$title Oligopolistic Competition - Examples from MP (OLIGOMCP,SEQ=133) * * References: * * Murphy F H, H.D. Sherali and A.L.Soyster "A mathematical * programming approach for determining oligopolistic market * equilibrium" Mathematical Programming 24 (1982) 92-106. * * Harker P T, "Oligopolistic equilibrium", Mathematical * Programming 30 (1984) 105-111 (NB: The cost function given * in this paper has a typo which has been corrected here.) * SETS F FIRMS /F1*F5/; * F(Q) = C Q + BETA/(BETA+1) L^(-1/BETA) Q^(BETA+1)/BETA * F'(Q) = C + (Q/L)^(1/BETA) TABLE DATA(F,*) COST FUNCTION DATA C L BETA F1 10 5 1.2 F2 8 5 1.1 F3 6 5 1.0 F4 4 5 0.9 F5 2 5 0.8 PARAMETER C(F), L(F), BETA(F); C(F) = DATA(F,"C"); L(F) = DATA(F,"L"); BETA(F) = DATA(F,"BETA"); POSITIVE VARIABLES P PRICE, Q(F) SUPPLY; EQUATIONS DEMAND SUPPLY - DEMAND BALANCE, PROFIT(F) NASH FIRST ORDER CONDITION; DEMAND.. SUM(F, Q(F)) =G= 5000 * P**(-1.1); PROFIT(F).. C(F) + (Q(F)/L(F))**(1/BETA(F)) =G= P - Q(F) * P**2.1 / 5500; MODEL OLIGOP /DEMAND.P, PROFIT.Q/; * INITIAL GUESS: Q.L(F) = 10; P.L = (5000/SUM(F, Q.L(F)))**(1/1.1); SOLVE OLIGOP USING MCP;