Question

2. Using the results for problem 1, determine the change in consumer surplus, producer surplus, and social welfare if the cartel members decide to merge as opposed to remaining a cartel. Next, compare the consumer surplus, producer surplus, and social welfare of the cartel to Cournot equilibrium.

From part 1:

1. Assume that the domestic demand equation for the Norwegian cartel example is Q = 100 – P, marginal cost equals 4, and there are four identical domestic firms.

a. Derive the aggregate Cournot output. Answer: q = 76.8

b. Now assume that the four identical firms form a cartel with a sales agency determining the allocation of domestic sales in the same manner as in the article. The world price, R, equals 2. Determine the firms’ equilibrium capacities, number of units sold domestically, and exports given the decision rule. Answer: capacity = 48, domestic q sold = 48, exports = 0

Answer 1

Assume that the domestic demand equation for the Norwegian cartel example is Q = 100 – P, marginal cost equals 4, and there are four identical domestic firms.

a. Derive the aggregate Cournot output.

q1 = q2 = q3 = q4 = (100 - 4)/5 = 19.2 units For all firms, market quantity Q = 19.2*4 = 76.8 units

b. Now assume that the four identical firms form a cartel. The world price is R = 2. Determine the firms’ equilibrium capacities, number of units sold domestically, and exports given the decision rule.

Demand is P = 100 - Q. At R = 2, cartel does not supply any unit to the world because world price is less than MC. Hence it uses MR = MC.

MR = 100 - 2Q. MC = 4

This implies we have 100 -2Q=4

Q = 96/2 = 48 units where all units are sold in domestic economy so exports = 0.