GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 * 2 * PROTOCD.GMS 3 * Sep 96 (PJW) 4 * 5 * GAMS program to solve several experiments using the PROTO model with 6 * Cobb-Douglas production. 7 * 8 9 * 10 * Turn off the symbol table and symbol listing. Also turn off the 11 * equation and variable listing produced by the solve statement. 12 * Generally this should only be done after a model is working properly. 13 * 14 16 OPTION LIMROW=0, LIMCOL=0; 17 18 * 19 * OK, now define the model's parameters: 20 * 21 22 SCALAR a Utility function parameter / 0.285 /; 23 SCALAR alpha Level of technology in production / 2.000 /; 24 SCALAR g Capital exponent in production / 0.500 /; 25 26 * 27 * These are exogenous variables: 28 * 29 30 SCALAR h Total endowment of hours / 100.0 /; 31 SCALAR p Numeraire price / 1.000 /; 32 SCALAR tc Initial consumption tax rate / 0.200 /; 33 SCALAR tx Initial intermediate tax rate / 0.0 /; 34 SCALAR tw Initial wage tax rate / 0.0 /; 35 36 37 * 38 * Now add some scalars to save base case information so that welfare 39 * calculations can be done for subsequent simulations. The initial 40 * values of these are not used so they are all set to 1 for simplicity. 41 * Setting these up as scalars rather than variables makes them a little 42 * easier to use and can be done because they do not appear in the 43 * actual equations of the model. 44 * 45 46 SCALAR pbase Base case purchasers price p*(1+t) / 1.000 /; 47 SCALAR wbase Base case wage rate / 1.000 /; 48 SCALAR ybase Base case income / 1.000 /; 49 SCALAR ev Equivalent variation / 1.000 /; 50 51 * 52 * OK, now set up the endogenous variables: 53 * 54 55 VARIABLES 56 y Income 57 w Wage rate 58 s Subsidy to households 59 c Quantity consumed 60 l Labor supplied 61 j Leisure consumed 62 q Quantity produced GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 63 x Intermediate goods demand 64 pc Purchasers price for consumers 65 px Purchasers price for firms 66 wh After-tax wage 67 walras Difference between RHS and LHS of Walras Law equation 68 util Utility 69 z Dummy for solver ; 70 71 * 72 * Here are the equations: 73 * 74 75 EQUATIONS 76 income Household income accounting identity 77 consum Household demand for goods 78 leisure Household demand for leisure 79 laborsup Household supply of labor 80 labordem Demand for labor by firms 81 intdem Intermediate goods demand 82 price Price from firm's cost function 83 govbudget Government budget constraint 84 p_con Purchaser's price to consumers 85 p_int Purchaser's price to firms 86 w_hh Household after-tax wage 87 utileq Indirect utility function 88 walraschk Calculate error in Walras Law 89 dummy Dummy equation for solver ; 90 91 income.. y =e= wh*h + s ; 92 consum.. pc*c =e= a*y ; 93 leisure.. wh*j =e= (1-a)*y ; 94 laborsup.. wh*l =e= a*y - s ; 95 labordem.. l =e= (q/alpha)*( (1-g)*px/(g*w) )**g ; 96 intdem.. x =e= (q/alpha)*( g*w/((1-g)*px) )**(1-g) ; 97 price.. p =e= (1/alpha)*((px/g)**g)*((w/(1-g))**(1-g)); 98 govbudget.. s =e= tc*p*c + tx*p*x + tw*w*l ; 99 p_con.. pc =e= p*(1+tc) ; 100 p_int.. px =e= p*(1+tx) ; 101 w_hh.. wh =e= w*(1-tw) ; 102 utileq.. util =e= (c)**a * (j)**(1-a) ; 103 walraschk.. walras =e= q - x - c ; 104 dummy.. z =e= 1000 ; 105 106 * 107 * The model consists of all of the equations: 108 * 109 110 MODEL proto /ALL/; 111 112 * 113 * Set initial values of variables appearing in denominators because 114 * GAMS will choose zero if we don't. Also, set a few other variables 115 * to help it find the solution. 116 * 117 118 w.L = 1 ; 119 px.L = 1 ; 120 q.L = 50 ; 121 y.L = 105 ; 122 123 * GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 C o m p i l a t i o n 124 * Constrain a few varialbles to be non-negative so that GAMS doesn't 125 * run into numerical errors. 126 * 127 128 w.lo = 0.1 ; 129 c.lo = 0.0 ; 130 j.lo = 0.0 ; 131 132 * 133 * Solve it using Nonlinear programming. Must give the 134 * algorithm something to minimize so use a dummy variable. 135 * 136 137 SOLVE proto USING NLP MINIMIZING z; 138 139 * 140 * Now save some base case variables for welfare calculations. Need to 141 * use the .L suffix for variables but don't need it with scalars. 142 * 143 144 pbase = pc.L ; 145 wbase = w.L ; 146 ybase = y.L ; 147 148 * 149 * Alternative 1: a 50% increase in the numeraire. 150 * 151 * Increase p to 1.5 and solve. After solving, calculate the 152 * equivalent variation for the experiment using the new utility 153 * and the base case prices and income. The EV for this experiment 154 * should be zero but calculate it just to check. 155 * 156 157 p = 1.5 ; 158 159 SOLVE proto USING NLP MINIMIZING z; 160 161 ev = util.L * (pbase/a)**a * (wbase/(1-a))**(1-a) - ybase ; 162 163 display ev ; 164 165 p = 1.0 ; 166 167 * 168 * Alternative 2: an increase in the consumption tax rate. 169 * 170 171 tc = 0.3 ; 172 173 SOLVE proto USING NLP MINIMIZING z; 174 175 ev = util.L * (pbase/a)**a * (wbase/(1-a))**(1-a) - ybase ; 176 177 display ev ; 178 179 tc = 0.2 ; 180 181 * 182 * Alternative 3: an increase in the intermediate goods tax. 183 * 184 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 C o m p i l a t i o n 185 tx = 0.1 ; 186 187 SOLVE proto USING NLP MINIMIZING z; 188 189 ev = util.L * (pbase/a)**a * (wbase/(1-a))**(1-a) - ybase ; 190 191 display ev ; 192 193 tx = 0.0 ; 194 195 * 196 * Alternative 4: an increase in the wage tax. 197 * 198 199 tw = 0.1 ; 200 201 SOLVE proto USING NLP MINIMIZING z; 202 203 ev = util.L * (pbase/a)**a * (wbase/(1-a))**(1-a) - ybase ; 204 205 display ev ; 206 207 tw = 0.0 ; 208 COMPILATION TIME = 0.010 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 Model Statistics SOLVE PROTO USING NLP FROM LINE 137 MODEL STATISTICS BLOCKS OF EQUATIONS 14 SINGLE EQUATIONS 14 BLOCKS OF VARIABLES 14 SINGLE VARIABLES 14 NON ZERO ELEMENTS 37 NON LINEAR N-Z 16 DERIVATIVE POOL 6 CONSTANT POOL 10 CODE LENGTH 235 GENERATION TIME = 0.020 SECONDS EXECUTION TIME = 0.020 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 Solution Report SOLVE PROTO USING NLP FROM LINE 137 S O L V E S U M M A R Y MODEL PROTO OBJECTIVE Z TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 137 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 1000.0000 RESOURCE USAGE, LIMIT 0.059 1000.000 ITERATION COUNT, LIMIT 13 1000 EVALUATION ERRORS 0 0 M I N O S 5.3 --- SPARC/SOLARIS 5.3.021-019 = = = = = 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. EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 23 200 FUNOBJ, FUNCON CALLS 0 50 SUPERBASICS 0 INTERPRETER USAGE 0.01 NORM RG / NORM PI 0.000E+00 LOWER LEVEL UPPER MARGINAL ---- EQU INCOME . . . EPS ---- EQU CONSUM . . . EPS ---- EQU LEISURE . . . EPS ---- EQU LABORSUP . . . EPS ---- EQU LABORDEM . . . EPS ---- EQU INTDEM . . . EPS ---- EQU PRICE -1.000 -1.000 -1.000 EPS ---- EQU GOVBUDGET . . . EPS ---- EQU P_CON 1.200 1.200 1.200 EPS ---- EQU P_INT 1.000 1.000 1.000 EPS ---- EQU W_HH . . . EPS ---- EQU UTILEQ . . . EPS ---- EQU WALRASCHK . . . EPS ---- EQU DUMMY 1000.000 1000.000 1000.000 1.000 INCOME Household income accounting identity CONSUM Household demand for goods LEISURE Household demand for leisure LABORSUP Household supply of labor LABORDEM Demand for labor by firms INTDEM Intermediate goods demand PRICE Price from firm's cost function GOVBUDGET Government budget constraint P_CON Purchaser's price to consumers P_INT Purchaser's price to firms W_HH Household after-tax wage UTILEQ Indirect utility function WALRASCHK Calculate error in Walras Law GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 Solution Report SOLVE PROTO USING NLP FROM LINE 137 DUMMY Dummy equation for solver LOWER LEVEL UPPER MARGINAL ---- VAR Y -INF 104.987 +INF . ---- VAR W 0.100 1.000 +INF . ---- VAR S -INF 4.987 +INF . ---- VAR C . 24.934 +INF . ---- VAR L -INF 24.934 +INF . ---- VAR J . 75.066 +INF . ---- VAR Q -INF 49.869 +INF . ---- VAR X -INF 24.934 +INF . ---- VAR PC -INF 1.200 +INF . ---- VAR PX -INF 1.000 +INF . ---- VAR WH -INF 1.000 +INF . ---- VAR WALRAS -INF . +INF . ---- VAR UTIL -INF 54.831 +INF . ---- VAR Z -INF 1000.000 +INF . Y Income W Wage rate S Subsidy to households C Quantity consumed L Labor supplied J Leisure consumed Q Quantity produced X Intermediate goods demand PC Purchasers price for consumers PX Purchasers price for firms WH After-tax wage WALRAS Difference between RHS and LHS of Walras Law equation UTIL Utility Z Dummy for solver **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 Model Statistics SOLVE PROTO USING NLP FROM LINE 159 MODEL STATISTICS BLOCKS OF EQUATIONS 14 SINGLE EQUATIONS 14 BLOCKS OF VARIABLES 14 SINGLE VARIABLES 14 NON ZERO ELEMENTS 37 NON LINEAR N-Z 16 DERIVATIVE POOL 6 CONSTANT POOL 10 CODE LENGTH 235 GENERATION TIME = 0.010 SECONDS EXECUTION TIME = 0.010 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 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 PROTO USING NLP FROM LINE 159 S O L V E S U M M A R Y MODEL PROTO OBJECTIVE Z TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 159 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 1000.0000 RESOURCE USAGE, LIMIT 0.019 1000.000 ITERATION COUNT, LIMIT 0 1000 EVALUATION ERRORS 0 0 M I N O S 5.3 --- SPARC/SOLARIS 5.3.021-019 = = = = = 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. EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 3 200 FUNOBJ, FUNCON CALLS 0 5 SUPERBASICS 0 INTERPRETER USAGE 0.00 NORM RG / NORM PI 0.000E+00 LOWER LEVEL UPPER MARGINAL ---- EQU INCOME . . . EPS ---- EQU CONSUM . . . EPS ---- EQU LEISURE . . . EPS ---- EQU LABORSUP . . . EPS ---- EQU LABORDEM . . . EPS ---- EQU INTDEM . . . EPS ---- EQU PRICE -1.500 -1.500 -1.500 EPS ---- EQU GOVBUDGET . . . EPS ---- EQU P_CON 1.800 1.800 1.800 EPS ---- EQU P_INT 1.500 1.500 1.500 EPS ---- EQU W_HH . . . EPS ---- EQU UTILEQ . . . EPS ---- EQU WALRASCHK . . . EPS ---- EQU DUMMY 1000.000 1000.000 1000.000 1.000 INCOME Household income accounting identity CONSUM Household demand for goods LEISURE Household demand for leisure LABORSUP Household supply of labor LABORDEM Demand for labor by firms INTDEM Intermediate goods demand PRICE Price from firm's cost function GOVBUDGET Government budget constraint P_CON Purchaser's price to consumers P_INT Purchaser's price to firms W_HH Household after-tax wage UTILEQ Indirect utility function WALRASCHK Calculate error in Walras Law GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 10 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 PROTO USING NLP FROM LINE 159 DUMMY Dummy equation for solver LOWER LEVEL UPPER MARGINAL ---- VAR Y -INF 157.480 +INF . ---- VAR W 0.100 1.500 +INF . ---- VAR S -INF 7.480 +INF . ---- VAR C . 24.934 +INF . ---- VAR L -INF 24.934 +INF . ---- VAR J . 75.066 +INF . ---- VAR Q -INF 49.869 +INF . ---- VAR X -INF 24.934 +INF . ---- VAR PC -INF 1.800 +INF . ---- VAR PX -INF 1.500 +INF . ---- VAR WH -INF 1.500 +INF . ---- VAR WALRAS -INF . +INF . ---- VAR UTIL -INF 54.831 +INF . ---- VAR Z -INF 1000.000 +INF . Y Income W Wage rate S Subsidy to households C Quantity consumed L Labor supplied J Leisure consumed Q Quantity produced X Intermediate goods demand PC Purchasers price for consumers PX Purchasers price for firms WH After-tax wage WALRAS Difference between RHS and LHS of Walras Law equation UTIL Utility Z Dummy for solver **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 11 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 E x e c u t i o n ---- 163 PARAMETER EV = 1.42109E-14 Equivalent variation GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 12 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 PROTO USING NLP FROM LINE 173 MODEL STATISTICS BLOCKS OF EQUATIONS 14 SINGLE EQUATIONS 14 BLOCKS OF VARIABLES 14 SINGLE VARIABLES 14 NON ZERO ELEMENTS 37 NON LINEAR N-Z 16 DERIVATIVE POOL 6 CONSTANT POOL 10 CODE LENGTH 235 GENERATION TIME = 0.000 SECONDS EXECUTION TIME = 0.010 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 13 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 PROTO USING NLP FROM LINE 173 S O L V E S U M M A R Y MODEL PROTO OBJECTIVE Z TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 173 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 1000.0000 RESOURCE USAGE, LIMIT 0.021 1000.000 ITERATION COUNT, LIMIT 0 1000 EVALUATION ERRORS 0 0 M I N O S 5.3 --- SPARC/SOLARIS 5.3.021-019 = = = = = 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. EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 6 200 FUNOBJ, FUNCON CALLS 0 8 SUPERBASICS 0 INTERPRETER USAGE 0.00 NORM RG / NORM PI 0.000E+00 LOWER LEVEL UPPER MARGINAL ---- EQU INCOME . . . EPS ---- EQU CONSUM . . . EPS ---- EQU LEISURE . . . EPS ---- EQU LABORSUP . . . EPS ---- EQU LABORDEM . . . EPS ---- EQU INTDEM . . . EPS ---- EQU PRICE -1.000 -1.000 -1.000 EPS ---- EQU GOVBUDGET . . . EPS ---- EQU P_CON 1.300 1.300 1.300 EPS ---- EQU P_INT 1.000 1.000 1.000 EPS ---- EQU W_HH . . . EPS ---- EQU UTILEQ . . . EPS ---- EQU WALRASCHK . . . EPS ---- EQU DUMMY 1000.000 1000.000 1000.000 1.000 INCOME Household income accounting identity CONSUM Household demand for goods LEISURE Household demand for leisure LABORSUP Household supply of labor LABORDEM Demand for labor by firms INTDEM Intermediate goods demand PRICE Price from firm's cost function GOVBUDGET Government budget constraint P_CON Purchaser's price to consumers P_INT Purchaser's price to firms W_HH Household after-tax wage UTILEQ Indirect utility function WALRASCHK Calculate error in Walras Law GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 14 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 PROTO USING NLP FROM LINE 173 DUMMY Dummy equation for solver LOWER LEVEL UPPER MARGINAL ---- VAR Y -INF 107.040 +INF . ---- VAR W 0.100 1.000 +INF . ---- VAR S -INF 7.040 +INF . ---- VAR C . 23.466 +INF . ---- VAR L -INF 23.466 +INF . ---- VAR J . 76.534 +INF . ---- VAR Q -INF 46.933 +INF . ---- VAR X -INF 23.466 +INF . ---- VAR PC -INF 1.300 +INF . ---- VAR PX -INF 1.000 +INF . ---- VAR WH -INF 1.000 +INF . ---- VAR WALRAS -INF . +INF . ---- VAR UTIL -INF 54.643 +INF . ---- VAR Z -INF 1000.000 +INF . Y Income W Wage rate S Subsidy to households C Quantity consumed L Labor supplied J Leisure consumed Q Quantity produced X Intermediate goods demand PC Purchasers price for consumers PX Purchasers price for firms WH After-tax wage WALRAS Difference between RHS and LHS of Walras Law equation UTIL Utility Z Dummy for solver **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 15 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 E x e c u t i o n ---- 177 PARAMETER EV = -0.361 Equivalent variation GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 16 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 PROTO USING NLP FROM LINE 187 MODEL STATISTICS BLOCKS OF EQUATIONS 14 SINGLE EQUATIONS 14 BLOCKS OF VARIABLES 14 SINGLE VARIABLES 14 NON ZERO ELEMENTS 38 NON LINEAR N-Z 16 DERIVATIVE POOL 6 CONSTANT POOL 10 CODE LENGTH 235 GENERATION TIME = 0.000 SECONDS EXECUTION TIME = 0.010 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 17 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 PROTO USING NLP FROM LINE 187 S O L V E S U M M A R Y MODEL PROTO OBJECTIVE Z TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 187 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 1000.0000 RESOURCE USAGE, LIMIT 0.022 1000.000 ITERATION COUNT, LIMIT 0 1000 EVALUATION ERRORS 0 0 M I N O S 5.3 --- SPARC/SOLARIS 5.3.021-019 = = = = = 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. EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 6 200 FUNOBJ, FUNCON CALLS 0 8 SUPERBASICS 0 INTERPRETER USAGE 0.00 NORM RG / NORM PI 0.000E+00 LOWER LEVEL UPPER MARGINAL ---- EQU INCOME . . . EPS ---- EQU CONSUM . . . EPS ---- EQU LEISURE . . . EPS ---- EQU LABORSUP . . . EPS ---- EQU LABORDEM . . . EPS ---- EQU INTDEM . . . EPS ---- EQU PRICE -1.000 -1.000 -1.000 EPS ---- EQU GOVBUDGET . . . EPS ---- EQU P_CON 1.200 1.200 1.200 EPS ---- EQU P_INT 1.100 1.100 1.100 EPS ---- EQU W_HH . . . EPS ---- EQU UTILEQ . . . EPS ---- EQU WALRASCHK . . . EPS ---- EQU DUMMY 1000.000 1000.000 1000.000 1.000 INCOME Household income accounting identity CONSUM Household demand for goods LEISURE Household demand for leisure LABORSUP Household supply of labor LABORDEM Demand for labor by firms INTDEM Intermediate goods demand PRICE Price from firm's cost function GOVBUDGET Government budget constraint P_CON Purchaser's price to consumers P_INT Purchaser's price to firms W_HH Household after-tax wage UTILEQ Indirect utility function WALRASCHK Calculate error in Walras Law GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 18 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 PROTO USING NLP FROM LINE 187 DUMMY Dummy equation for solver LOWER LEVEL UPPER MARGINAL ---- VAR Y -INF 97.468 +INF . ---- VAR W 0.100 0.909 +INF . ---- VAR S -INF 6.559 +INF . ---- VAR C . 23.149 +INF . ---- VAR L -INF 23.342 +INF . ---- VAR J . 76.658 +INF . ---- VAR Q -INF 42.439 +INF . ---- VAR X -INF 19.291 +INF . ---- VAR PC -INF 1.200 +INF . ---- VAR PX -INF 1.100 +INF . ---- VAR WH -INF 0.909 +INF . ---- VAR WALRAS -INF . +INF . ---- VAR UTIL -INF 54.494 +INF . ---- VAR Z -INF 1000.000 +INF . Y Income W Wage rate S Subsidy to households C Quantity consumed L Labor supplied J Leisure consumed Q Quantity produced X Intermediate goods demand PC Purchasers price for consumers PX Purchasers price for firms WH After-tax wage WALRAS Difference between RHS and LHS of Walras Law equation UTIL Utility Z Dummy for solver **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 19 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 E x e c u t i o n ---- 191 PARAMETER EV = -0.645 Equivalent variation GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 20 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 PROTO USING NLP FROM LINE 201 MODEL STATISTICS BLOCKS OF EQUATIONS 14 SINGLE EQUATIONS 14 BLOCKS OF VARIABLES 14 SINGLE VARIABLES 14 NON ZERO ELEMENTS 39 NON LINEAR N-Z 18 DERIVATIVE POOL 6 CONSTANT POOL 10 CODE LENGTH 252 GENERATION TIME = 0.000 SECONDS EXECUTION TIME = 0.010 SECONDS VERID SOL-25-078 GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 21 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 PROTO USING NLP FROM LINE 201 S O L V E S U M M A R Y MODEL PROTO OBJECTIVE Z TYPE NLP DIRECTION MINIMIZE SOLVER MINOS5 FROM LINE 201 **** SOLVER STATUS 1 NORMAL COMPLETION **** MODEL STATUS 2 LOCALLY OPTIMAL **** OBJECTIVE VALUE 1000.0000 RESOURCE USAGE, LIMIT 0.031 1000.000 ITERATION COUNT, LIMIT 0 1000 EVALUATION ERRORS 0 0 M I N O S 5.3 --- SPARC/SOLARIS 5.3.021-019 = = = = = 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. EXIT -- OPTIMAL SOLUTION FOUND MAJOR ITNS, LIMIT 5 200 FUNOBJ, FUNCON CALLS 0 7 SUPERBASICS 0 INTERPRETER USAGE 0.00 NORM RG / NORM PI 0.000E+00 LOWER LEVEL UPPER MARGINAL ---- EQU INCOME . . . EPS ---- EQU CONSUM . . . EPS ---- EQU LEISURE . . . EPS ---- EQU LABORSUP . . . EPS ---- EQU LABORDEM . . . EPS ---- EQU INTDEM . . . EPS ---- EQU PRICE -1.000 -1.000 -1.000 EPS ---- EQU GOVBUDGET . . . EPS ---- EQU P_CON 1.200 1.200 1.200 EPS ---- EQU P_INT 1.000 1.000 1.000 EPS ---- EQU W_HH . . . EPS ---- EQU UTILEQ . . . EPS ---- EQU WALRASCHK . . . EPS ---- EQU DUMMY 1000.000 1000.000 1000.000 1.000 INCOME Household income accounting identity CONSUM Household demand for goods LEISURE Household demand for leisure LABORSUP Household supply of labor LABORDEM Demand for labor by firms INTDEM Intermediate goods demand PRICE Price from firm's cost function GOVBUDGET Government budget constraint P_CON Purchaser's price to consumers P_INT Purchaser's price to firms W_HH Household after-tax wage UTILEQ Indirect utility function WALRASCHK Calculate error in Walras Law GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 22 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 PROTO USING NLP FROM LINE 201 DUMMY Dummy equation for solver LOWER LEVEL UPPER MARGINAL ---- VAR Y -INF 96.904 +INF . ---- VAR W 0.100 1.000 +INF . ---- VAR S -INF 6.904 +INF . ---- VAR C . 23.015 +INF . ---- VAR L -INF 23.015 +INF . ---- VAR J . 76.985 +INF . ---- VAR Q -INF 46.030 +INF . ---- VAR X -INF 23.015 +INF . ---- VAR PC -INF 1.200 +INF . ---- VAR PX -INF 1.000 +INF . ---- VAR WH -INF 0.900 +INF . ---- VAR WALRAS -INF . +INF . ---- VAR UTIL -INF 54.570 +INF . ---- VAR Z -INF 1000.000 +INF . Y Income W Wage rate S Subsidy to households C Quantity consumed L Labor supplied J Leisure consumed Q Quantity produced X Intermediate goods demand PC Purchasers price for consumers PX Purchasers price for firms WH After-tax wage WALRAS Difference between RHS and LHS of Walras Law equation UTIL Utility Z Dummy for solver **** REPORT SUMMARY : 0 NONOPT 0 INFEASIBLE 0 UNBOUNDED 0 ERRORS GAMS 2.25.078 SPARC/SOLARIS 10/20/99 11:36:34 PAGE 23 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 E x e c u t i o n ---- 205 PARAMETER EV = -0.500 Equivalent variation EXECUTION TIME = 0.010 SECONDS VERID SOL-25-078 USER: Campus Site License G950505:1340AR-SOL University of Texas at Austin **** FILE SUMMARY INPUT /home/fac2/wilcoxen/mosaic/cge/protocd/gams/protocd.gms OUTPUT /home/fac2/wilcoxen/mosaic/cge/protocd/gams/protocd.lst