# Problem set 4

Problem set #4

Part I due on Friday, May 2nd, in class. Part II due on Monday, May 5th at 5:00 p.m. in the box outside of HIllcrest.

Part I.

Please pass in on Friday an update on your group projects.  Among the elements to share:

• The research question(s) that you are addressing
• A justification for these questions: why are they important?
• The format you will use to share your results.
• The preliminary results
• Questions you may have for me (we can review some of these in class on Friday

Part II

1. Explain the circumstances under which an economist would advice a small business to close down even if they are earning positive accounting profits. Under what conditions might the economist’s advice change, even if the positive accounting profits do not change.

2.  At Colorado College, students take one mini-course per month (a sort of permanent winter term!)  Imagine that a student has  3.00 GPA after taking ten courses, assuming that F=0, D=1, and so on.  For the next five courses (the student’s 11th to 15th course), the student earns the following grades, in this order: F, D, C, B, A.  In a table, show the numerical marginal grade for each of these courses as well as the average grade. Explain conceptually how the marginal grade can be rising even as the average grade is falling. Generally for a student at this college, under what conditions will marginal grade and the average grade both be rising?

3. The A&W Root Beer shop south of Middlebury closes every fall and reopens in the spring. True or false?: A&W should only re-open in the spring when it’s expected daily revenue is greater than it’s daily total cost.  Explain your answer.

4. Consider the short-run production of a small firm that makes sweaters. These sweaters are made using a combination of labor and knitting machines. In the short run, the firm has signed a lease to rent one machine for \$240 per day. Therefore, in the short run, the firm cannot vary the amount of knitting machines it uses. However, the firm can vary the amount of labor it employs.

The first two columns in the table below show the production level that the firm can achieve at various amounts of labor:

 Labor (# workers per day) Total Output Marginal Product 0 0 — 1 4 2 10 3 13 4 15 5 16

a)  Calculate the marginal product (using the final column here).

b)  If the wage for these workers is \$60 day, fill in the correct data in all of these columns:

 Labor Output Fixed Cost Variable Cost Total Cost Average Fixed Cost Average Variable Cost Average Total Cost Marginal Cost 0 1 2 3 4 5

c)  With a well-labelled graph, plot the following for this firm: marginal cost, average variable cost, average total cost, and average fixed cost.

d)  If the price of one of these sweaters was set at \$30, how many sweaters would this small firm make? At this level, would the firm be making a positive or negative profit? Show your answer.

e) If the price of one of these sweaters was set at \$60, what would happen to this market in the long run? What would happen to this small firm? Justify your answers.

5. Under what conditions does a short run ATC have a positive slope? Under what conditions does a long run ATC have a positive slope? Explain why, in perfectly competitive markets, the slope of both of these will end up being zero.

6. Paulo’s Ping Pong Balls is a firm that operates in a competitive market. The ping pong balls sell for \$3 per package. Fill in the following table with the class’s help and identify the profit-maximizing level of output.

 Output Total Revenue Total Cost Profit Marginal Revenue Marginal Cost 0 \$1.50 —- —- 1 2.00 2 3.00 3 4.50 4 6.50 5 9.00 6 12.00 7 15.50 8 19.50 9 24.00

7. You have landed a job in production management for Midd Signs, Inc. Your costs are shown below.”

Quantity                       Average Total Cost

500                                     200

501                                     201

Your current level of production is 500 signs; all of them have been ordered by your regular customers. You then get a text from a new customer who wants to buy one sign and offers you \$450 for it.

a. Should you accept this offer?

b. What would be the net change in the firm’s profit if they did produce this sign (the 501st production)?

8.  Here’s an article about the closing several years ago of a beloved bakery in San Francisco. Using the graphical models of monopoly and/or perfect competition, show these three phases of the bakery’s history:

• The bakery could barely keep up with the demand from store patrons and restaurants which wanted deliveries, Hoffman said. “All these breads were totally unusual at this time,” Hoffman said. “Nobody was doing them.”
• By 1994, the bread business finally started proving somewhat profitable again, Hoffman said. But it soon began to drop off as other bakeries’ breads began competing with Tassajara’s on supermarket shelves.
• Finally, after years of losses, Hoffman concluded it was time to cease bread operations and focus on the dessert business. “We’d been subsidizing it for a couple of years and just couldn’t do it anymore,” Hoffman said.

9.  Assume that our ping pong producer above is making a unique kind of Ping Pong – it has the Midd trademark.  Assume that the producer faces the following demand for its product, with the costs the same as we saw above. Fill in the columns of the table below.

If this producer can operate as a monopolist, what is the profit maximizing-level of ping-pong production? Compared to your result in #6 above, illustrate the change in social welfare associated with this outcome.

 Quantity Price Total Revenue Total Cost Profit Marginal Revenue Marginal Cost 0 10 \$1.50 —- —- 1 9 2.00 2 8 3.00 3 7 4.50 4 6 6.50 5 5 9.00 6 4 12.00 7 3 15.50 8 2 19.50 9 1 24.00