$TITLE Model M52-MCP.GMS: Closed Economy Monopoly with IRS * uses MCP $ONTEXT Production Sectors Consumers Markets | X N Y W | CONS ---------------------------------------------------------- PX | 100 -100 | PY | 100 -100 | PF | 20 | -20 PU | 200 | -200 PW | -32 -8 -60 | 100 PZ | -48 -12 -40 | 100 MK | -20 | 20 $OFFTEXT PARAMETERS A Scale parameter for utility function, SIGMA Elasticity of substitution, INCOMEM Monopoly profit (in welfare units), INCOMEC Factor owners' income, ENDOW Endowment scale multiplier, FCOST Fixed costs scale multiplier, MODELSTAT; SIGMA = 9; ENDOW = 1; FCOST = 1; A = 0.5**(1/(1-SIGMA)); POSITIVE VARIABLES X Y W PX PY PU PZ PW CONS ENTRE SHAREX MARKUP; EQUATIONS DX Demand for X DY Demand for Y DW Demand for W PRICEX MR = MC in X PRICEY Zero profit condition for Y (PY = MC) PRICEW Zero profit condition for W SKLAB Supply-demand balance for skilled labor UNLAB Supply-demand balance for unskilled labor ICONS Consumer (factor owners') income IENTRE Entrepreneur's profits SHX Share of X in expenditure MK Markup equation; PRICEX.. (PW**0.40)*(PZ**0.60) =G= PX*(1 - MARKUP); PRICEY.. (PW**0.60)*(PZ**0.40) =G= PY; PRICEW.. A*((PX/1.25)**(1-SIGMA) + PY**(1-SIGMA))**(1/(1-SIGMA)) =G= PU; DX.. X*80 =E= A*(PX/1.25)**(-SIGMA)* ((PX/1.25)**(1-SIGMA) + PY**(1-SIGMA))**(SIGMA/(1-SIGMA)) *W*200/1.25; DY.. Y*100 =E= A*PY**(-SIGMA)* ((PX/1.25)**(1-SIGMA) + PY**(1-SIGMA))**(SIGMA/(1-SIGMA)) *W*200; DW.. W*200 =E= CONS/PU; SKLAB.. 100*ENDOW =E= 0.40*(PW**0.60)*(PZ**(0.40-1))*Y*100 + 0.60*(PW**0.40)*(PZ**(0.60-1))*X*80 +12*FCOST; UNLAB.. 100*ENDOW =E= 0.60*(PW**(0.60-1))*(PZ**0.40)*Y*100 + 0.40*(PW**(0.40-1))*(PZ**0.60)*X*80 + 8*FCOST; ICONS.. CONS =E= PZ*100*ENDOW + PW*100*ENDOW + MARKUP*PX*X*80 -PZ*12*FCOST - PW*8*FCOST; SHX.. SHAREX =E= 80*PX*X / (80*PX*X + 100*PY*Y) ; MK.. MARKUP =E= 1/(SIGMA - (SIGMA-1)*SHAREX); MODEL M52 /DX.PX, DY.PY, DW.PU, PRICEX.X, PRICEY.Y, PRICEW.W, SKLAB.PZ, UNLAB.PW, ICONS.CONS, SHX.SHAREX, MK.MARKUP/; OPTION MCP=MILES; OPTION LIMROW=0; OPTION LIMCOL=0; $OFFSYMLIST OFFSYMXREF OFFUELLIST OFFUELXREF CONS.L = 200; X.L = 1; Y.L = 1; W.L = 1; PX.L = 1.25; PY.L = 1; PZ.L = 1; PW.L = 1; PU.L = 1; CONS.L = 180; ENTRE.L = 20; SHAREX.L = 0.5; MARKUP.L = 0.20; PY.FX = 1; *M52.ITERLIM = 0; SOLVE M52 USING MCP; MODELSTAT = M52.MODELSTAT - 1.; INCOMEM = W.L*((MARKUP.L*PX.L*X.L*80 - PW.L*8*FCOST - PZ.L*12*FCOST)/ (PX.L*X.L*80 + PY.L*Y.L*100)); INCOMEC = W.L - INCOMEM; DISPLAY INCOMEM, INCOMEC; * counterfactual: marginal-cost pricing MARKUP.FX = 0; SOLVE M52 USING MCP; INCOMEM = W.L*((MARKUP.L*PX.L*X.L*80 - PW.L*8*FCOST - PZ.L*12*FCOST)/ (PX.L*X.L*80 + PY.L*Y.L*100)); INCOMEC = W.L - INCOMEM; DISPLAY INCOMEM, INCOMEC; * counterfactual: double the size of the economy MARKUP.LO = -INF; MARKUP.UP = INF; ENDOW = 2; SOLVE M52 USING MCP; INCOMEM = W.L*((MARKUP.L*PX.L*X.L*80 - PW.L*8*FCOST - PZ.L*12*FCOST)/ (PX.L*X.L*80 + PY.L*Y.L*100)); INCOMEC = W.L - INCOMEM; DISPLAY INCOMEM, INCOMEC; * counterfactual: cut the size of the economy by 25% ENDOW = 0.75; SOLVE M52 USING MCP; INCOMEM = W.L*((MARKUP.L*PX.L*X.L*80 - PW.L*8*FCOST - PZ.L*12*FCOST)/ (PX.L*X.L*80 + PY.L*Y.L*100)); INCOMEC = W.L - INCOMEM; DISPLAY INCOMEM, INCOMEC;