Question

Consider a market with demand and cost curves characterized by Q(P) = 17 - P and

C = 5Q respectively. The market is served by 5 identical firms which operate as a Cournot Oligopoly. Find the total quantity, price, profit, and consumer surplus and deadweight loss in this market.

Answer 1

The total market demand is: Q(P) = 17 - P, or P = 17 - Q.

The profit is maximized at MR = MC, so:

MR = TR'(Q) = 17 - 2Q,

MC = TC'(Q) = 5,

17 - 2Q = 5,

Q = 6,

P = 17 - 6 = 11.

Total profit is:

$TP = TR - TC = 11×6 - 5×6 = 36.$

Consumer surplus is:

$CS = 0.5×(17 - 11)×6 = 18.$

In competitive equilibrium MC = D, so:

17 - Q = 5,

Q = 12, P = 17 - 12 = 5.

The deadweight loss is:

$DWL = 0.5×(11 - 5)×(12 - 6) = 18.$