$TITLE Model M23: Introduces joint production SCALAR TA Ad-valorem tax rate for X sector inputs /0/; POSITIVE VARIABLES A ! Activity level for Sector A, B ! Activity level for Sector B, 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, PW ! Price index for welfare (expenditure function), CONS ! Income definition for CONS; EQUATIONS PRF_A Zero profit for sector A PRF_B Zero profit for sector B 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 MKT_W Supply-demand balance for aggregate demand I_CONS Income definition for CONS; * Write the profit constraints as inequalities -- the tax can cause sector A to shut down completely: PRF_A.. 100 * PL**0.4 * PK**0.6 * (1+TA) =G= 100 * (0.8 * PX**(1+2.0) + 0.2 * PY**(1+2.0))**(1/(1+2.0)); PRF_B.. 100 * PL**0.6 * PK**0.4 =G= 100 * (0.2 * PX**(1+1.5) + 0.8 * PY**(1+1.5))**(1/(1+1.5)); PRF_W.. 200 * PX**0.5 * PY**0.5 =E= 200 * PW; MKT_X.. 80 * A * (PX/(0.8*PX**(1+2.0)+0.2*PY**(1+2.0))**(1/(1+2.0)))**2 + 20 * B * (PX/(0.2*PX**(1+1.5)+0.8*PY**(1+1.5))**(1/(1+1.5)))**1.5 =E= 100 * W * PX**0.5 * PY**0.5 / PX; MKT_Y.. 20 * A * (PY/(0.8*PX**(1+2.0)+0.2*PY**(1+2.0))**(1/(1+2.0)))**2.0 + 80 * B * (PY/(0.2*PX**(1+1.5)+0.8*PY**(1+1.5))**(1/(1+1.5)))**1.5 =E= 100 * W * PX**0.5 * PY**0.5 / PY; MKT_W.. 200 * W =E= CONS / PW; MKT_L.. 100 =E= 40 * A * PL**0.4 * PK**0.6 / PL + 60 * B * PL**0.6 * PK**0.4 / PL; MKT_K.. 100 =E= 60 * A * PL**0.4 * PK**0.6 / PK + 40 * B * PL**0.6 * PK**0.4 / PK; I_CONS.. CONS =E= 100*PL + 100*PK + TA*100*A*PL**0.4*PK**0.6; MODEL ALGEBRAIC /PRF_A.A, PRF_B.B, PRF_W.W, MKT_X.PX, MKT_Y.PY, MKT_L.PL, MKT_K.PK, MKT_W.PW, I_CONS.CONS /; * Check the benchmark: A.L =1; B.L =1; W.L =1; PX.L =1; PY.L =1; PL.L =1; PK.L =1; PW.FX =1; CONS.L =200; TA = 0; ALGEBRAIC.ITERLIM = 0; SOLVE ALGEBRAIC USING MCP; * Solve the same counterfactuals: TA = 0.10; ALGEBRAIC.ITERLIM = 1000; SOLVE ALGEBRAIC USING MCP; TA = 1.00; SOLVE ALGEBRAIC USING MCP; * ----------------------------------------------------------------- * Excercise: Revise the model structure to represent an * infinite elasticity of transformation in sector * A. You will need to rewrite the model with * two sectors A1 and A2. These will have identical * cost structure, one producing good X and the * other producing good Y. * -----------------------------------------------------------------