Problem 1: Strategic Inventory Decision. You manage XYZ Car Rental and are currently faced with making an important inventory decision. Specifically, you must commit to the number of cars to purchase from the auto manufacturers, and this decision will determine your car rental inventory over the next 6 months. Assume that you are able to rent your entire inventory each day. For example, if you have 50 cars, you can rent 50 cars each day. (In practice you cannot be at capacity at all times, but let's make this simplification.)

You are one of three competitors making a similar inventory decision, and you do not know what decisions your competitors will make. Marginal cost, after accounting for what you pay for a car and the costs of renting cars, is $10, and all competitors have the same costs. The daily aggregate demand for car rentals is Q = 100 - P where Q is total quantity demanded and P is the market price. For simplicity, assume each rental is a daily rental, and that prices adjust to rent the entire inventories of all competitors each day.

1. How many cars should you purchase for your inventory to rent each day?
2. Explain how you arrived at your answer using the Cournot model.

Problem 2: Strategic Merger Decision. You still manage XYZ Car Rental and are currently faced with making an important merger decision. Specifically, you are one of three firms in the car rental market and you are deciding whether to merge with one of your rivals. Apart from the prospect for merger, the situation is unchanged from the situation in problem 3. That is, assume that you are able to rent your entire inventory each day, and you are one of three symmetric competitors. You compete with your competitors through your inventory decision. You do not know what decisions your competitors will make. Marginal cost, after accounting for what you pay for a car and the costs of renting cars, is $10, and all competitors have the same marginal costs. The daily aggregate demand for car rentals is Q = 100 - P where Q is total quantity demanded and P is the market price. For simplicity, assume each rental is a daily rental, and that prices adjust to rent the entire inventories of all competitors each day. There are no efficiencies associated with the merger.

1. Suppose you believe that as a condition for proceeding with the merger, the antitrust authority will require you to spin off assets that will open a new car rental firm that will have the same marginal cost as each firm prior to the merger. Should you propose the merger to senior management in this case? Explain.
2. Suppose you believe that the antitrust authority will allow the merger without conditions.
3. If your post-merger competitor can adjust its car inventory in response to the merger, should you propose the merger to senior management? Explain.
4. If your post-merger competitor is capacity constrained for the foreseeable future (meaning that it cannot rent more cars than its pre-merger inventory), should you propose the merger to senior management? Explain.
5. Explain intuitively the logic for any difference in the answers to (a) and (b).