ECON 461 Problem Set 2 Summer 2017 Each question will receive equal weight in grading.
1. Let market inverse demand for a duopoly market be given by the equation
r
Q
p=
;
N
where Q = q1 + q2 is total output.
Let the market be supplied by two quantity-setting …rms, …rms that act
as Cournot duopolists in a static, one-period model.
Let each …rm produce with constant marginal and average cost c per unit.
Find Cournot equilibrium outputs, price, and pro…t per …rm.
Show the derivations of your answers.
2. Consider a duopoly in which two …rms produce di¤erent varieties of a
di¤erentiated product at constant average and marginal cost 1 per unit. Let
the equations of the inverse demand curves be
1
p1 = 11 (q1 + q2 )
2
1
p2 = 11 ( q1 + q2 )
2
(both equations valid where the implied prices and quantities are nonnegative).
(a) …nd Nash equilibrium prices, quantities, and payo¤s for a one-shot
game if both …rms set quantities.
(b) …nd Nash equilibrium prices, quantities, and payo¤s for a one-shot
game if both …rms set prices.
(c) Compare equilibrium prices in (a) and (b). Which type of competition
(in quantities or in prices) has lower equilibrium prices? Why?
Show the derivations of your answers.
3. Based on the material The Structure of American Industry, discuss in
your own words the impact of
(a) the behavior of oil suppliers that are not members of OPEC, and oil
consumers; and
(b) the behavior of OPEC members
on the ability of OPEC to restrict output and in‡uence the price of crude
oil.
1

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