Problem
Suppose that the market demand function for a product is given by q = 306 - p. There are two firms in this market: Firm 1 and Firm 2. Entry is impossible. Products are undifferentiated. Production is a one-time game i.e. it is not repeated. The total cost of production for Firm i is c(qi) = 10qi. (i.e. the marginal cost is $10, and we ignore the fixed costs.)
a) Suppose that both firms set their quantity simultaneously. The total output is q = q1 + q2, where q1 is the output from Firm 1 and q2 is the output from Firm 2. Calculate the quantity each firm produces in the Cournot equilibrium, and determine the market price.
b) Suppose that Firm 1 sets its quantity first, and Firm 2 follows. Calculate the quantity each firm produces in the Stackelberg equilibrium, and determine the market price.
c) Suppose that both firms set their prices simultaneously. Calculate the quantity they produce in the Bertrand equilibrium, and determine the price(s) set by each firm.