EconS425 - Homework #4 (Due on April 8th, 2015)

EconS425 - Homework #4 (Due on April 8th, 2015)
1. Exercise 2 from Chapter 9 in Shy (page 249)
2. A monopoly with constant marginal costs m = $10 faces the inverse demand curve p = 50 – Q.
The interest rate is r = 10%. An inventor discovers a way to reduce marginal costs to m = $6
(with no additional fixed costs) and receives a permanent patent for that invention. Up to how
much is the monopoly prepared to pay for a permanent license to use the invention
(i) if it is certain that the inventor will not offer the invention to any other firm?
(ii) if it knows that the inventor may offer the invention to a potential entrant instead?
3. A government wants to stimulate research and development and must choose between two
policies to do so. The first one consists of increasing the length of the patent from 17 to 18 years,
while the relevant interest rate is projected to stay at 7%. The second policy would leave patent
length at 17 years, but reduce the interest rate from 7% to 6%. Say the inverse annual demand for
the yet-to-be invented new good is p = 100 – 2Q, is constant over the years, and marginal cost is
constant at 20. Which policy is more effective? Do you need all the information above to answer
that question?
4.
An increase in R&D induced by, say, government subsidies could result in a higher rate of
product obsolescence, with new products replacing older ones at a faster rate. How does this
“side-effect” of the subsidies affect firms’ incentives to invest in research? (Hint: distinguish
between firms with and without market power.)
5. Considers a monopolist with the following demand curve: P=390-2Q. The monopolist faces
MCM=ACM=30.
a. Solve for the profit-maximizing level of monopoly output, price, and profits.
b. Suppose a potential entrant is considering entering, but the monopolist has a cost
advantage. The potential entrant faces costs MCPE=ACPE=40. Assuming the monopolist
continues to profit-maximize, solve the residual demand curve for the entrant.
c. Assume the potential entrant follows the Cournot assumption about the monopolist’s
output. Solve for the potential entrant’s output, price, and profits in this scenario. What
are the new monopoly profits?
d. Is there a price the monopolist could charge to deter entry? Solve for the limit price and
output that will completely deter entry. What is monopoly profit at this point?
6. Consider the problem described in 5.
a. Make an extensive form of the game based on your solutions in problem 5
b. Solve for the Nash equilibrium of the game. If the monopolist threatens ahead of time to
limit price, is the threat credible? Explain
7. Let us analyze an entry-deterrence game in the automobile market where an incumbent (firm 1)
operates as a monopolist during the first period and a potential entrant (firm 2) must decide
whether or not to enter to this market in the second period. The incumbent’s costs are privately
know by the incumbent, they can be low (c1=0) or high (c1=2). The potential entrant does not
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Instructor: Ana Espinola
exactly know the cost structure of the incumbent, but it knows the probability distribution of cost
functions. Firm 2 know that the unit cost of firm 1 satisfies:
Finally, the market demand function in each period is given by p=10-Q, where Q is the aggregate
amount sold to consumers, firm 2’s unit-production cost is c2=1 and firm 2 has to pay an entry
cost of F2=9 if it enters at t=2.
a. Draw the two-period, signaling, entry-deterrence game
b. Solve the game assuming a high-cost incumbent: obtain firm 2’s expected profit. If entry
occurs in t=2, what is firm 1’s best strategy? (calculate firm 1’s profits and output level in
period 1)
c. Solve the game assuming a low-cost incumbent: obtain firm 2’s profit. Discuss the signal
firm 1 uses to deter entry.
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Instructor: Ana Espinola