Consider a market with (inverse) demand p = 100 – 2Q. There are two fi

Consider a market with (inverse) demand p = 100 – 2Q. There are two firms in the market with constant marginal and average costs of $10.

a. Determine the Cournot equilibrium quantities and price
b. What would be the collusive (joint-profit maximizing) price and quantity?
c. Derive the deadweight loss from (i) Cournot Dupoly, (ii) Collusion, and (iii) Perfect competition in this market with the two firms.

ANSWER

a. q1 = q2 = 15
p = 100 – 2(30 ) = 40
b. 100 – 4Q = 10 Q = 22.5, q = 11.25
p = 55
c. DWL from P.C. = 0
DWL from monopoly = .5(45 – 22.5 )(55 – 10 ) = 506.25
DWL from duopoly = .5(45 – 30 )(40 – 10 ) = 225