Homework on Mergers:

In the following questions, consider a hypothetical industry consisting of 4 firms, each of which makes luxury pens. Customers of pens can buy either luxury pens or cheap pens. There are one hundred equally sized producers of cheap pens. Each firm has a marginal cost of 10 and faces the following demand curve. All answers must be typed.

Firm 1: q₁ = 300 -12p₁ + 2p₂ + 2p₃ + 2p₄

Firm 2: q₂ = 300 -12p₂ + 2p₁ + 2p₃ + 2p₄

Firm 3: q₃ = 300 -12p₃ + 2p₁ + 2p₂ + 2p₄

Firm 4: q₄ = 300 -12p₄ + 2p₁ + 2p₂ + 2p₃

1. First use the critical elasticity test (CE) to see if luxury pens are a relevant antitrust market, or whether we would need to expand the market to include all pens. If luxury pens are an antitrust market, would a merger between Firm 1 and Firm 2 be likely to cause concern at the federal antitrust agencies? (Note: consult the HMGLs section 5.3).

To answer this question, you will need to calculate the pre-merger equilibrium in this market, assuming that you conclude that luxury pens constitute a separate market from cheap pens.

2. Suppose that Firm 1 and Firm 2 want to merge. Ignore all pens but the luxury kind, notwithstanding what you may have said in you r answer to the first question. After the merger, their products will both continue to be sold and will be known as brand 1 and brand 2. They have shown that the merger will allow each brand to reduce its marginal (=average) cost by 50 percent. Taking a unilateral effects approach, calculate the UPPI for both merging firms and decide if post-merger prices are likely to rise or fall, compared to pre-merger prices. Does your answer change if the merger only reduces the marginal costs of brand 1 and brand 2 by 20 percent?

3. Now calculate the post-merger equilibrium prices and see if the predictions you made using unilateral effects were correct.