$TITLE Model M35: Closed 2x2 economy with public good using Samuelson rule SCALAR VG1 Preference index for public goods for consumer 1 /1/; POSITIVE VARIABLES X ! Activity level for sector X, Y ! Activity level for sector Y, W1 ! Activity level for sector W1 (Hicksian welfare index), W2 ! Activity level for sector W2 (Hicksian welfare index), G ! Activity level for government sector, 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, PW1 ! Price index for welfare 1(expenditure function), PW2 ! Price index for welfare 2(expenditure function), PG1 ! Private valuation of the public good (consumer 1), PG2 ! Private valuation of the public good (consumer 2), PG ! Private valuation of the public good GOVT ! Budget restriction for government, CONS1 ! Income definition for CONS1, CONS2 ! Income definition for CONS2, LGP ! Level of government provision, TAX ! Uniform value-added tax rate; EQUATIONS PRF_X Zero profit for sector X PRF_Y Zero profit for sector Y PRF_W1 Zero profit for sector W1 (Hicksian welfare index) PRF_W2 Zero profit for sector W2 (Hicksian welfare index) PRF_G Zero profit in government sector MKT_X Supply-demand balance for commodity X MKT_Y Supply-demand balance for commodity Y MKT_G Supply-demand balance for commodity G MKT_L Supply-demand balance for primary factor L MKT_K Supply-demand balance for primary factor K MKT_W1 Supply-demand balance for aggregate demand consumer 1 MKT_W2 Supply-demand balance for aggregate demand consumer 2 MKT_G1 Private valuation of the public good (consumer 1) MKT_G2 Private valuation of the public good (consumer 2) I_G Budget restiktion for government I_CONS1 Income definition for CONS1 I_CONS2 Income definition for CONS2 A_LGP Auxiliary for government provision, A_TAX Auxiliary for government provision; * Zero profit conditions: PRF_X.. 100 * (PL**(5*1.25/10) * PK**(3*1.25/10))*(1+TAX)/1.25 =G= 100 * PX; PRF_Y.. 100 * (PL**(5*1.25/10) * PK**(3*1.25/10))*(1+TAX)/1.25 =G= 100 * PY; PRF_G.. 50 * (PL**0.5 * PK**0.5 )*(1+TAX)/1.25 =G= 50 * PG; PRF_W1.. PX**( 30 /( 100 + VG1 * 50 * PG1)) * PY**( 70 /( 100 + VG1 * 50 * PG1)) * (PG1/0.5)**( 50 * VG1 * PG1 / ( 100 + VG1 * 50 * PG1) ) =E= PW1 * ( 125/ (100 + VG1 * 0.5 *50) ) ; PRF_W2.. 125 * PX**(70/125) * PY**(30/125) * (PG2/0.5)**(25/125) =E= 125 * PW2; * Market clearing conditions: MKT_X.. 100 * X =G= 70 * W1 * PW1/PX * ( 125/ (100 + VG1 * 0.5 *50) )+ 30 * W2 * PW2/PX ; MKT_Y.. 100 * Y =G= 30 * W1 * PW1/PY * ( 125/ (100 + VG1 * 0.5 *50) )+ 70 * W2 * PW2/PY; MKT_G.. 50 * G =G= GOVT/ PG; MKT_W1.. 125 * W1 =G= CONS1 / PW1; MKT_W2.. 125 * W2 =G= CONS2 / PW2; MKT_L.. 50 + 50 =G= (50 * X * PX + 30 * Y * PY + 20 * G * PG) * 1.25/(PL*(1+TAX)); MKT_K.. 50 + 50 =G= (30 * X * PX + 50 * Y * PY + 20 * G * PG) * 1.25/(PK*(1+TAX)); MKT_G1.. 50 * LGP =G= 50 * VG1 * W1 * PW1 * ( 125/ (100 + VG1 * 0.5 *50) )* 0.5/PG1; MKT_G2.. 50 * LGP =G= 50 * W2 * PW2 * 0.5/PG2; * Income constraints: I_G.. GOVT =G= TAX * PL * (X*50 * PX + Y*30 * PY + G*20 * PG) * 1.25/(PL*(1+TAX)) + TAX * PK * (X*30 * PX + Y*50 * PY + G*20 * PG) * 1.25/(PK*(1+TAX)); I_CONS1.. CONS1 =E= 50*PL + 50*PK + 50*LGP*PG1; I_CONS2.. CONS2 =E= 50*PL + 50*PK + 50*LGP*PG2; * Auxiliary constraints: A_LGP.. LGP =E= G; A_TAX.. PG =E= PG1 + PG2; MODEL ALGEBRAIC /PRF_X.X, PRF_Y.Y, PRF_W1.W1, PRF_W2.W2, PRF_G.G, MKT_X.PX, MKT_Y.PY, MKT_L.PL, MKT_K.PK, MKT_W1.PW1, MKT_W2.PW2, MKT_G.PG, MKT_G1.PG1, MKT_G2.PG2, I_G.GOVT, I_CONS1.CONS1, I_CONS2.CONS2, A_LGP.LGP, A_TAX.TAX /; * Check the benchmark: X.L =1; Y.L =1; W1.L =1; W2.L =1; G.L =1; PL.FX =1; PX.L =1; PY.L =1; PK.L =1; PG.L =1; PW1.L =1; PW2.L =1; CONS1.L =125; CONS2.L =125; GOVT.L =50; TAX.L =0.25; LGP.L =1; PG1.L =0.5; PG2.L =0.5; ALGEBRAIC.ITERLIM = 0; SOLVE ALGEBRAIC USING MCP; * What happens to consumer 2 welfare if consumer 1 decides * she would like more public output: ALGEBRAIC.ITERLIM = 2000; VG1 = 2; SOLVE ALGEBRAIC USING MCP;