Department of Economics, SUFFOLK UNIVERSITY
Jonathan Haughton
ECONOMICS 311: Intermediate Microeconomic Theory
ASSIGNMENT 8
Answers to this assignment are due back by Monday, November 23, 2015.
1.
Duopoly game
Consider a duopoly, where each firm may choose among three strategies: zero, small, or large levels of
output. The normal-form payoff matrix, which shows profits, is as follows:
Output of firm A
a.
b.
c.
2.
Zero
Small
Large
Zero
0, 0
1500, 0
2000, 0
Output of firm B
Small
0, 1500
1300, 1300
1400, 800
Large
0, 2000
800, 1400
500, 500
The protocol for this game is sequential: firm A moves first, then firm B, and the game ends.
a. Find the “subgame-perfect equilibrium” (i.e. the outcome, assuming that the players
choose rationally when it is their turn).
b. Is there a first-mover or last-mover advantage?
c. Is the solution efficient for the two firms together (i.e. is combined profit maximized)?
Now change the game: firm A moves first, then firm B moves, then A can revise its own decision,
and the game ends (so A has both the first move and the last move).
a. Find the subgame-perfect equilibrium.
b. Is the solution efficient for the two firms?
c. Does firm A benefit more than in a.a.?
Now change the game again. This time it is a simultaneous game, so both firms make their
choices at the same time, or at least without knowing, when they make their choices, what the
other firm has chosen.
a. Are there one or more dominant equilibria in this game?
b. Are their one or more Nash equilibria in this game?
Duopoly and differentiated products
So far, we have assumed that the two firms in the duopoly produce an identical product. We also
assumed an (inverse) industry demand curve given by
P = 100 – Y = 100 – (y1 + y2),
and zero costs.
N0w let the two firms produce somewhat different goods, and define s as a similarity index of the two
firms’ products, where s ranges from 1 (identical products) to 0 (completely different products, so neither
has any effect on the market for the other). We now assume that
P1 = 100 – y1 – s y2
P2 = 100 – s y1 – y2.
Assume quantity competition, meaning that each firm observes the quantity sold by the other firm and
reacts to it, as in the Cournot model.
Ec 311: Intermediate Microeconomic Theory
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a.
b.
c.
3.
Assume s = ½ . Find and graph the firms’ reaction curves, and find the Nash-Cournot solution
(i.e. the quantity produced by each firm, the price charged by each firm, and the profit earned by
each firm).
What happens to the price, quantity, and profit of each firm as s approaches zero?
What happens to the price, quantity, and profit of each firm as s approaches 1?
Dilemmas
It is widely believed that emissions of carbon dioxide (CO 2) are contributing to the “greenhouse effect”
and causing the planet to warm up. Most observers believe that this warming will ultimately be
damaging to the world economy, and perhaps even to the human species. Assume, for now, that every
country realizes that the world would be better off if CO2 emissions were reduced. Yet essentially no
country is seriously reducing its CO2 emissions. Why not? Frame this problem as one of the Prisoner’s
dilemma. Be brief.
Ec 311: Intermediate Microeconomic Theory
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