Consider a market in which demand equals Q = D(p) = 94 ― p, where p denotes the price
and Q total quantity. Assume that two firms are active in the market. Each firm has marginal
costs MC = 10 and fixed costs F = 0.
In the week 3 assignment, we saw that:
 In the Nash equilibrium of Cournot competition where two firms set their quantities
simultaneously, 1 = 2 = 28 and 1 = 2 = 784.
 If the two firms form a monopolist cartel, the cartel produces Q = 42 and earns a joint
profit of = 1764.
Now, assume that two companies compete à la Stackelberg: Firm 1 sets its quantity first and
then firm 2 sets its quantity after observing firm 1’s quantity. Assume that firm 2 has already
entered the market. Find the subgame perfect Nash equilibrium outcome following the steps
below:
(a) If firm 1 produces quantity 1, what is firm 2’s best-response? (Hint: It is a function of 1)
(b) Write down firm 1’s profit function, as a function of 1 and 2. Then rewrite it as a function
of 1, by plugging in your answer from part (a).
(c) Find firm 1’s profit-maximizing quantity.
(d) Find firm 2’s best-response to firm 1’s quantity you found in part (c).
(e) Find the equilibrium price.
(f) Find each firm’s profit in the equilibrium.
(g) Complete the following statements by filling in one of the following: higher, lower, or the
same.
Compared to the Cournot-Nash equilibrium outcome:
 Firm 1’s quantity is ____________ in the Stackelberg equilibrium outcome.
 Firm 1’s profit is ____________ in the Stackelberg equilibrium outcome.
 Firm 2’s quantity is ____________ in the Stackelberg equilibrium outcome.
 Firm 2’s profit is ____________ in the Stackelberg equilibrium outcome.
 Two firms’ combined quantity is ____________ in the Stackelberg equilibrium
outcome.
 Two firms’ combined profit is ____________ in the Stackelberg equilibrium
outcome.
 The price is ____________ in the Stackelberg equilibrium outcome.

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