$TITLE: Model M62-MPS: Large-Group Monopolistic Competition, uses MPS/GE $ONTEXT Production Sectors Consumers Markets | XI X N Y W | CONS ENTR ---------------------------------------------------------------------- PX | 100 -100 | CX ! 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 ENDOW Size index for the economy INDEX Price index for the X goods EP Elasticity of substitution among X varieties; ENDOW = 1; EP = 5; $ONTEXT $MODEL:M62 $SECTORS: X ! Activity level for sector X Y ! Activity level for sector Y W ! Activity level for sector W (Hicksian welfare index) N ! Activity level -- sector X fixed costs = number of firms XI ! Activity level -- marginal cost of X $COMMODITIES: PX ! Price index for commodity X (gross of markup) CX ! Marginal cost index for commodity X (net markup) PY ! Price index for commodity Y PW ! Price index for unskilled labor PZ ! Price index for skilled labor PF ! Unit price of inputs to fixed cost PU ! Price index for welfare (expenditure function) $CONSUMERS: CONS ! Income level for consumer CONS ENTRE ! Entrepreneur (converts markup revenue to fixed cost) $AUXILIARY: XQADJ ! Quantity adjustment (positive when X>1) XPADJ ! X output subsidy rate (positive when X>1) $PROD:X s:1 O:PX Q: 80 P:1.25 A:CONS N:XPADJ M:-1 I:CX Q: 80 P:1.25 $PROD:Y s:1 O:PY Q:100 I:PW Q: 60 I:PZ Q: 40 $PROD:XI s:1 O:CX Q: 80 A:ENTRE T:0.20 I:PW Q: 32 I:PZ Q: 48 $PROD:N s:1 O:PF Q:20 I:PZ Q:12 I:PW Q: 8 $PROD:W s:1.0 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:PX Q:80 R:XQADJ $DEMAND: ENTRE D:PF Q:20 $CONSTRAINT:XQADJ XQADJ =E= (N**(1/(EP-1)))*X - X; $CONSTRAINT:XPADJ XPADJ =E= (N**(1/(EP-1))) - 1; $OFFTEXT $SYSINCLUDE mpsgeset M62 * Adjust bounds so that the auxiliary variables can take on * negative values: XQADJ.LO = -INF; XPADJ.LO = -INF; * Benchmark replication: PY.FX = 1; PX.L = 1.25; CX.L = 1.25; $INCLUDE M62.GEN SOLVE M62 USING MCP; INDEX = (N.L*CX.L**(1-EP))**(1/(1-EP)); DISPLAY INDEX; * Counterfactual: expand the size of the economy ENDOW = 2; $INCLUDE M62.GEN SOLVE M62 USING MCP; INDEX = (N.L*CX.L**(1-EP))**(1/(1-EP)); DISPLAY INDEX;