Two firms, i = 1, 2, compete on the production of buttons. They each choose a
quantity of buttons si. The price of buttons is given by 100 −s1 −s2. Thus firm 1's revenue is
s1(100 −s1 −s2) and firm 2's revenue is s1(100 −s1 −s2). Firm 1's cost of production is 's' subscript(1)^2 and
Firm 2's cost of production is (2)s subscript(2)^2. Thus, firm 1's profit is
u1(s1, s2) = s1(100 −s1 −s2) −s subscript(1)^2
and firm 2's profit is
u2(s2, s1) = s2(100 −s1 −s2) −2 s subscript(2)^2.
 

 

1. What is Firm i's best response to s−i if s−i > 100?
2. What is Firm i's best response to s−i if s−i < 100?
3. What is Firm i's best response to s−i if s−i = 100?
4. Is there an equilibrium where some firm produces 100 or more buttons?
5. Solve for the Nash equilibrium.

Answer rating: 100% (QA)

To find the best response of Firm i to si we need to maximize the profit function of Firm i with respect to its own quantity choice given the quantity ... View the full answer