Simon Fraser University
ECON 302
Spring 2016
S. Lu
Problem Set 5
Due on February 22, at 2:30pm
Remember to show your work on all questions.
1. Consider the following game:
Work Hard
Reward Effort
5,5
Not Reward Effort
4,-5
Work Normally
0,2
1,-3
Goof Off
1,0
0,0
a) Show that this game is dominance solvable and find the solution.
[If you’re stuck, see if one of the player 2’s (i.e. the column player’s) pure strategies is
dominated by a mixed strategy. Hint: Can a strategy that is a best-response to one of
player 1’s strategies be strictly dominated in the first round of iterated dominance?]
b) Are there any Nash equilibria in this game that are not pure? Explain.
2. In the following game, let p be the probability that player 1 plays Top, and q be the
probability that player 2 plays Right:
Left
Right
Top
0,0
3,-1
Bottom
1,2
2,4
a) On a graph with p on the horizontal and q on the vertical, draw each player’s best
response (make sure you indicate which line is which player).
b) Find all Nash equilibria, and relate them to your graph.
Questions 3 and 4 refer to the following setup:
The demand curve in a market is Q = 6-P. Firm A and B are the only sellers, their marginal costs
are constant at 2 and 3 respectively, and there is no fixed cost. They produce identical goods.
3. a) What is the socially efficient outcome? (Specify the quantity for each firm.)
b) Find the quantity produced by each firm and the price under Cournot competition.
c) What is each firm’s profit under Cournot competition?
4. Assume Bertrand competition (firms pick price). Assume that firms can pick any real number
as their price (it doesn’t have to be a multiple of 0.01).
a) Explain why neither price can be below 2 in a pure-strategy equilibrium.
b) Explain why neither price can be above 3 in a pure-strategy equilibrium.
c) Suppose firm A gets the entire market if A and B set the same price. Show that “Both
firms set price P” is a Nash equilibrium for all P in the interval [2,3].
d) [OPTIONAL] Suppose firms A and B share the market 50/50 if they set the same price.
Show that there exists no pure-strategy NE in the Bertrand price-setting game.
Questions 5 through 7 refer to the following setup:
It’s year 2017, and Boeing is launching the B797 while Airbus is launching the A360. Assume
that the companies stop selling their other planes, and there are no other plane makers in the
world (sorry, Bombardier).
Airline companies view B797’s and A360’s as perfect substitutes, and the demand for these
planes is: Q(P) = 5500 – 10P, where P is in millions of US dollars.
Airbus and Boeing have the same cost function: C(q) = 40000 + 100q + 0.05q2, where the cost is
in millions of US dollars. Assume that the $40 billion constant in the cost function is the sunk
cost of developing the aircraft, so it is borne even if q=0.
5. Let’s first warm up by reviewing monopoly behaviour.
a) What price would Boeing charge if Airbus did not exist?
b) What would Boeing’s profit be if Airbus did not exist?
c) Suppose Boeing and Airbus merge. What is the cost function of the combined company?
Be very careful.
d) What is the profit of the merged company?
6. Suppose Airbus and Boeing simultaneously choose quantity (Cournot competition).
a) Suppose Airbus chooses a quantity of qA. What is Boeing’s best response?
b) Compute the equilibrium price under the Airbus-Boeing Cournot duopoly.
c) What is each firm’s profit?
d) Is your answer from 6c more or less than half of your answer from 5d? Without
calculations, explain why this is the case.
7. Suppose Airbus and Boeing simultaneously choose price (Bertrand competition), and each
company gets half the market if they choose the same price.
a) Let Pm be your answer to 5a. What is Boeing’s best response if Airbus chooses a price
above Pm? Answer this question without calculations.
b) What is the socially efficient quantity of airplanes? Derive society’s cost function
carefully.
c) What is the price Peff such that if both Airbus and Boeing charge it, the market outcome is
efficient?
d) Show that it is a NE for both firms to charge Peff.
e) [OPTIONAL] Show that it is a NE for both firms to charge $270 million for each plane.
f) [OPTIONAL] Verify that if both firms charge $270 million, they are both pricing above
marginal cost. Why is that a NE here, while in class we got P=MC under Bertrand
competition?