GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 1 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m C o m p i l a t i o n 1 sets q quantity demanded and supplied /qd11,qd12,qs11,qs12,qd21,qd22, qs21,qs22/ 2 qd1(q) /qd11,qd12/ 3 qd2(q) /qd21,qd22/ 4 qs1(q) /qs11,qs12/ 5 qs2(q) /qs21,qs22/; 6 7 alias(qd1,qqd1); 8 alias(qd2,qqd2); 9 alias(qs1,qqs1); 10 alias(qs2,qqs2); 11 12 table aa1(qd1,qqd1) Quadratic Component of Consumer Demand in Market 1 13 qd11 qd12 14 qd11 -0.00478 -0.00796 15 qd12 -0.00796 -0.0259 16 17 table aa2(qd2,qqd2) Quadratic Component of Consumer Demand in Market 2 18 qd21 qd22 19 qd21 -0.02753 -0.07342 20 qd22 -0.07342 -0.21178 21 22 table bb1(qs1,qqs1) Quadratic Component of Producer Supply in Market 1 23 qs11 qs12 24 qs11 0.007097 0.001577 25 qs12 0.001577 0.025684 26 27 table bb2(qs2,qqs2) Quadratic Component of Producer Supply in Market 2 28 qs21 qs22 29 qs21 0.004457 0.00195 30 qs22 0.00195 0.030853 31 32 parameter a1(qd1) Linear Component of Consumer Demand in Market 1 33 /qd11 14.252, 34 qd12 33.119/; 35 36 parameter a2(qd2) Linear Compenent of Consumer Demand in Market 2 37 /qd21 74.372, 38 qd22 203.658/; 39 40 parameter b1(qs1) Linear Component of Producers Supply in Market 1 41 /qs11 -4.780, 42 qs12 -15.140/; 43 44 parameter b2(qs2) Linear Component of Producers Supply in Market 2 45 /qs21 -3.296, 46 qs22 -11.864/; 47 48 variables w total social welfare 49 quant(q) quantity of each good produced and consumed; 50 51 positive variable quant(q); 52 53 equations sb social welfare 54 mkt1 market for good 1 55 mkt2 market for good 2; 56 57 sb.. sum(qd1,a1(qd1)*quant(qd1)+.5*sum(qqd1,quant(qd1)*aa1(qd1,qqd1) *quant(qqd1))) 58 -sum(qs1,b1(qs1)*quant(qs1)+.5*sum(qqs1,quant(qs1)*bb1(qs1,qqs1) *quant(qqs1))) GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 2 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m C o m p i l a t i o n 59 +sum(qd2,a2(qd2)*quant(qd2)+.5*sum(qqd2,quant(qd2)*aa2(qd2,qqd2) *quant(qqd2))) 60 -sum(qs2,b2(qs2)*quant(qs2)+.5*sum(qqs2,quant(qs2)*bb2(qs2,qqs2) *quant(qqs2))) =e= w; 61 mkt1.. quant("qd11")-quant("qs11")+quant("qd21")-quant("qs21") =e= 0; 62 mkt2.. quant("qd12")-quant("qs12")+quant("qd22")-quant("qs22") =e= 0; 63 64 model trade using /all/; 65 solve trade using nlp maximizing w; 66 67 GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 3 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Symbol Listing SYMBOL TYPE REFERENCES A1 PARAM DECLARED 32 DEFINED 33 REF 57 A2 PARAM DECLARED 36 DEFINED 37 REF 59 AA1 PARAM DECLARED 12 DEFINED 12 REF 57 AA2 PARAM DECLARED 17 DEFINED 17 REF 59 B1 PARAM DECLARED 40 DEFINED 41 REF 58 B2 PARAM DECLARED 44 DEFINED 45 REF 60 BB1 PARAM DECLARED 22 DEFINED 22 REF 58 BB2 PARAM DECLARED 27 DEFINED 27 REF 60 MKT1 EQU DECLARED 54 DEFINED 61 IMPL-ASN 65 REF 64 MKT2 EQU DECLARED 55 DEFINED 62 IMPL-ASN 65 REF 64 Q SET DECLARED 1 DEFINED 1 REF 2 3 4 5 49 51 QD1 SET DECLARED 2 DEFINED 2 REF 7 12 32 4*57 CONTROL 57 QD2 SET DECLARED 3 DEFINED 3 REF 8 17 36 4*59 CONTROL 59 QQD1 SET DECLARED 7 REF 12 2*57 CONTROL 57 QQD2 SET DECLARED 8 REF 17 2*59 CONTROL 59 QQS1 SET DECLARED 9 REF 22 2*58 CONTROL 58 QQS2 SET DECLARED 10 REF 27 2*60 CONTROL 60 QS1 SET DECLARED 4 DEFINED 4 REF 9 22 40 4*58 CONTROL 58 QS2 SET DECLARED 5 DEFINED 5 REF 10 27 44 4*60 CONTROL 60 QUANT VAR DECLARED 49 IMPL-ASN 65 REF 51 3*57 3*58 3*59 3*60 4*61 4*62 SB EQU DECLARED 53 DEFINED 57 IMPL-ASN 65 REF 64 TRADE MODEL DECLARED 64 DEFINED 64 IMPL-ASN 65 REF 65 W VAR DECLARED 48 IMPL-ASN 65 REF 60 65 SETS Q quantity demanded and supplied QD1 QD2 QQD1 Aliased with QD1 QQD2 Aliased with QD2 QQS1 Aliased with QS1 QQS2 Aliased with QS2 QS1 QS2 PARAMETERS A1 Linear Component of Consumer Demand in Market 1 A2 Linear Compenent of Consumer Demand in Market 2 AA1 Quadratic Component of Consumer Demand in Market 1 AA2 Quadratic Component of Consumer Demand in Market 2 GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 4 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Symbol Listing PARAMETERS B1 Linear Component of Producers Supply in Market 1 B2 Linear Component of Producers Supply in Market 2 BB1 Quadratic Component of Producer Supply in Market 1 BB2 Quadratic Component of Producer Supply in Market 2 VARIABLES QUANT quantity of each good produced and consumed W total social welfare EQUATIONS MKT1 market for good 1 MKT2 market for good 2 SB social welfare MODELS TRADE using COMPILATION TIME = 0.050 SECONDS VERID AXU-25-089 GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 5 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Equation Listing SOLVE TRADE USING NLP FROM LINE 65 ---- SB =E= social welfare SB.. - W + (14.252)*QUANT(QD11) + (33.119)*QUANT(QD12) + (4.78)*QUANT(QS11) + (15.14)*QUANT(QS12) + (74.372)*QUANT(QD21) + (203.658)*QUANT(QD22) + (3.296)*QUANT(QS21) + (11.864)*QUANT(QS22) =E= 0 ; (LHS = 0) ---- MKT1 =E= market for good 1 MKT1.. QUANT(QD11) - QUANT(QS11) + QUANT(QD21) - QUANT(QS21) =E= 0 ; (LHS = 0) ---- MKT2 =E= market for good 2 MKT2.. QUANT(QD12) - QUANT(QS12) + QUANT(QD22) - QUANT(QS22) =E= 0 ; (LHS = 0) GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 6 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Column Listing SOLVE TRADE USING NLP FROM LINE 65 ---- W total social welfare W (.LO, .L, .UP = -INF, 0, +INF) -1 SB 0 (OBJECTIVE) ---- QUANT quantity of each good produced and consumed QUANT(QD11) (.LO, .L, .UP = 0, 0, +INF) (14.252) SB 1 MKT1 0 (DUAL) QUANT(QD12) (.LO, .L, .UP = 0, 0, +INF) (33.119) SB 1 MKT2 0 (DUAL) QUANT(QS11) (.LO, .L, .UP = 0, 0, +INF) (4.78) SB -1 MKT1 0 (DUAL) REMAINING 5 ENTRIES SKIPPED GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 7 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Model Statistics SOLVE TRADE USING NLP FROM LINE 65 MODEL STATISTICS BLOCKS OF EQUATIONS 3 SINGLE EQUATIONS 3 BLOCKS OF VARIABLES 2 SINGLE VARIABLES 9 NON ZERO ELEMENTS 17 NON LINEAR N-Z 8 DERIVATIVE POOL 15 CONSTANT POOL 28 CODE LENGTH 362 GENERATION TIME = 0.033 SECONDS EXECUTION TIME = 0.033 SECONDS VERID AXU-25-089 GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 8 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Solution Report SOLVE TRADE USING NLP FROM LINE 65 S O L V E S U M M A R Y MODEL TRADE OBJECTIVE W TYPE NLP DIRECTION MAXIMIZE SOLVER MINOS5 FROM LINE 65 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 130064.9984 RESOURCE USAGE, LIMIT 0.173 1000.000 ITERATION COUNT, LIMIT 12 1000 EVALUATION ERRORS 0 0 GAMS/MINOS 5.4 Aug 1, 1996 002.103.030-033.030 AXP/OSF B. A. Murtagh, University of New South Wales and P. E. Gill, W. Murray, M. A. Saunders and M. H. Wright Systems Optimization Laboratory, Stanford University. Work space allocated -- 0.04 Mb EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 1 200 FUNOBJ, FUNCON CALLS 33 0 SUPERBASICS 6 INTERPRETER USAGE 0.00 NORM RG / NORM PI 1.871E-09 LOWER LEVEL UPPER MARGINAL ---- EQU SB . . . -1.000 ---- EQU MKT1 . . . 3.349 ---- EQU MKT2 . . . 5.829 SB social welfare MKT1 market for good 1 MKT2 market for good 2 LOWER LEVEL UPPER MARGINAL ---- VAR W -INF 1.3006E+5 +INF . W total social welfare ---- VAR QUANT quantity of each good produced and consumed LOWER LEVEL UPPER MARGINAL QD11 . 1078.015 +INF . QD12 . 722.361 +INF EPS QS11 . 977.349 +INF EPS QS12 . 756.408 +INF EPS QD21 . 1174.639 +INF EPS QD22 . 526.901 +INF . QS21 . 1275.305 +INF EPS GAMS 2.25.089 DEC AXP/UNIX 09/22/03 14:45:46 PAGE 9 G e n e r a l A l g e b r a i c M o d e l i n g S y s t e m Solution Report SOLVE TRADE USING NLP FROM LINE 65 VAR QUANT quantity of each good produced and consumed LOWER LEVEL UPPER MARGINAL QS22 . 492.854 +INF EPS **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS EXECUTION TIME = 0.017 SECONDS VERID AXU-25-089 USER: Charles Moss G961213:1904AP-AXU University of Florida **** FILE SUMMARY INPUT /usr/users/chuck/Assignment02-2003.gms OUTPUT /usr/users/chuck/Assignment02-2003.lst