IO Field exam, January 2007
Answer two of the following three questions. If you need to make additional assumptions, do so
but comment on why you need to and the reasonableness of the assumptions.
I. Describe at least two different empirical approaches to estimate the relationship between
the number of firms in an industry and market power (defined by the mark-up of price
over marginal cost). For each approach, discuss the data requirements and the possible
sources of bias in the estimates of market power.
II. Two firms, indexed by n, compete against each other à la Hotelling. Specifically,
suppose firm 0 is located at 0 on the linear city, firm 1 is located at 1 on the linear city,
and a unit mass of consumers are located uniformly along the interval from 0 to 1. The
firm locations are fixed. Consumers buy at most one unit of the good that these two firms
sell. A consumer located at x has a value for the good sold by firm 0 of v – tx and she has
a value for the good sold by firm 1 of v – t(1-x). Assume v > 0, t > 0, and denote the cost
of producing the good as c, where v > c 0. The timing is that the firms announce their
prices simultaneously and, then, each consumer decides from whom to buy if she chooses
to buy at all.
(a) Fully characterize the pure-strategy symmetric Nash-Bertrand equilibria of the game.
How does the equilibrium played depend on t?
(b) Consider the following changes in the structure of the game. First, set c = 0. Continue to
assume that a given consumer gains no additional utility from units—other than the
first—purchased from the same firm (e.g., a consumer who purchases one unit from firm
0 gains no utility from purchasing any more units from firm 0). Assume now, however,
that a consumer can gain additional utility if she purchases an additional unit from the
other firm. Specifically assume the gross benefit for a consumer at location x from one
unit only from 0 remains v – tx; the gross benefit from one unit only from 1 remains v –
t(1-x); and the gross benefit from one unit from each firm is av – t, where 2 a 1.
Fully characterize the pure-strategy symmetric equilibria of the game. How does the
equilibrium played depend on t? [Hint: If you’re having trouble, think about the solution
for the two extreme values of a, 1 and 2.]
III. Answer both parts, with reference both to economic principles and to actual industries:
a. If antitrust enforcement is vigorous, does that make price regulation unnecessary or
even harmful?
b. If an industry is price regulated, does that make antitrust enforcement unnecessary or
even harmful?