Game Theory

1 Two sides of the same coin A monopolist faces demand given by p(Q) = 24 − 2Q. Its costs are given by C(Q) = Q2 .

a. Express the firm’s profits as a function of Q.

b. Suppose that the monopolist chooses quantity. Solve for the monopoly quantity Qm. Then solve for the monopoly price pm.

c. Now suppose that the firm chooses price.

Express the firm’s profits as a function of p. Solve for the firm’s optimal price pm, then solve for the associated quantity Qm. (Hint: you should find the same price and quantity in parts b and c.)

d. Draw a clearly labeled graph representing this market.

Be sure to draw the demand curve, the marginal cost curve, and the marginal revenue curve. Label the price and quantity axes at each point where these curves intersect each other or the axes.

Finally, label the monopoly solution (Qm, pm).

e. Using your answers to the previous parts, calculate the producer surplus, consumer surplus, and deadweight loss. 2 Remember to stretch The Davis Turkey Trot is an annual race event held just before Thanksgiving. (It’s fun!)

a. Demand to register in the 5K race is given by p(Q) = 80− 1 2Q.

Compute the elasticity of demand as a function of Q, simplifying your answer as much as possible. For what value of Q is demand perfectly inelastic? For what value of Q is demand unit elastic?

b. Demand for running shoes is given by p(Q) = Q− 1 2 .

Compute the elasticity of demand. (Hint: this is a special function for which the elasticity is constant.) If Fleet Feet Sports has a monopoly on the sale of running shoes, what price markup will it choose?

Copyright c 2018 by Brendan M. Price. All rights reserved. 1 3 Blockbuster drugs Suppose that GlaxoSmithKline (GSK) has just acquired an exclusive right to develop a promising new antidepressant.

Developing the drug would cost GSK $4 billion up front, but once it is developed, the drug can be produced at zero marginal cost. GSK’s financial analysts estimate that the demand for the new drug (in dollars) would be p(Q) = 120 − 1 1,000,000Q, where Q is the number of prescriptions sold.

a.If GSK develops the drug, how many prescriptions will it decide to sell (Qm), and what price will it charge (pm)?

b. Given your answers to part a, is it privately optimal (i.e., profit-maximizing) for GSK to develop the drug? Justify your answer.

c. Consumers would benefit from the availability of the new drug.

Given that the drug would create consumer surplus, would society as a whole benefit from GSK developing the drug (assuming that, after, doing so, GSK charges pm)? Justify your answer.

Last Updated on March 26, 2019

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