$TITLE: M2-1.GMS introductory model using MCP * simple supply and demand model (partial equilibrium) PARAMETERS A intercept of supply on the P axis (MC at Q = 0) B change in MC in response to Q - this is dP over dQ C intercept of demand on the Q axis (demand at P = 0) D response of demand to changes in price - dQ over dP TAX a tax rate used later for experiments; A = 2; C = 6; B = 1; D = -1; NONNEGATIVE VARIABLES P price of good X X quantity of good X; EQUATIONS SUPPLY supply relationship (marginal cost ge price) DEMAND quantity demanded as a function of price; SUPPLY.. A + B*X =G= P; DEMAND.. X =G= C + D*P; MODEL EQUIL /SUPPLY.X, DEMAND.P/; OPTION MCP = PATH; SOLVE EQUIL USING MCP; * counter factual 1: shift the supply curve (marginal cost) up/left A = 7; SOLVE EQUIL USING MCP; * country factual 2: shift the supply curve (marginal cost) down/right A = -7; SOLVE EQUIL USING MCP; * exercise 1: extract economic information from the solution PARAMETERS CONSPRICE consumer price PRODPRICE producer price (equal to marginal cost) TAXREV tax revenue (note tax base is producer price) CONSURP1 consumer surplus with no tax CONSURP2 consumer surplus with 25% tax PROSURP1 producer "surplus" with no tax PROSURP2 producer "surplus" with 25% tax DWL net loss from the tax; EQUATIONS SUPPLY2; SUPPLY2.. (A + B*X)*(1+TAX) =G= P; MODEL EQUIL2 /SUPPLY2.X, DEMAND.P/; A = 2; TAX = 0; SOLVE EQUIL2 USING MCP; CONSURP1 = (-C/D - P.L)*X.L/2; PROSURP1 = (P.L/(1+TAX) - A)*X.L/2; TAX = 0.25; SOLVE EQUIL2 USING MCP; CONSURP2 = (-C/D - P.L)*X.L/2; PROSURP2 = (P.L/(1+TAX) - A)*X.L/2; CONSPRICE = P.L; PRODPRICE = P.L/(1+TAX); TAXREV = PRODPRICE*TAX*X.L; DISPLAY CONSPRICE, PRODPRICE, TAXREV; DWL = CONSURP1 + PROSURP1 - (CONSURP2 + PROSURP2 + TAXREV); DISPLAY CONSURP1, PROSURP1, CONSURP2, PROSURP2, TAXREV, DWL; *exercise 2, mismatch the complementary variables TAX = 0; MODEL EQUIL3 /SUPPLY.P, DEMAND.X/; SOLVE EQUIL3 USING MCP; P.L = 0; X.L = 6; A = 7; SOLVE EQUIL3 USING MCP; A = -7; SOLVE EQUIL3 USING MCP;