Problem Set 5a Hints

Thursday, 11/15/01

1. In the following table, you will find a firm’s short run total costs for several different levels of output:

If the price of output is $10, what is the profit maximizing level of output for this firm?

Either do this by brute force, calculating profit for every level of output or use the rule that Dr. Schwab gave in lecture.

2. Do Problem 5 on page 312 in Mankiw. Bob's lawn-mowing service is a profit-maximizing, competitive firm. Bob mows lawns for $27 each. His total cost each day is $280, of which $30 is a fixed cost. He mows 10 lawns a day. What can you say about Bob's short-run decision regarding shut down and his long-run decision regarding exit?

Recall from lecture that you stay in the market in the short run if you are able to at least cover your variable costs. In the short run case, fixed cost is a sunk cost like the fee to reserve the tennis court - it's gone, don't worry about it anymore. What you need to do is figure out first how much revenue Bob makes and compare that to his variable costs. That will give you the shutdown decision.

In the long run, there are no fixed costs. In the long run, everything is a variable cost and you want to make sure that you can cover your (now entirely variable) costs with the revenue you make. If you can't cover in the long run, you exit. What's the difference between long run variable costs and short run variable costs? That will make all the difference.

3. Consider a monopolist who faces the following demand schedule:

(a) Calculate marginal revenue for each level of output. (b) Show that for this firm, marginal revenue always equals new price + (change in price times old quantity) and that marginal revenue is therefore always less than price. (c) If this firm produces output at a constant average and marginal cost of $12, what is its profit maximizing level of output?

For part a, just do the arithmetic out. In part b, verify that it is true by writing out the various equations for each quantity level. In part c, remember that the profit maximizing level of output is always the one where marginal revenue equals marginal cost.

4. Suppose you are a monopolist in the market for Good A and the market for Good B. There are two consumers, Consumer 1 and Consumer 2. Each will buy either 0 or 1 unit of Good A and each will buy either 0 or 1 unit of Good B. The maximum they would be willing to pay for these goods (i.e., their reservation prices) are as follows:

Consumer	Good A	Good B
1	15	22
2	22	15

You produce both goods at a constant average and marginal cost of $10. (a) If you do not engage in price discrimination and you do not bundle these goods, what price will you charge in each market? How much profit willyou earn? (b) If you do engage in price discrimination but you do not bundle these goods, what prices will you charge in each market? How much profit will you earn? (c) If you do not engage in price discrimination but you do bundle these goods, that is, you offer Goods A and B as a package, what price will you charge for the package? How much profit will you earn?

For part a, you only get to charge one price for Good A and one price for Good B. Treat the two markets as separate and figure out what is the best price to pick. Remember that there are only two prices you even need to bother looking at. For part b, you get to charge each guy whatever you want for each good. If you really want to maximize your profit, you're going to get each for all that you can squeeze out of him. For part c, you want to think about the bundling case given by Dr. Schwab in lecture. You do this problem the exact same way he did the word processor and spreadsheet example.