$TITLE Model M24: Introduces the use of specific factors SCALAR TX Ad-valorem tax rate for X sector inputs /0/; POSITIVE VARIABLES X ! Activity level for sector X, Y ! Activity level for sector Y, W ! Activity level for sector W (Hicksian welfare index), PX ! Price index for commodity X, PY ! Price index for commodity Y, PL ! Price index for primary factor L, PK ! Price index for primary factor K, PKY ! Price index for sector-specific input for sector X, PKX ! Price index for sector-specific input for sector Y, 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_W Zero profit for sector W (Hicksian welfare index) 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_K Supply-demand balance for primary factor K MKT_KX Supply-demand balance for sector-specific input for sector X MKT_KY Supply-demand balance for sector-specific input for sector Y MKT_W Supply-demand balance for aggregate demand I_CONS Income definition for CONS; * Zero profit conditions: PRF_X.. 100 * PL**0.25 * PKX**0.25 * PK**0.5 * (1+TX) =G= 100 * PX; PRF_Y.. 100 * PL**0.75 * PKY**0.10 * PK**0.15 =G= 100 * PY; PRF_W.. 200 * PX**0.5 * PY**0.5 =E= 200 * PW; * Market clearing conditions: MKT_X.. 100 * X =G= 100 * W * PW/PX; MKT_Y.. 100 * Y =G= 100 * W * PW/PY; MKT_W.. 200 * W =G= CONS / PW; MKT_L.. 100 =G= 25 * X * PX/(PL*(1+TX)) + 75 * Y * PY/ PL; MKT_K.. 65 =G= 50 * X * PX/(PK*(1+TX)) + 15 * Y * PY/PK; MKT_KY.. 10 =G= 10 * Y * PY/ PKY; MKT_KX.. 25 =G= 25 * X * PX/(PKX*(1+TX)); * Income constraints: I_CONS.. CONS =E= 100 * PL + 10 * PKY + 25 * PKX + 65 * PK + 25 * X * PX/(PL*(1+TX)) * PL * TX + 50 * X * PX/(PK*(1+TX)) * PK * TX + 25 * X * PX/(PKX*(1+TX))* PKX *TX; MODEL ALGEBRAIC /PRF_X.X, PRF_Y.Y, PRF_W.W, MKT_X.PX, MKT_Y.PY, MKT_L.PL, MKT_KY.PKY, MKT_KX.PKX, MKT_K.PK, MKT_W.PW, I_CONS.CONS /; * Check the benchmark: X.L =1; Y.L =1; W.L =1; PL.FX =1; PX.L =1; PY.L =1; PKY.L =1; PKX.L =1; PK.L =1; PW.L =1; CONS.L =200; TX = 0; ALGEBRAIC.ITERLIM = 0; SOLVE ALGEBRAIC USING MCP; TX = 0.5; ALGEBRAIC.ITERLIM = 1000; SOLVE ALGEBRAIC USING MCP;