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Econ 100C, Fall 2021

PROBLEM SET 5

Oligopoly models are covered in IMVH section G3.

Consider a market with only two producers, each with constant marginal cost: MC1 = 20, MC2 = 50. Market demand is Q = 400 – P. (Ignore fixed costs at the beginning.)

A. Basic cases

a. If the two firms compete as Cournot oligopolists, find their reaction functions and solve for the Cournot equilibrium quantities and price.

b. Suppose Firm 1 tries to acquire Firm 2, arguing that the joint venture will be able to streamline certain processes and lower costs. A top management consulting firm has even produced a report which shows that marginal cost will indeed be lowered to only MC = 10. Assuming this is accurate, do you think government regulators should allow the merger to proceed? Explain your reasoning.

B. Now suppose that Firm 1 (which has more efficient technology) contacts Firm 2 to offer a deal:

● Firm 1 will give Firm 2 access to its technology (which is more efficient), in exchange for a licensing fee of 2,000 paid each period by Firm 2.

● As part of the licensing agreement (which is a legally enforceable contract), firm 1 will impose a limit on how much output firm 2 can produce. And, in order to act equitably, Firm 1 will commit to producing the same quantity as well.

- Does it make sense for Firm 1 to offer this deal?

- Should Firm 2 accept it?

- Should government regulators allow it?

Hint: start by asking what quantity would Firm 1 assign to Firm 2 to make? (assuming that it will have to produce the same amount)

C. Firm 2 is at a disadvantage because it has higher costs – so in the simultaneous competition game it will earn lower profits. But what if the game was sequential? Suppose Firm 2 could be the first mover, so that Firm 1 observes Firm 2’s production each period before deciding how much to produce themselves.

a. What will be the outcome under this Stackelberg competition scenario?

b. How much would firm 2 be willing to pay each period in order to impose this order in the game, as opposed to simultaneous interactions?

c. [Optional extension: if Firm 2 simply couldn’t find a way to be the first mover, could it still achieve the desired Stackelberg outcome by telling Firm 1 that it will produce the amount from that case? Think carefully about why or why not.]

D. Go back to thinking of the interactions as simultaneous. One reasonable question is: why are there only two firms? Could economies of scale account for this?

a. Supposing that new entrants would only have access to the less efficient production process (MC=50), how high would fixed cost have to be in order to keep a 3rd firm from entering, even without additional barriers to trade?

b. What about in order to keep even the 2nd firm from entering?

E. Now suppose that firms in this industry compete by setting prices instead of quantities. Find the Bertrand equilibrium price and quantity in the market, as well as the number of firms. Continue to assume that Firm 1’s marginal cost is 20, any other firm’s marginal cost is 50, and that there are no fixed costs. Will market price be near the competitive level? How m What profits do firms 1 and 2 earn? Will Firm 2 remain in the market? If not, is Firm 1 still constrained in the price it sets?