Question

Biwei’s firm with market power faces a demand curve for its product of P=100–10Q, which is also the firm’s average revenue curve. The corresponding marginal revenue curve is MR=100-20Q. Assume that the firm faces a marginal cost curve of MC=10+10Q. (20 points)

1) If the firm cannot price-discriminate, what is the profit-maximizing level of output and price?

2) If the firm cannot price-discriminate, what are the levels of consumer and producer surplus in the market, assuming the firm maximizes its profit? Calculate the deadweight loss from market power.

3) If the firm has the ability to practice perfect price discrimination, what is the firm’s output?

4) If the firm practices perfect price discrimination (fully extract consumer surplus according to their marginal use values), what are the levels of consumer and producer surplus? What is the deadweight loss from market power?

Answer 1

Demand is P = 100 - 10Q and MR = 100 - 20Q. Also MC = 10 + 10Q

1) If the firm cannot price-discriminate, its profit-maximizing level of output and price are determined using MR = MC. This gives Quantity at 100 - 20Q = 10 + 10Q or Q = 90/30 = 3 units and Price P = 100 - 10*3 = $70 per unit.

2) If the firm cannot price-discriminate, Consumer surplus is 0.5*(100 - 70)*3 = $90 and producer surplus = 0.5*(70 - 10 + 70 - 40)*3 = $135. Deadweight loss = 0.5*(70 - 40)*(4.5 - 3) = $22.50

3) If the firm has the ability to practice perfect price discrimination, it will charge each consumer his reservation price so that P = MC is used. Hence the quatity supplied is 100 - 10Q = 10 + 10Q or Q = 90/20 = 4.5 units

4) Consumer surplus is extracted entirely so it is 0. Producer surplus = 0.5*(100 - 10)*4.5 = $202.50. There is no deadweight loss