Eco 350k: Homework 3 Suppose that the widget industry had three firms

Eco 350k: Homework 3

Suppose that the widget industry had three firms: firm 1, firm 2 and firm 3. Each firm faced a demand curve that looks like the following:

Q_i = 100 -3P_i +2P_j +2P_k where i=1,2,3.

Assume that each firm has a marginal cost of 10. Then before a merger the payoffs for each firm are as follows.

π₁ = (P₁ – 10)(100 – 3P₁ +2P₂ + 2P₃)

π₂ = (P₂ – 10)(100 – 3P₂ + 2P₁ + 2P₃)

π₃ = (P₃ – 10)(100 – 3P₃ + 2P₁ + 2P₃)

In equilibrium, each firm chooses its price to maximize profits, given the prices chosen by the other firms.

Question 1: Find the equilibrium prices pre-merger. This will require you to solve three equations in three unknowns.

Now suppose that a merger takes place between firm 1 and firm 2, and that as a result of the efficiencies made possible by the merger, the marginal costs of product 1 and product 2 both become zero.

Question 2: Based on UEA, do you expect the post-merger prices for products 1 and 2 to be higher than the pre-merger prices?

Question 3: calculate the post-merger prices, with MC₁ = MC₂ =0 and MC₃ = 10. Is the result consistent with what you got using UEA?