Overview
Part A: Monopoly with entry choice
Firm A has a marginal cost of , and the market demand is . The firm has to pay an entry fee of $36 before it can produce and sell its product. (20 pts in total)
(a)If A enters, how much is its optimal operating profit? (You do not need to include the entry fee when calculating the operating profit.) (2 pts)
(b)Will A enter? (2 pts)
Part B: Cournot Competition with entry choice.
Now suppose that before A’s entry, it learns that there is a potential competitor, firm B, whose marginal cost is . We will analyze whether A still wants to enter. A knows that B will also need to pay an entry fee of $25. If a firm does not enter, it does not pay the entry fee and does not earn any operating profit. If a firm enters, it pays the entry fee, and its operating profit depends on the competition. If only one firm enters, it will choose the price and quantity as a monopolist. If both enter, the two firms will play a Cournot game, with the market demand being .
First consider what will happen in a Cournot competition if both firms enter.
(c)For any given , write down firm A’s best response, i.e., A’s optimal choice of (as a function of ). (2 pts)
(d)For any given , write down firm B’s optimal choice of (as a function of ). (2 pts)
(e)Solve the two best response functions simultaneously to obtain the equilibrium and . (2 pts)
(f)How much is the equilibrium price? (2 pts)
(g)How much is each company’s operating profit in the Cournot equilibrium? (2 pts)
Now consider the two firms’ entry choices.
(h)Will firm B enter? Will firm A enter? (3 pts)
(i)In the entry equilibrium, how much is the equilibrium price? (3 pts)
Part C: Entry Game with Stackelberg Capacity Competition
Now consider a sequential entry game with capacity competition. First, firm B chooses whether to enter and chooses its capacity . Then, firm A chooses whether to enter and chooses . As before, the market demand is . Entry costs and marginal costs are also the same as before.
(j)Suppose B enters and chooses . For what values of is it optimal for firm A to enter? (5pts)
(Hint: Suppose firm A enters. What quantity does firm A choose? What is the price? What is the operating profit of firm A?)
(k)Given firm A’s best response, what does firm B choose? (5pts)
(l)How do consumer surplus, producer surplus, and total surplus compare in Parts A, B, and C? Provide intuition. (5pts)