$TITLE M3-6.GMS: Introduces a labor supply or labor/leisure activity $ONTEXT Activity T transforms leisure into labor supply Initially, the consumer has 200 units of leisure and supplies 100 to the market, retaining 100 as leisure X, Y and Leisure are all Cobb-Douglas substitutes Production Sectors Consumers Markets | A B W T | CONS --------------------------------------------------------- PX | 100 -100 | PY | 100 -100 | PW | 300 | -300 PLS | -40 -60 100 | PL | -100 -100 | 200 PK | -60 -40 | 100 --------------------------------------------------------- PL will denote the CONSUMER (HOUSEHOLD) price of labor PLS will denote the PRODUCER price or COST of labor to the firms $OFFTEXT PARAMETERS TL ad-valorem tax rate on labor WELFARE true welfare - including the value of leisure REALCONS observed market value of consumption of X and Y; TL = 0; NONNEGATIVE VARIABLES X Activity level for sector X Y Activity level for sector Y T Labor supply (transforms leisure to labor) W Activity level for sector W PX Price index for commodity X PY Price index for commodity Y PL Price index for primary factor L (household price) PLS Price index for labor supply (producer cost) PK Price index for primary factor K PW Price index for welfare (expenditure function) CONS Income definition for CONS; EQUATIONS PRF_X Zero profit for sector X PRF_Y Zero profit for sector Y PRF_T Zero profit for sector T PRF_W Zero profit for sector W MKT_X Supply-demand balance for commodity X MKT_Y Supply-demand balance for commodity Y MKT_L Supply-demand balance for primary factor L MKT_LS Supply-demand balance for Leisure MKT_K Supply-demand balance for primary factor K MKT_W Supply-demand balance for aggregate demand I_CONS Income definition for CONS; * Zero profit conditions: PRF_X.. 100*(PLS**0.4 * PK**0.6) =G= 100*PX; PRF_Y.. 100*(PLS**0.6 * PK**0.4) =G= 100*PY; PRF_T.. 100*(PL *(1+TL)) =G= 100 * PLS; PRF_W.. 300*(PY**(1/3) * PX**(1/3)) * PL**(1/3) =G= 300 * PW; * Market clearing conditions: MKT_X.. 100*X =G= 300*W*(1/3)*PW /PX; MKT_Y.. 100*Y =G= 300*W*(1/3)*PW /PY; MKT_W.. 300*W =G= CONS/PW; MKT_L.. 200 =G= 100*T + 300*W*(1/3)*PW/PL; MKT_LS.. 100*T =G= 40*X*PX/PLS + 60*Y*PY/PLS; MKT_K.. 100 =G= 60*X*PX/PK + 40*Y*PY/PK; * Income constraints: I_CONS.. CONS =E= 200*PL + 100*PK + TL*100*T*PL; MODEL LABLEIS /PRF_X.X, PRF_Y.Y, PRF_T.T, PRF_W.W, MKT_X.PX, MKT_Y.PY, MKT_L.PL, MKT_LS.PLS, MKT_K.PK, MKT_W.PW, I_CONS.CONS /; X.L =1; Y.L =1; W.L =1; T.L =1; PL.L =1; PLS.L =1; PX.L =1; PY.L =1; PK.L =1; PW.FX =1; CONS.L =300; TL = 0; LABLEIS.ITERLIM = 0; SOLVE LABLEIS USING MCP; LABLEIS.ITERLIM = 1000; SOLVE LABLEIS USING MCP; WELFARE = W.L; REALCONS = (PX.L*X.L*100 + PY.L*Y.L*100)/ (PX.L**0.5*PY.L**0.5*200); DISPLAY WELFARE, REALCONS; TL = 0.5; SOLVE LABLEIS USING MCP; WELFARE = W.L; REALCONS = (PX.L*X.L*100 + PY.L*Y.L*100)/ (PX.L**0.5*PY.L**0.5*200); DISPLAY WELFARE, REALCONS;