Question

Let demand for car batteries be such that Q= 100-2p. Assume constant marginal costs of 15. Compute the equilibrium price, quantity, consumer surplus, producer surplus and if relevant deadweight loss for:

1. Two firms engaged in Cournot Competition.

2. Two firms engaged in Bertrand competition.

Answer 1

First consider the case of Cournot competition. Demand is P = 50 - 0.5Q. Here each firm produces (50 - 15)/(3*0.5) = 23.33 units. Then the market price is 50 - 0.5*(23.33 + 23.33) = $26.67 per unit. Consumer surplus is 0.5*(50 - 26.67)*(23.33*2) = $544. Producer surplus to each firm = (26.67 - 15)*23.33 = $272. Deadweight loss = 0.5*(26.67 - 15)*(30 - 23.33) = $39.

Now consider the Bertrand competition for identical goods. Price is equal to marginal cost so price is $15 per unit. Market quantity is 100 - 2*15 = 70 units and each firm produces 35 units. Consumer surplus is 0.5*(50 - 15)*70 = $1225 and producer surplus is $0. Also deadweight loss is 0 since competitive output is produced.