$TITLE Model M52-MPS: Monopoly with IRTS - calibrated to zero profits $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 SIGMA Elasticity of substitution in demand, FCOST Ratio of fixed costs to benchmark, ENDOW Level of factor endowment, INCOMEM Income of the monopolist, INCOMEC Inome of the factor owners TAX; SIGMA = 9; FCOST = 1; ENDOW = 1; TAX = 0; $ONTEXT $MODEL:M52 $SECTORS: X ! Activity level -- monopolist sector X Y ! Activity level -- competitive sector Y W ! Welfare index for the consumer $COMMODITIES: PU ! Welfare price index for the consumer PX ! Price index for X (gross of markup) PY ! Price index for Y (gross of markup) PW ! Price index for labor PZ ! Price index for capital $CONSUMERS: CONS ! All consumers $AUXILIARY: SHAREX ! Value share of X in total consumption MARKUP ! Markup based on Marshallian demand $PROD:X s:1 O:PX Q: 80 A:CONS N:MARKUP I:PW Q: 32 A:CONS T:TAX I:PZ Q: 48 A:CONS T:TAX $PROD:Y s:1 O:PY Q:100 I:PW Q: 60 I:PZ Q: 40 $PROD:W s:sigma O:PU Q:200 I:PX Q: 80 P:1.25 I:PY Q:100 $DEMAND:CONS D:PU Q:200 E:PW Q:(100*ENDOW) E:PZ Q:(100*ENDOW) E:PW Q:(-8*FCOST) E:PZ Q:(-12*FCOST) $CONSTRAINT:SHAREX SHAREX*(80*PX*X + 100*PY*Y) =G= 80*PX*X; $CONSTRAINT:MARKUP MARKUP =E= 1/(SIGMA - (SIGMA-1)*SHAREX); $OFFTEXT $SYSINCLUDE mpsgeset M52 * Benchmark replication: PX.L = 1.25; SHAREX.L = 0.5; MARKUP.L = 0.20; $INCLUDE M52.GEN 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: marginal-cost pricing MARKUP.FX = 0; $INCLUDE M52.GEN 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; $INCLUDE M52.GEN 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; TAX = -0.1; $INCLUDE M52.GEN 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; $EXIT * counterfactual: cut the size of the economy by 25% ENDOW = 0.75; $INCLUDE M52.GEN 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;