Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a, b > 0(a) Calculate the profit-maximizing quantity-price combination and for a monopolist. (b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities and for their identical products simultaneously. Also compute market output and market price. (c) Calculate the perfectly competitive equilibrium price and market output. (d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute the Nash equilibrium quantities as functions of n. Also compute market output and market price. (e) Verify (i) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n = 1; (ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2; (iii) that letting n approach infinity yields the same market price and output as in part (c). 4. Suppose that firms' marginal and average costs are constant and equal to c and that inversemarket demand is given by P = a - bQ. where a, b>0(a) Calculate the profit-maximizing quantity-price combination Q" and P" for a monopolist.(b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities gand g2for their identical products simultaneously. Also compute market output and marketprice.(c) Calculate the perfectly competitive equilibrium price and market output.(d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Computethe Nash equilibrium quantities as functions of n. Also compute market output and market price.(e) Verify (1) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n= 1;(ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2;(iii) that letting n approach infinity yields the same market price and output as in part (c).

"Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Answered: Suppose that firms’ marginal and…

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter15: Imperfect Competition

Section: Chapter Questions

Problem 15.2P

See similar textbooks

Related questions

Question

Suppose that firms’ marginal and average costs are constant and equal to c and that inverse market demand is given by P = a – bQ, where a, b > 0

(a) Calculate the profit-maximizing quantity-price combination and for a monopolist.

(b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities and for their identical products simultaneously. Also compute market output and market price.

(d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute the Nash equilibrium quantities as functions of n. Also compute market output and market price.

(e) Verify (i) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n = 1;

(ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2;

(iii) that letting n approach infinity yields the same market price and output as in part (c).

4. Suppose that firms' marginal and average costs are constant and equal to c and that inverse
market demand is given by P = a - bQ. where a, b>0
(a) Calculate the profit-maximizing quantity-price combination Q" and P" for a monopolist.
(b) Calculate the Nash equilibrium quantities for Cournot duopolists, which choose quantities g
and g2
for their identical products simultaneously. Also compute market output and market
price.
(c) Calculate the perfectly competitive equilibrium price and market output.
(d) Suppose now that there are n identical firms in a Cournot model (oligopoly). Compute
the Nash equilibrium quantities as functions of n. Also compute market output and market price.
(e) Verify (1) that the monopoly outcome from part (a) can be reproduced in part (d) by setting n= 1;
(ii) that the duopoly outcome from part (b) can be reproduced in part (d) by setting n = 2;
(iii) that letting n approach infinity yields the same market price and output as in part (c).

Definition Video Definition Point where the demand and supply curves intersect. At the equilibrium price the quantity supplied of a good is equal to the quantity demanded. When the market is not in equilibrium, market surplus or market shortage occurs. The region that is above the price equilibrium indicates market surplus and the region below the price equilibrium indicates market shortage. Video

Expert Solution