$TITLE Model M28: two households with different preferences and endowments 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, WA ! Activity level for sector WA (Hicksian welfare index), WB ! Activity level for sector WB (Hicksian welfare index), PX ! Price index for commodity X, PY ! Price index for commodity Y, PK ! Price index for primary factor K, PL ! Price index for primary factor L, PWA ! Price index for welfare A(expenditure function), PWB ! Price index for welfare B(expenditure function), CONSA ! Income definition for CONSA, CONSB ! Income definition for CONSB; EQUATIONS PRF_X Zero profit for sector X PRF_Y Zero profit for sector Y PRF_WA Zero profit for sector WA (Hicksian welfare index) PRF_WB Zero profit for sector WB (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_WA Supply-demand balance for aggregate demand consumer A MKT_WB Supply-demand balance for aggregate demand consumer B I_CONSA Income definition for CONSA I_CONSB Income definition for CONSB; * Zero profit conditions: PRF_X.. 100 * (PL**0.25 * PK**0.75) * (1+2*TX) =G= 100 * PX; PRF_Y.. 100 * (PL**0.75 * PK**0.25) =G= 100 * PY; PRF_WA.. 100 * PX**0.4 * PY**0.6 =G= 100 * PWA; PRF_WB.. 100 * PX**0.6 * PY**0.4 =G= 100 * PWB; * Market clearing conditions: MKT_X.. 100 * X =G= 40 * WA * PWA/PX + 60 * WB * PWB/PX; MKT_Y.. 100 * Y =G= 60 * WA * PWA/PY + 40 * WB * PWB/PY; MKT_WA.. 100 * WA =G= CONSA / PWA; MKT_WB.. 100 * WB =G= CONSB / PWB; MKT_L.. 90 + 10 =G= 25 * X * PX/(PL*(1+2*TX)) + 75 * Y * PY/PL; MKT_K.. 10 + 90 =G= 75 * X * PX/(PK*(1+2*TX)) + 25 * Y * PY/PK; * Income constraints: I_CONSA.. CONSA =E= 90*PL + 10*PK + TX * 100 * X * PX/(1+2*TX); I_CONSB.. CONSB =E= 10*PL + 90*PK + TX * 100 * X * PX/(1+2*TX); MODEL ALGEBRAIC /PRF_X.X, PRF_Y.Y, PRF_WA.WA, PRF_WB.WB, MKT_X.PX, MKT_Y.PY, MKT_L.PL, MKT_K.PK, MKT_WA.PWA, MKT_WB.PWB, I_CONSA.CONSA, I_CONSB.CONSB /; * Check the benchmark: X.L =1; Y.L =1; WA.L =1; WB.L =1; PL.FX =1; PX.L =1; PY.L =1; PK.L =1; PWA.L =1; PWB.L =1; CONSA.L =100; CONSB.L =100; TX =0; ALGEBRAIC.ITERLIM = 0; SOLVE ALGEBRAIC USING MCP; ALGEBRAIC.ITERLIM = 2000; TX =0.25; SOLVE ALGEBRAIC USING MCP;