2. Hospital Mergers. Suppose you are a hospital executive and you're considering two possible mergers: with hospitals A or B. You want to pick the merger that will allow you to raise the price at your hospital the most and you have great antitrust lawyers so you're not worried about antitrust scrutiny. Assume you know that hospital A has similar prices to you, a profit margin of 55%, and you've estimated that 15% of your patients would choose hospital A if your hospital was unavailable. Suppose alternatively that hospital B has prices that are 5% higher than yours, it's profit margin is 50%, and you've estimated that 30% of your patients would choose hospital B if your hospital was unavailable. Assume that all the hospitals and insurers in market have roughly the same bargaining ability. (10 points) (a) Use the first order approximation of a price increase from a merger to estimate how much you'll be able to raise prices at your hospital after merging with hospital A versus with hospital B. (4 points) (b) Which merger would you choose if all you cared about was maximizing profits? Why? (2 points) (c) Suppose your antitrust lawyers told you that if the predicted price effect of the merger is over 5%, there is a 50% chance the FTC will sue to block the merger. but if the predicted price effect of the merger is under 5% the chance the FTC will sue you is only 10%. They believe you'll win the case with probability 1, because they're so good, but the cost of the court case will be equal to the discounted present value of a 3% price increase. Now which merger do you choose if all you care about is maximizing profits? Why? (4 points)