSldHref, arr[ii].mOrigVis, arr[= ii].mAdvDelay, arr[ii].mAdvOnClk ); if( arr[ii].mOrigVis ) this.mList[ii].mSldIdx =3D idx++; } this.mNumVisSlds =3D idx-1; this.fEndShow =3D fEnd; } function GetSldList() { return gSldStack[gSldStack.length-1] } function GetCurSld() { return parent.GetSldList().mList[parent.gCurSld - 1]= } gSldStack =3D new Array(); gSldStack[0] =3D new SldList(gMainDoc,gCurSld,1) function ToggleOtlPane() { frmset=3Ddocument.all("PPTHorizAdjust") frm=3Ddocument.all("PPTOtl") if( gOtlOpen ) frmset.cols=3D"*,100%" else frmset.cols=3D"25%,*" gOtlOpen=3D!gOtlOpen frm.noResize=3D!frm.noResize UpdOtNavPane() } function ToggleNtsPane() { frmset=3Ddocument.all("PPTVertAdjust") frm=3Ddocument.all("PPTNts") if( gNtsOpen ) frmset.rows=3D"100%,*" else frmset.rows=3D"*,20%" gNtsOpen=3D!gNtsOpen UpdNtsPane() } /********************************************* Custom Shows implementation When ViewCustomShow() is called, we create a new array that is a subset of the slides in=20 the main doc. This list pushed on a stack so we can return after the end of the custom show. *********************************************/ function ViewCustomShow(idx,fEnd) { if( !IsFullScrMode() ) return; var sldList =3D new Array(); var custShow =3D custShowList[idx-1]; var jj =3D 0; for( ii=3D0;ii<custShow.length;ii++ ) { if( custShow[ii] <=3D gMainDoc.length ) sldList[jj++] =3D gMainDoc[custShow[ii]-1]; } if (sldList.length > 0) { PushSldList(sldList,fEnd); gCurSld =3D 1; } else if( PPTSld.event ) PPTSld.event.cancelBubble=3Dtrue } function PushSldList(arr,fEnd) { var ii =3D gSldStack.length; gSldStack[ii] =3D new SldList(arr,gCurSld,fEnd); GoToSld( gSldStack[ii].mList[0].mSldHref ); } function PopSldList() { if (gSldStack[gSldStack.length-1].fEndShow) EndShow() else { gCurSld =3D gSldStack[gSldStack.length-1].mCurSld; gSldStack[gSldStack.length-1] =3D null; gSldStack.length--; var sldList =3D gSldStack[gSldStack.length-1]; GoToSld( sldList.mList[gCurSld - 1].mSldHref ); } } var custShowList=3Dnew Array(); /********************************************* Navigation button implementation There are 2 types of buttons: ImgBtn, TxtBtn implemented as function objects. They share a similiar interface so the event handlers can call SetActive, for example, on a button=20 object without needing to know exactly=20 what type of button it is. **********************************************/ //---------------------------------- function ImgBtn( oId,bId,w,action ) //---------------------------------- { var t=3Dthis t.Perform =3D _IBP t.SetActive =3D _IBSetA t.SetInactive=3D _IBSetI t.SetPressed =3D _IBSetP t.SetDisabled=3D _IBSetD t.Enabled =3D _IBSetE t.ChangeIcon =3D null t.UserAction =3D action t.ChgState =3D _IBUI t.mObjId =3D oId t.mBorderId=3D bId t.mWidth =3D w t.mIsOn =3D t.mCurState =3D 0 } function _IBSetA() { if( this.mIsOn ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _IBSetI() { if( this.mIsOn ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0=20 } } function _IBSetP() { if( this.mIsOn ) { obj=3Dthis.ChgState( gShadowClr,gHiliteClr,2 ) obj.style.posLeft+=3D1; obj.style.posTop+=3D1 } } function _IBSetD() { =20 obj=3Dthis.ChgState( gFaceClr,gFaceClr,0 ) obj.style.posTop=3D0=20 } function _IBSetE( state ) { var t=3Dthis GetObj( t.mBorderId ).style.visibility=3D"visible" if( state !=3D t.mIsOn ) { t.mIsOn=3Dstate if( state ) t.SetInactive() else t.SetDisabled() } } function _IBP() { var t=3Dthis if( t.mIsOn ) { if( t.UserAction !=3D null ) t.UserAction() if( t.ChangeIcon ) { obj=3DGetObj(t.mObjId) if( t.ChangeIcon() ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-4)*t.mWidth else obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-0)*t.mWidth } t.SetActive() } =20 } function _IBUI( clr1,clr2,nextState ) { var t=3Dthis SetBorder( GetObj( t.mBorderId ),clr1,clr2 ) obj=3DGetObj( t.mObjId ) obj.style.posLeft=3Dobj.style.posLeft+(t.mCurState-nextState)*t.mWidth-obj= .style.posTop t.mCurState=3DnextState return obj } //----------------------------------------- function TxtBtn( oId,oeId,action,chkState ) //----------------------------------------- { var t=3Dthis t.Perform =3D _TBP t.SetActive =3D _TBSetA t.SetInactive=3D _TBSetI t.SetPressed =3D _TBSetP t.SetDisabled=3D _TBSetD t.SetEnabled =3D _TBSetE t.GetState =3D chkState t.UserAction =3D action t.ChgState =3D _TBUI t.mObjId =3D oId t.m_elementsId=3D oeId t.mIsOn =3D 1 } function _TBSetA() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gHiliteClr,gShadowClr,0,0 ) } function _TBSetI() { var t=3Dthis if( t.mIsOn && !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) } function _TBSetP() { if( this.mIsOn ) this.ChgState( gShadowClr,gHiliteClr,1,1 ) } function _TBSetD() { =20 this.ChgState( gFaceClr,gFaceClr,0,0 ) this.mIsOn =3D 0 } function _TBSetE() { var t=3Dthis if( !t.GetState() ) t.ChgState( gFaceClr,gFaceClr,0,0 ) else t.ChgState( gShadowClr,gHiliteClr,1,1 ) t.mIsOn =3D 1 } function _TBP() { var t=3Dthis if( t.mIsOn ) {=20 if( t.UserAction !=3D null ) t.UserAction() if( !t.GetState ) return if( t.GetState() ) t.SetPressed() else t.SetActive() } =20 } function _TBUI( clr1,clr2,lOffset,tOffset ) { SetBorder( GetObj( this.mObjId ),clr1,clr2 ) Offset( GetObj( this.m_elementsId ),lOffset,tOffset ) } function Offset( obj, top, left ){ obj.style.top=3Dtop; obj.style.left=3Dle= ft } function SetBorder( obj, upperLeft, lowerRight ) { s=3Dobj.style; s.borderStyle =3D "solid" s.borderWidth =3D 1=20 s.borderLeftColor =3D s.borderTopColor =3D upperLeft s.borderBottomColor=3D s.borderRightColor =3D lowerRight } function GetBtnObj(){ return gBtnArr[window.event.srcElement.id] } function BtnOnOver(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetActive() } function BtnOnDown(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetPressed() } function BtnOnOut(){ b=3DGetBtnObj(); if( b !=3D null ) b.SetInactive() } function BtnOnUp() { b=3DGetBtnObj() if( b !=3D null ) b.Perform() else Upd() } function GetNtsState(){ return parent.gNtsOpen } function GetOtlState(){ return parent.gOtlOpen } function GetOtlTxtState(){ return parent.gOtlTxtExp } function NtsBtnSetFlag( fVal ) { s=3Ddocument.all.item( this.m_flagId ).style s.display=3D"none" if( fVal ) s.display=3D"" else s.display=3D"none" } function _BSetA_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etActive() } function _BSetI_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etInactive() } function _BSetP_Border(){ b =3D gBtnArr[this.mObjId]; if( b !=3D null ) b.S= etPressed() } function _BSetA_BorderImg() {=20 b =3D gBtnArr[this.mBorderId]=20 if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gHiliteClr,gShadowClr,2 ) obj.style.posTop=3D0 } } function _BSetI_BorderImg() {=20 b =3D gBtnArr[this.mBorderId] if( b !=3D null && this.mIsOn && !b.GetState() ) { obj=3Dthis.ChgState( gFaceClr,gFaceClr,1 ) obj.style.posTop=3D0 } } var gHiliteClr=3D"THREEDHIGHLIGHT",gShadowClr=3D"THREEDSHADOW",gFaceClr=3D"= THREEDFACE" var gBtnArr =3D new Array() gBtnArr["nb_otl"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOtlPan= e,GetOtlState ) gBtnArr["nb_otlElem"] =3D new TxtBtn( "nb_otl","nb_otlElem",parent.ToggleOt= lPane,GetOtlState ) gBtnArr["nb_nts"] =3D new ImgBtn( "nb_nts","nb_ntsBorder",10,parent.ToggleN= tsPane ) gBtnArr["nb_nts"].SetActive =3D _BSetA_BorderImg; gBtnArr["nb_nts"].SetInactive =3D _BSetI_BorderImg; gBtnArr["nb_ntsBorder"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.= ToggleNtsPane,GetNtsState ) gBtnArr["nb_ntsElem"] =3D new TxtBtn( "nb_ntsBorder","nb_ntsElem",parent.To= ggleNtsPane,GetNtsState ) gBtnArr["nb_prevBorder"] =3D gBtnArr["nb_prev"]=3D new ImgBtn( "nb_prev","n= b_prevBorder",30,parent.GoToPrevSld ) gBtnArr["nb_nextBorder"] =3D gBtnArr["nb_next"]=3D new ImgBtn( "nb_next","n= b_nextBorder",30,parent.GoToNextSld ) gBtnArr["nb_sldshw"]=3D new ImgBtn( "nb_sldshw","nb_sldshwBorder",18,parent= .FullScreen ) gBtnArr["nb_sldshwBorder"] =3D new TxtBtn( "nb_sldshw","nb_sldshwBorder",pa= rent.FullScreen,null ) gBtnArr["nb_sldshwBorder"].SetActive =3D _BSetA_Border; 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style=3D'font-family:Arial;font-size:9pt'> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>1</font></div> </td> <td width=3D"100%"> <div id=3DPPTP1 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0001.htm');" id=3DPPTL1>Cost Functions a= nd the Estimation of Flexible Functional Forms</a></font></div> <div id=3DPPTC1 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Lecture XVIII</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>2</font></div> </td> <td> <div id=3DPPTP2 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0002.htm');" id=3DPPTL2>Flexible Functio= nal Forms</a></font></div> <div id=3DPPTC2 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>The crux of the dual approach is then to estimate a manifestation of behavior that economist know something about.</li> <ul> <li>Thus, instead of estimating production functions that are purely physical forms that economist have little expertise in developing, = we could estimate the cost function that represents cost minimizing behavior.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>3</font></div> </td> <td> <div id=3DPPTP3 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0003.htm');" id=3DPPTL3>"We then wo= uld be able..."</a></font></div> <div id=3DPPTC3 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>We then would be able to determine whether the properties of these = cost functions are consistent with our hypotheses about technology.</li> <li>However, it is often the direct implications of the cost minimizing behavior that we are interested in:</li> <ul> <li>How will farmers react to changes in agricultural prices through commodity programs?</li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>4</font></div> </td> <td> <div id=3DPPTP4 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0004.htm');" id=3DPPTL4>"What is th= e impact of..."</a></font></div> <div id=3DPPTC4 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <ul> <li>What is the impact of a change in input prices (say in an increase= in fuel prices) on agricultural output?</li> <br> <br> <br> </ul> <li>Thus, the dual cost function results are usually sufficient for most question facing agricultural economists.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>5</font></div> </td> <td> <div id=3DPPTP5 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0005.htm');" id=3DPPTL5>"Given that= we are interested..."</a></font></div> <div id=3DPPTC5 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Given that we are interested in estimating the cost function directl= y, the next question involves how to specify the cost function?</li> <ul> <li>One approach to the estimation of cost functions would then be to hypothesize a primal production function and derive the theoretical= ly consistent specification for the cost function based on this primal= .</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>6</font></div> </td> <td> <div id=3DPPTP6 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0006.htm');" id=3DPPTL6>"However&qu= ot;</a></font></div> <div id=3DPPTC6 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>However, this approach would appear too restrictive.</li> <li>Thus, economists have typically turned to flexible functional forms that allow for a wide variety of technologies.</li> </ul> <br> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>7</font></div> </td> <td> <div id=3DPPTP7 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0007.htm');" id=3DPPTL7>"A basic ap= proach to the..."</a></font></div> <div id=3DPPTC7 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>A basic approach to the specification of a cost function is to assume that an unspecified function exists, and then derive a closed form approximation of the function.</li> <ul> <li>One typical approach from optimization theory involves the Taylor series expansion:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>8</font></div> </td> <td> <div id=3DPPTP8 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0008.htm');" id=3DPPTL8>General Form of Univariate Taylor Expansion</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>9</font></div> </td> <td> <div id=3DPPTP9 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0009.htm');" id=3DPPTL9>"The real p= roblem is that..."</a></font></div> <div id=3DPPTC9 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>The real problem is that we don’t know the value of x<sup>*</= sup>.<span style=3D'mso-spacerun:yes'> </span>As a result, we approximat= e this term with a residual:</li> <br> <br> <br> <li>Given this approach, we can conjecture the relative size of the approximation error based on the relative size of the third derivat= ive of the cost function.</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>10</font></div> </td> <td> <div id=3DPPTP10 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0010.htm');" id=3DPPTL10>"Extending= this result to vector..."</a></font></div> <div id=3DPPTC10 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Extending this result to vector space, we have:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>11</font></div> </td> <td> <div id=3DPPTP11 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0011.htm');" id=3DPPTL11>"Given tha= t the cost function..."</a></font></div> <div id=3DPPTC11 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Given that the cost function is a function of input prices w and ou= tput levels y, we could then stack the two into a single vector and deri= ve the flexible functional form:</li> <br> <br> <br> <ul> <li>This form is typically referred to as the quadratic cost function.<span style=3D'mso-spacerun:yes'> </span>It is a second-order Taylor series expansion to an unknown cost function.<= /li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>12</font></div> </td> <td> <div id=3DPPTP12 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0012.htm');" id=3DPPTL12>"Following= the general concept (..."</a></font></div> <div id=3DPPTC12 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <ul> <li>Following the general concept (and ignoring for the moment the err= or of approximation), Shephard’s lemma can be applied to this c= ost specification:</li> </ul> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>13</font></div> </td> <td> <div id=3DPPTP13 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0013.htm');" id=3DPPTL13>Flexible Cost S= ystem</a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>14</font></div> </td> <td> <div id=3DPPTP14 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0014.htm');" id=3DPPTL14>"Why have I imposed symmetry"</a></font></div> <div id=3DPPTC14 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Why have I imposed symmetry?</li> <li>Why am I only estimating three demand curves?</li> </ul> <li>One generalization of the Taylor series approach involves a transformation of variables.<span style=3D'mso-spacerun:yes'> </span>Specifically, if we assume:</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>15</font></div> </td> <td> <div id=3DPPTP15 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0015.htm');" id=3DPPTL15>"The cost = function can be..."</a></font></div> <div id=3DPPTC15 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>The cost function can be expressed as:</li> <br> <br> <br> <br> <br> <li>This formulation complicates the Shephard’s lemma results slightly:</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>16</font></div> </td> <td> <div id=3DPPTP16 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0016.htm');" id=3DPPTL16><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>17</font></div> </td> <td> <div id=3DPPTP17 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0017.htm');" id=3DPPTL17>"Note that= letting l go..."</a></font></div> <div id=3DPPTC17 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <ul> <li>Note that letting l go to zero implies</li> </ul> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>18</font></div> </td> <td> <div id=3DPPTP18 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0018.htm');" id=3DPPTL18><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>19</font></div> </td> <td> <div id=3DPPTP19 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0019.htm');" id=3DPPTL19>Fourier Expansi= on</a></font></div> <div id=3DPPTC19 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>In a univariate sense, any function can be approximated by a series = of sine and cosine curves:</li> <br> <br> <br> <li> where the l<sub>I</sub> are different periodicities.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>20</font></div> </td> <td> <div id=3DPPTP20 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0020.htm');" id=3DPPTL20>"Extending= this representation to a..."</a></font></div> <div id=3DPPTC20 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Extending this representation to a multivariate formulation:</li> <br> <br> <br> <li> where l<sub>i</sub> is a constant for periodicity and k<sub>a</sub>= is referred to as an Elementary Multi-Index:</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>21</font></div> </td> <td> <div id=3DPPTP21 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0021.htm');" id=3DPPTL21><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>22</font></div> </td> <td> <div id=3DPPTP22 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0022.htm');" id=3DPPTL22>K=3D1</a></font= ></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>23</font></div> </td> <td> <div id=3DPPTP23 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0023.htm');" id=3DPPTL23>K=3D2</a></font= ></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>24</font></div> </td> <td> <div id=3DPPTP24 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0024.htm');" id=3DPPTL24>"This representation minimizes the Sobolev..."</a></font></div> <div id=3DPPTC24 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>This representation minimizes the Sobolev Norm, which says that it d= oes a better job approximating the derivatives of the function.<span style=3D'mso-spacerun:yes'> </span>In fact, it represents up t= o the k<sup>th</sup> derivative of the function.</li> <li>Note that if the cost function is specified as a multivariate Fourier expansion, the system of demand equations can be defined by Shephard’s lemma.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>25</font></div> </td> <td> <div id=3DPPTP25 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0025.htm');" id=3DPPTL25>Estimation of C= ost Systems</a></font></div> <div id=3DPPTC25 class=3DCTxt style=3D'display:none'><font size=3D2> <ul> <li>Regardless of the function form, cost functions are typically estima= ted as systems of equations using Seemingly Unrelated Regression, Iterat= ed Seemingly Unrelated Regression, or Maximum Likelihood.</li> <li>I prefer the use of Maximum Likelihood based on a concentrated likelihood function.</li> </ul> </font></div> </td> </tr> <tr onmouseover=3D"Over(this)" onmouseout=3D"Out(this)" onclick=3D"Follow(= this)" style=3D'cursor:hand'> <td align=3Dright valign=3Dtop> <div class=3DsldNum><font size=3D2>26</font></div> </td> <td> <div id=3DPPTP26 class=3DPTxt><font size=3D2><a href=3D"javascript:GoToSld('slide0026.htm');" id=3DPPTL26><span style=3D'mso-spacerun:yes'> </span></a></font></div> </td> </tr> </table> </div> <div style=3D'display:none'><a href=3D"../Lecture18-2005.htm"></a><a 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