1 Monopoly profit maximization

Pfeitzer is a monopolist for a new drug that makes people feel thinner. It is producing its wonderdrug according to the following production function:

q = f(K,L) = 2K^1/4L^1/4

Input prices for labor L and capital K are w = 8 and r = 2, respectively. The optimal capital-labor ratio is hence K/L = 4 and labor as a function of output is L(q) = q²/8 and K(q) = q²/2. [This is just a reminder of how the cost function can be derived.] Total production cost as a functionof output is therefore c(q) = wL(q) + rK(q) = 2q². On top of that, the firm has incurred costs of 250 for research and development (which have already been paid, so it is a sunk cost) and pays an additional 2 per unit of output sold for advertising.1 The total cost function is thus

C(q) = 250 + 2q + 2q².

The incerse demand function is

p(q) = 66 - 2q.

(a) What is marginal cost and marginal revenue?

(b) What is the optimal price and quantity the monopolist should charge / sell?

(c) What is the monopolist's profit? Should the firm shut down in the short or long run?

2 Market Power

Consider the same firm as in the problem above, the Pfeitzer Corporation, for sub-questions (a) and (b) below.

(a) What is the elasticity of demand at the monopoly's quantity?

(b) What percentage of the price is due to costs and what is due to markup?

(c) [Remember: do not refer to the Pfeizer Corporation anymore] Figure 1 below shows the demand and cost curves facing a monopoly. If the firm is a profit maximizer, what will its Lerner index be?

3 Natural Monopoly

The average cost for a typical electric-power-production firm is AC = 100 - 10Q + Q2 where Q is measured in billion kilowatt hours per day. At the current regulated price, consumers demand 4 billion kilowatt hours per day. Is this market a natural monopoly? If demand increases to 10 billion kilowatt hours, is this market a natural monopoly? Explain.

4 Welfare Consequences

(a) Figure 2 below shows the demand and marginal cost curves for a monopoly. What is the deadweight loss (DWL) of this monopoly? What does this DWL represent?

(b) Can you identify the consumer surplus in Figure 2? Explain.

(c) [Do not refer to figure 2 any longer.] In general, there is a DWL associated with monopoly because

i. Consumers are willing to pay more for the last unit of output than it cost to produce.

ii. The cost of the last unit produced is more than consumers are willing to pay for it.

iii. The producer surplus is larger than in a competitive market.

iv. None of the above.

           figure 1

                    Figure 1