# Entry Game With Two Pharmaceutical Analysis Paper

ECON 6555 Homework 2

Due Date: Thursday, January 22 (at the beginning of class)

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1. Consider an entry game with two pharmaceutical firms, an incumbent (I) and a

potential entrant (E). Market demand for a baldness cure is given by p = 100 – Q.

Each firm has constant marginal cost equal to \$40. If there is only one firm supplying

the market (i.e. the Incumbent), it will behave like a monopolist. If the Entrant enters,

the two firms will compete and receive profits of \$400 each. Suppose the timing of

the game is as follows:

1. The Incumbent decides whether to offer the Entrant \$450 to not enter.

2. The Entrant decides whether to enter the industry. If the Entrant enters, it forfeits

any payment from the Incumbent.

3. Active firms compete.

(a) Draw the game-tree for this problem. You will need to calculate the payoff to the

incumbent if the Entrant does not enter.

(b) Solve for the Subgame Perfect Nash Equilibrium.

Note: Pharmaceutical companies have been known to pay generic manufacturers to

not enter an industry when their patent protection expires. See:

http://blogs.wsj.com/health/2009/06/23/pay-for-delay-lawsuits-cost-consumers-35-

billion-a-year/

2. Consider a simplified version of the Solow Growth Model. Assume per capita output

is given by qt=Akt

α

. Assume depreciation, δ, is not 100 percent such that the amount of

capital available at time t+1, kt+1, is given by kt+1 = sqt + (1-δ)kt.

(a) Assume A=100, s=0.25, δ=0.5, α=0.5, and k0=100. What is the “steady state” level

of capital and output per worker? Solve for this mathematically.

(b) Using Excel, verify your answers from part (a). Include an Excel print-out with

(c) How does your answer to part (a) change if s rises to 0.5? Explain.

3. Suppose the per capita production function in period 1 is given by q1=3k1

0.5 and the per

capita production function in period 2 is given by q2=9k2

0.5.

(a) What is the change in total factor productivity (or A) between periods 1 and 2?

(b) If k1=9 and k2=16, what share of the rise in per capita income (or output) is

attributable to technical change? What share is attributable to capital accumulation?

Be sure to include a well-labeled diagram to answer parts (a) and (b)!

Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2013), “The Next

(a) Calculate k and q for 1950-2011. Note that you have K and Q.

(b) Assume that α (the capital share) is always equal to 0.33. Calculate ΔA/A and A for

1950-2011 using Excel.(c) Graph the time series of A for 1950-2011.

(d) Calculate qNTC (q without technical change) for 2011. What share of the difference

between q1950 and q2011 is due to increases in k and what share is due to increase in A?

Note: print the full table of your output for parts (a) and (b).

(e) What might explain the slow-down in the 1970s and subsequent rise in the 1980s

and 1990s?

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