Question

Suppose a monopoly with constant marginal cost of 10 sells its product to identical consumers. Each consumer has an inverse demand curve given by P = 210 − 10Q.

(a) Find the price and quantity the monopolist chooses if it can only set one price, and it can not use a two-part tariff. What is the monopolist’s profit on each consumer?

(b) Now suppose the monopolist can use a two-part tariff. What is the profit maximizing choice of the fixed fee (f) and the per unit charge (p)? How much profit does the monopoly make on each consumer?

(c) Would your answer to part (b) change if the monopoly used perfect price discrimination instead of a two-part tariff?

(d) Suppose we relax the assumption that consumers are identical. Use words to explain what happens to the choice of F and P with a single two-part tariff as consumers’ preferences for the good diverge.

Answer 1

a).

Consider the given problem here the market demand function is, => P = 210 – 10*q, => MR = 210 – 20*q, and MC=10. Now, at the equilibrium the MR must be equal to MC.

=> MR = MC, => 210 – 20*q = 10, => q = 200/20 = 10, => q=10. The demand function is given by.

=> P = 210 – 10*q = 210 – 10*10 = 110, => P = 110. So, the profit maximizing price and quantity are “P=$110” and “q=10”.

Now, the maximum profit of the monopolist is “A = P*q – MC*q = (P-MC)*q = (110-10)*10 = $1,000 on each consumer.

b).

Now, let’s assume the monopolist can use two-part tariff, => the monopolist will charge “F=fixed fee” and the unit price for each unit purchased. Here all the consumers are same types, => they having identical demand schedule, => the monopolist will charge per unit price exactly equal to MC and the F=fixed fee exactly equal to the size of the consumer surplus.

=> P=MC, => 210 – 10*q = 10, => q = 200/10 = 20, => P=10 and q=20.

Now the fixed fee is given by, => F = 0.5*q*(210-10) = 0.5*20*200 = $2000, => F = $2,000.

The profit of the monopolist is, => A = Fixed Fee + P*q = 2,000 + 10*20 = $2,200.

c).

In perfect price discrimination a monopolist will charge different price to different consumer depending on their willing ness to pay. Here all consumers are identical having demand schedule, “P=210-10*q”. So, here the monopolist will supply output to each consumer by the condition P=MC.

=> P = MC, => 210 – 10*q = 10, => q = 20. The total willingness to pay of each consumer is given by.

=> TWP = 0.5*(210-MC)*q + MC*q = 0.5*200*20 + 10*20 = 2000 + 200 = 2,200, => TWP = 2,200.

So, the monopolist will charge “2200” and will supply 20 units of output to each consumer.

d).

If we relax the assumption of identical consumers, => each and every consumer having different demand schedule and willingness to pay, => to maximize profit the monopolist have to consider all types of consumer in to account and decide the optimum per unit price (P) that maximize the total profit. The “Fixed Fee” will be the consumer surplus of the lower types of consumer having lower willingness to pay.

So, here each consumer will pay “P > MC” for each unit of good consumed and a fixed fee (F).