CHAPTER 7 Costs CHAPTER OUTLINE 7.1 Measuring Costs

CHAPTER 7 Costs

CHAPTER OUTLINE

7.1 Measuring Costs Economic Cost Capital Costs 7.2 Short-Run Cost Short-Run Cost Measures Short-Run Cost Curves Production Functions and the Shapes of Cost Curves Effects of Taxes on Costs Short-Run Cost Summary 7.3 Long-Run Cost Input Choice How Long-Run Cost Varies with Output The Shape of Long-Run Cost Curves Estimating Cost Curves Versus Introspection 7.4 Lower Costs in the Long-Run Long-Run Average Cost as the Envelope of Short-Run Average Cost Curves Short-Run and Long-Run Expansion Paths How Learning by Doing Lowers Costs 7.5 Cost of Producing Multiple Goods

TEACHING TIPS

The material in Chapter 7 is undoubtedly some of the most important in the entire text. If students are to have any significant level of understanding of how firms make production decisions when faced with var- ious industry structures and levels of market power, they must have a sound understanding of cost. For this reason, you may want to build in an extra class period for this chapter over and above what you think it will require. This way, if you are on schedule, you can always use the day to have the class work on problem sets or applications. If you are running behind, the extra day will prevent you from having to rush through this important material.

You might begin by asking the class for the kinds of costs that firms must consider. You are likely to get most or all of the private, explicit costs—labor, materials and capital—but you may or may not get sug- gestions of opportunity costs and social costs. Once you have completed a list, you can distinguish between cost types, and discuss the importance of measuring cost as opportunity costs. You may want to take five minutes or so to discuss externalities, and give some examples of firms’ attempts to internalize them (and why they would do so), such as the production of dolphin-safe tuna. Finally, some students may question the lack of attention paid to materials as an input and question the assumption that material use is inde- pendent of the capitalÐlabor mix.

As with the production definitions, you can use a running example of output and cost figures that are pre- sented in a table, and subsequently in graphs. Remind students whenever possible that the information here is directly related to the production function. The text makes specific note of the shape of the variable cost curve and its relationship to the diminishing marginal returns to labor. This link is further reinforced by equa- tions 7.1 (MC = w/MPL) and 7.2 (AVC = w/APL). Marginal cost and marginal product curves can be described as inverted images of one another, noting that the characteristic “check-mark” or “fish hook” shape is always there in one if it is there in the other for any given production function. The same applies to the average product and average cost curves (as well as their intersection with their respective marginal curves).

41 42 ❈ Part One\Teaching Aids When covering long-run cost, you shouldn’t need to spend too much time on isocost lines, other than to show the equation for the definition of cost and note the similarity to the budget constraint. The one point worth emphasizing here is that unlike the budget constraint in utility maximization, the isocost line is the objective function rather than the constraint. The comparison of the minimization of cost to the maximization of utility can be continued throughout the discussion of the tangency rule (MRTS = w/r).

The section on the shape of the long-run cost curves and the relationship between long- and short-run cost is where you may need to slow down significantly. You may need to spend a good deal of time describing how long-run cost curves are related to the different short-run curves, and presenting a verbal and graphi- cal depiction of the envelope theorem. If it seems that the class is really struggling with the graphs, I keep a set of correctly drawn graphs that I will photocopy and hand out to the class. That way, students can take notes right on the handouts.

This is a great place to make use of a computer-equipped classroom. By entering a cost function such as C = 2/3q3 Ð 12q2 + 90q, which has ranges of increasing and decreasing returns, you can show the total, average, and marginal cost curves for a typical cost function, and discuss points of inflection, intersection, and the relationship between the curves. If you decide to use this specific function, you will need to com- pute values for C, AC, and MC through an output level of 16 to see the curve shapes well.

Section 7.5 introduces scope economies. The presentation in the text is brief and straightforward. You may choose to introduce more of the technical material associated with scope economies, such as incremental cost and stand-alone cost, but at the intermediate level, conceptual understanding is most important. You might begin the discussion by asking the class if they can think of any single-product firms (they frequently cannot). Ask them why this is so. Although they don’t use the terminology of scope economies, the class often gives responses that refer to these types of savings. Once you get through the basic terminology, you can choose several large firms, such as Ford or GE, and ask the class for possible sources of scope economies. If there is a current merger or buyout in the news, you may want to have the class search through an article in the Wall Street Journal for mention of savings the firm(s) hopes to generate that amount to scope economies.

ADDITIONAL APPLICATION

Economies of Scale and Scope in Teaching

Is it less expensive per head to teach more studentsÐthat is, are there scale economies in teaching? Nelson and Hevert (1992) estimate a short-run cost function for departments at the University of Delaware, where output is measured as the number of student credit hours.1

We expect short-run scale economies if the fixed costs of administration, physical plant, libraries, and computer centers are large. If so, the average fixed costs are a major component of average total cost. Nelson and Hevert (1992) do not find evidence of economies or diseconomies of scale if a department increases quantity by increasing the number of classes (holding class size fixed). In contrast, they find substantial economies of scale if output is increased by increasing class size.

What are the implications of these findings for marginal cost? In a lecture class, if enrollment is increased by 50%, holding class size constant, the marginal cost falls by 7% for a lower-level undergraduate course, 22% for an upper level undergraduate course, and 21% for a graduate course. If class size is increased by 50% and enrollment is held constant, the corresponding changes are 17%, 12%, and 5%. That is, increasing either class size or enrollment lowers marginal cost.

1 Nelson, Randy, and Kathleen T. Hevert, “Effect of Class Size on Economies of Scale and Marginal Costs in Higher Education,” Applied Economics, 24(5), May 1992:473-82. Chapter 7\Costs ❈ 43 Cohn, Rhine, and Santos (1989) studied economies of scope in teaching in schools across the country.2 They measure teaching output as the number of undergraduate and graduate full-time enrollments (that is, they do not control for qualitative differences). They measure research output indirectly using funds raised for sponsored research (presumably, if more funds are available, more good research is produced). At pub- lic colleges and universities, they find virtually no scope economies (SC = -.064) at average output levels. For higher levels of output, however, they do find scope economies. At private schools, they find economies of scope at average levels of output (SC = 0.179) and much higher levels of scope economies at larger output levels. These results indicate that it is less expensive to produce large amounts of teaching and research at the same institution as separate ones. Put differently, teaching and research are comple- mentary. The cost savings from scope are larger at larger institutions.

1. How might the results in these two studies change if quality of education were introduced as an additional variable? How might this be accomplished? 2. What do you believe are possible sources of scope economies in education and research? Might they be more prevalent in some disciplines than others?

Entrée Economics—The Cost of a Meal3

Recently, at an upscale New York restaurant, a patron was served a pork chop that cost the eatery about $6.25, incuding the chop, spices, garnish, and assorted vegetables, and sauce. The price? $23.50. While a nearly 400 percent markup may seem exorbitant, it is commonplace in the restaurant industry. Even worse is the markup for salmon. Brian Buckley, Director of Management Studies at Peter Kump’s New York Cooking School, noted that while people believe salmon is an elegant dish, and while some even have visions of Alaska when ordering, they are actually purchasing farm-raised fish that costs the restaurant about $2.50 per pound. The resulting markup comes to about 900 percent. Markups vary substantially from food to food even within the same restaurant. At the Sunset Grille in Nashville, demand restricts the restaurant’s ability to mark up its best tenderloin; thus the fairly small markup of 200 percent. However, like many restaurants, the Grille has a target markup of 300 percent. It makes up the difference on vegetables— both side dishes and vegetarian entrées are marked up by as much as 500 percent.

Why do these markups seem so outrageous? The Wall Street Journal reporter Eileen Daspin observes, “(T)o be fair, focusing on the cost of a restaurant meal’s raw ingredients is like calculating the value of a Picasso based on the cost of the paint.” Eating out as opposed to eating the same food at home involves many other costs, such as labor, capital (including lease payments, which can be extraordinary in popular downtown locations), and atmosphere. Nevertheless, some retaurants track costs of materials down to the last pinch of spice. Steve Uliss, chef-partner of Tennessee’s Real Barbecue Real Fast restaurants in Massachusetts, claims “If someone with a heavy hand is portioning out seven ounces of beans, we check it out.” In addition, if all of these markups make it seem like the restaurant business is a no-lose proposi- tion, think again. “According to Dun and Bradstreet, 100 out of every 10,000 U.S. restaurants failed in 1997,” notes Daspin.

1. Do ingredients represent a variable cost for restaurants? (Can they be substituted with labor or capital?) 2. If materials represent such a small fraction of total cost, they why would firms bother to look for employees who are “heavy handed” with the side orders?

DISCUSSION QUESTIONS

1. In the short run, are the following examples of fixed or variable costs? 2 Cohn, Elchanan, Sherrie L.W. Rhine, and Maria C. Santos, “Institutions of Higher Education as Multi-product Firms: Economies of Scale and Scope,” Review of Economics and Statistics, 71(2), May 1989: 284-90. 3 Based on Daspin, Eileen, “Entrée Economics,” The Wall Street Journal, March 10, 2000, W1, W4. 44 ❈ Part One\Teaching Aids a) A manufacturing firm builds a new plant. b) A doctor rents an office on a month-to-month basis. c) A firm hires an unskilled worker. d) A firm hires an engineer. 2. When would you expect a production possibility curve to be a straight line, and when would you expect that it would be bowed out away from the origin? 3. Does cost of production depend on demand for a product? 4. Give examples of firms where the long run is reached within a few weeks. Give other examples of where the long run takes years to reach. 5. Give some examples of joint production where you would expect to see economies of scope, no economies of scope, and diseconomies of scope. Explain why in each case. 6. Suppose we measure the output of a sports team as the number of fans that attend a game. Which team costs would be considered fixed, and which might be variable over the course of the season?

ADDITIONAL QUESTIONS AND MATH PROBLEMS

1. Suppose a firm employs labor as its only variable input. All workers are paid $20 per day. Output per day and variable cost are shown in Table 7.1 below. Complete the table, showing labor, average variable cost and marginal cost for the first eight units of output. Draw a graph showing average and marginal cost.

Table 7.1 q VC L AVC MC

120 240 360 480 5 120 6 160 7 240 8 320

2. True or False, explain your answer. “I paid $25 for the materials to make these flower arrangements, and sold them at the craft fair for $25, so I just broke even.”

3. Suppose a firm treats capital improvement projects as expenses rather than as investments (which are amortized). How might this affect the firm’s input usage decisions?

4. Suppose a firm’s average cost curve is described by the equation AC = 2q2-16q + 90. At what output level does the marginal cost curve cross the average cost curve?

5. Explain the relationship between the shape of the marginal cost curve and the marginal product of labor curve.

6. Use a graph to show the marginal cost of attendance for a movie theater (not including the cost of snacks, just attendance).

7. If input prices are w = 4, and r = 1, and q = 4K.5L.5, what is the least cost input combination required to produce 40 units of output? Suppose instead that capital was fixed at 16 units. What would be the implications for labor usage and total cost? Chapter 7\Costs ❈ 45 8. If input prices are w = 3, and r = 2, and q = 10KL, what is the least cost input combination required to produce 60 units of output? How would input usage change if output is increased to 240 units? Sketch the solutions on a graph.

9. In question #8, suppose the government, in an effort to increase employment, offers firms in this industry a $1 per unit subsidy. How would this affect input usage (assume q = 60). How is this likely to affect employment in the capital goods (K) industry?

10. Two firms currently produce the goods q1, and q2 separately. Their cost functions are C(q1) = 25 + q1, and C(q2) = 35 + 2q2. By merging, they can produce the two goods jointly with costs described by the function C(q1,q2) = 45 + q1 + q2. Are there scope economies in this case that would justify the merger?

ANSWERS TO ADDITIONAL QUESTIONS AND MATH PROBLEMS

1. See Table 7.2 and Figure 7.1 below.

Table 7.2

q VC L AVC MC

1 20 1 20 20 2 40 2 20 20 3 60 3 20 20 4 80 4 20 20 5 120 6 24 40 6 160 8 26.67 40 7 240 12 34.29 80 8 320 16 40 80

Figure 7.1

80 MC 70 60 50 40 AVC 30 20 10

12 345678 q 46 ❈ Part One\Teaching Aids 2. The statement is false because the individual has failed to account for the opportunity cost of his or her time. Unless the activity of craft-making produces utility as well (which for many, it does), this person has lost the value of his or her wage times the hours required to make the flower arrangements.

3. By expensing all costs of capital improvements in the current period, the firm will be biased toward increases in labor rather than capital. Capital improvements will only be made when their cost is less than the value of the increase in output in a single period, which is rarely the case. For this reason, firms must be careful to recognize the difference between expenditures that only increase output in the current period, and investments in capital goods that will increase output over several periods.

4. To find this point, recall that the marginal cost curve crosses the average cost curve at the minimum point of the average cost curve. To find the minimum, take the derivative of AC, and set it equal to zero.

dAC/dq = 4q Ð 16 = 0 q* = 4

Thus, MC = AC when output is four units.

5. MC and MPL are inverted images of one another. For a typical production function, with fixed input prices, marginal product rises at first, then falls as diminishing returns set in. The marginal cost curve falls while marginal product is rising because additional units of labor, purchased at a fixed price, produce increasing quantities of output. When marginal product begins to fall, marginal cost rises because more and more units of labor are required to produce an addition unit of output.

6. See Figure 7.2 The output level Q* represents capacity.

Figure 7.2

Q* Q, Attendance Chapter 7\Costs ❈ 47

7. As shown in equation 7B.7, minimizing cost requires that MRTS = w/r. Since MRTS = MPL /MPK, set the ratio of marginal products equal to the ratio of input prices, then substitute into the output constraint.

K/L = 4/1 40 = 4(4L).5L.5 = 8L L* = 5 K* = 20. C = 4(5) + 1(20) = 40

If capital is fixed at 16 units, least cost production is not possible. Instead, labor must be increased to 6.25 units. Total cost increases from $40 to $41.

8. Solve as above in problem 6. L* = 2, K* = 3. If output is increased but input prices remain the same with a Cobb-Douglas function, the input ratio does not change. L* = 4, K* = 6. See Figure 7.3.

Figure 7.3 K 12

6 Q = 240

3 Q = 60

L 24 6

9. The effective wage rate for the firm is reduced to $2 per unit. Re-solving with the new lower rate yields

K/L = 2/2 K = L 60 = 10(L)L L* = 2.44 K* = 2.44

Although the lower rate increases employment in this industry, employment is likely to fall in the capital industry, because fewer capital goods are demanded with subsidized wage rates. 48 ❈ Part One\Teaching Aids 10. Using the equation for scope economies given in Section 7.5 of the chapter, scope economies exist if SC>0. In this case, scope economies do exist as the following expression is greater than zero for all values of both outputs.

SC = [25 + q1 + 35 + q2 Ð (45 + q1 + q2)]/ 45 + q1 + q2