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The ability of market economies to supply material goods and services to members of their societies is one of the strongest arguments for using the market as a means of orga- nizing society. Just consider the coordination needed to pro- vide you a freshly brewed Starbucks latte in the morning. Trees had to be harvested and made into paper; the paper had to be processed and made into cups and printed with the Starbucks logo. Coffee beans had to be grown, picked, roasted, and ground. The espresso maker parts had to be made and assembled. The ingredients were produced in 20 different countries and shipped to a Starbucks near you at the right time and in the right quantities. Finally, a barista

had to be paid enough to prepare coffee (and label it with the customer’s misspelled name) when people want it—on the way to their jobs, in which they were producing goods that people from many other countries will end up consuming. Somehow markets are able to channel individuals’ imagination, creativity, and drive into the production of material goods and services that other people want. They do this by giving people incentives to supply goods and services to the market. Ultimately all supply comes from individuals. Individuals control the factors of production such as land, labor, and capital. Why do individuals supply these factors to the market? Because they want something in return. This means that industry’s ability to supply goods depends on individuals’ willingness to supply the factors of production they control. This connection was obvious in the formerly socialist countries such as Russia when consumer goods were often unavailable. People in those countries stopped working (supplying their labor). They reasoned: Why supply our labor if there’s nothing to get in return? The analysis of supply is more complicated than the analysis of demand. In the supply process, people first offer their factors of production to the market. Then the factors are transformed by firms, such as GM or IBM, into goods that consumers want. Production is the name given to that transformation of factors into goods and services. To simplify the analysis, economists separate out the consideration of the supply of factors of production (considered in detail in a later chapter) from the supply of produced goods. This allows us to assume that the prices of factors of production are constant, which simplifies the analysis of the supply of pro- duced goods enormously. There’s no problem with doing this as long as you remember that behind any produced good are individuals’ factor supplies. Ulti- mately people, not firms, are responsible for supply.

Production is not the application of tools to materials, but logic to work.

—Peter Drucker “ ”

chapter 11

Production and Cost Analysis I

After reading this chapter, you should be able to:

LO11-1 Explain the role of the firm in economic analysis.

LO11-2 Describe the production process in the short run.

LO11-3 Calculate fixed costs, variable costs, marginal costs, total costs, average fixed costs, average variable costs, and average total costs.

LO11-4 Distinguish the various cost curves and describe the relationships among them.

Chapter 11 Learning Map/Microeconomics_10th_Edition_by_David_Col 272.pdf

Production is not the application of tools to materials, but logic to work.

—Peter Drucker “ ”

chapter 11

Production and Cost Analysis I

After reading this chapter, you should be able to:

LO11-1 Explain the role of the firm in economic analysis.

LO11-2 Describe the production process in the short run.

LO11-3 Calculate fixed costs, variable costs, marginal costs, total costs, average fixed costs, average variable costs, and average total costs.

LO11-4 Distinguish the various cost curves and describe the relationships among them.

Chapter 11 Learning Map/Microeconomics_10th_Edition_by_David_Col 273.pdf

Chapter 11 ■ Production and Cost Analysis I 225

Even with the analysis so simplified, there’s still a lot to cover—so much, in fact, that I devote two chapters (this chapter and the next) to considering production, costs, and supply. In this chapter, I introduce you to the production process and short-run cost analysis. Then, in the next chapter, I focus on long-run costs and how cost analysis is used in the real world.

The Role of the Firm With goods that already exist, such as housing and labor, the law of supply is rather intuitive. Their supply to the market depends on people’s opportunity costs of keeping their houses and time for themselves and of supplying them to the market. But many of the things we buy (such as smartphones, cars, and jackets) don’t already exist; they must be conceived of and produced. The supply of such goods depends on production. Thus, for such goods, one needs a theory of production to underpin the theory of supply. A key concept in production is the firm. A firm is an economic institution that transforms factors of production into goods and services. A firm (1) organizes factors of production and/or (2) produces goods and/or (3) sells produced goods to individuals, businesses, or government. Which combination of activities a firm will undertake depends on the cost of undertaking each activity relative to the cost of subcontracting the work out to another firm. Some firms don’t have a physical location and don’t “produce” anything; they simply subcontract out all production. An example is Perdue chickens. Perdue does not raise any chickens itself. It hires farmers to raise chickens. It provides the farmers with chicks and a detailed set of directions about how to raise them into chickens. Perdue then hires another company to pick up the adult chickens for slaughter, puts its label on the processed chickens, and ships them to supermarkets. While most firms are not totally virtual, more and more of the organizational structures of businesses are being separated from the production process. As cost structures change because of techno- logical advances such as the Internet, an increasing number of well-known firms will likely concentrate on organizational instead of production activities.

Firms Maximize Profit Economists assume that firms maximize profit. Profit is defined as follows:

Profit = Total revenue − Total cost

In accounting, total revenue equals total sales times price; if a firm sells 1,000 pairs of earrings at $5 each, its total revenue is $5,000. For an accountant, total costs are the wages paid to labor, rent paid to owners of capital, interest paid to lenders, and actual payments to other factors of production. If the firm paid $2,000 to employees to make the earrings and $1,000 for the materials, rent, and interest, total cost is $3,000. In determining what to include in total revenue and total costs, accountants focus on such explicit revenues and explicit costs. That’s because they must have quantifi- able measures that go into a firm’s income statement. For this reason, you can think of accounting profit as explicit revenue less explicit cost. The accounting profit for the earring firm described above is $2,000.

The Difference between Economists’ Profits and Accountants’ Profits Economists have different measures of revenues and costs and hence have a different measure of profit. The difference is that economists’ specification of revenues and costs is based on opportunity costs, not accounting costs. So, economists include in

Firms:

1. Organize factors of production, and/or

2. Produce goods and services, and/or

3. Sell produced goods and services.

More and more of the organizational structures of business are being separated from the production process.

Accounting focuses on explicit costs and revenues; economics focuses on both explicit and implicit costs and revenues.

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revenue and costs both explicit and implicit costs and revenues. Their measure of profit is both explicit and implicit revenue less both explicit and implicit costs. As discussed in Chapter 2, implicit costs are costs that you don’t directly pay but that are part of the opportunity costs of a decision. Implicit revenues are revenues that you don’t receive but that increase your net wealth. Economists’ measure of profit includes these implicit costs and implicit revenues. Let’s consider some examples. Implicit costs include the opportunity costs of the factors of production provided by the owners of the business. Say that the owner of our earring firm could have earned $1,500 working elsewhere if she did not own the earring firm. The opportunity cost of working in her own business is $1,500. It is an implicit cost of doing business and would be included as a cost. For economists, total cost is explicit payments to the factors of production plus the opportunity cost of the factors provided by the owners of the firm. Total cost of the earring firm is $3,000 in explicit cost plus $1,500 in implicit cost, or $4,500. Generally, implicit costs must be estimated and are not directly measurable, which is why accountants do not include them. Implicit revenues include the increase in the value of assets. Say the earring firm owns a kiosk whose market value rises from $10,000 to $11,000. The economic con- cept of revenue would include the $1,000 increase in the value of the kiosk as part of total revenue. For economists, total revenue is the amount a firm receives for selling its product or service plus any increase in the value of the assets owned by the firm. Total revenue of the earring firm is $5,000 in explicit revenue plus $1,000 in implicit revenue, or $6,000. For economists,

Economic profit = (Explicit and implicit revenue) − (Explicit and implicit cost)

REAL-WORLD APPLICATION

In Chapter 3, we discussed the types of firms that exist in real life, and explained how they are one of the most im- portant of the economic institutions. They are the organi- zations that translate factors of production into consumer goods. Types of real-world firms include sole proprietor- ships, partnerships, corporations, for-profit firms, nonprofit firms, and cooperatives. Each type has its own problems, and organizational theory is a key area of research in eco- nomics. One of those areas of research considers why the nature of firms changes over time. Much of the research in organizational theory is based upon the work of Chicago economist Ronald Coase, who pointed out that in order to understand the firm, one must understand that how activities are organized in firms de- pends on the transaction costs (costs of undertaking trades through the market) it faces. Production internal to the firm reduces transaction costs but also can increase costs since internal-to-the-firm production involves com- mand and control and is not subject to the competition of the market. (Coase won a Nobel Prize for his work in 1991.) The Internet has lowered transaction costs, significantly changing how firms are organized. It used to be that firms hired employees for the long term. The most significant

Transaction Costs and the Internet transaction cost was the hiring—finding an employee who matched a need, negotiating pay, paying for the employee to move, and then training that employee. After hiring, transaction costs were pretty low; when a firm had a need, it assigned the project in-house, providing additional train- ing when necessary. The original transaction cost could be spread over a number of projects. Now a firm can identify a need and outsource the work by posting it on Internet sites such as freelancer.com for freelancers to bid on. The firm has no obligation to the freelancer other than to pay for the service, which lowers the transaction cost enormously. The freelancer can be anywhere in the world, working in any time zone, and proj- ect managers can oversee the work through online com- munications such as WebEx or Skype. Setting up a clothing line and need a fashion designer? Need to develop a web- site? Post the project online. The key point to remember is that as transaction costs change, the efficient structure of firms changes, which brings about a change in the nature of firms. Whereas large com- mand and control companies such as IBM once arose to lower transaction costs, now in some industries the efficient firms are small, fragmenting production into ever smaller parts.

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So in this case, economic profit is ($5,000 + $1,000) − ($3,000 + $1,500) = $1,500. The difference really has to do with measurability. Implicit costs must be estimated, and the estimations can sometimes be inexact. General accounting rules do not permit such inexactness because it might allow firms to misstate their profit, something accounting rules are designed to avoid.

The Production Process As I stated at the beginning of the chapter, supply is the key to the market’s ability to provide the goods people want. Underlying supply is production; firms are important because they control the production process.

Q-1 What distinguishes accounting profit from economic profit?

ADDED DIMENSION

the firm’s total output less the cost of the inputs bought from other firms. For example, if a desk assembly firm spends $4,000 on component parts and sells its output for $6,000, its value added is $2,000, or 33⅓ percent of its revenue.

When you add up all the stages of production, the value added of all the firms in- volved must equal 100 per- cent, and no more, of the total output. When I discuss “a firm’s” production of a good in this book, to relate that dis- cussion to reality, you should think of that firm as a compos- ite of all the firms contributing to the production and distri- bution of that product.

Why is it important to re- member that there are various stages of production? Be- cause it brings home to you

how complicated producing a good is. If any one stage gets messed up, the good doesn’t get to the consumer. Producing a better mousetrap isn’t enough. The firm also must be able to get it out to consumers and let them know that it’s a better mousetrap. The traditional economic model doesn’t bring home this point. But if you’re ever planning to go into business for yourself, you’d better re- member it. Many people’s dreams of supplying a better product to the market have been squashed by this reality.

Value Added and the Calculation of Total Production This book (like all economics textbooks) treats production as if it were a one-stage process—as if a single firm transforms a factor of produc- tion into a consumer good. Economists write like that to keep the analysis manage- able. (Believe me, it’s compli- cated enough.) But you should keep in mind that real- ity is more complicated. Most goods go through a variety of stages of production. For example, consider the production of desks. One firm transforms raw materials into usable raw materials (iron ore into steel); another firm trans- forms usable raw materials into more usable inputs (steel into steel rods, bolts, and nuts); another firm transforms those inputs into desks, which it sells wholesale to a general distributor, which then sells them to a retailer, which sells them to consum- ers. Many goods go through five or six stages of production and distribution. As a result, if you added up all the sales of all the firms, you would overstate how much total production was taking place. To figure out how much total production is actually tak- ing place, economists use the concept value added. Value added is the contribution that each stage of production makes to the final value of a good. A firm’s value added is

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228 Microeconomics ■ Production and Cost Analysis

The Long Run and the Short Run The production process is generally divided into a long-run planning decision, in which a firm chooses the least expensive method of producing from among all possible methods, and a short-run adjustment decision, in which a firm adjusts its long-run planning decision to reflect new information. In a long-run decision, a firm chooses among all possible production techniques. This means that it can choose the size of the plant it wants, the type of machines it wants, and the location it wants. The firm has fewer options in a short-run decision, in which the firm is constrained in regard to what production decisions it can make. The terms long run and short run do not necessarily refer to specific periods of time independent of the nature of the production process. They refer to the degree of flexibility the firm has in changing its inputs. In the long run, by definition, the firm can vary the inputs as much as it wants. In the short run, some of the flexibility that existed in the long run no longer exists. In the short run, some inputs are so costly to adjust that they are treated as fixed. So in the long run, all inputs are variable; in the short run, some inputs are fixed.

Production Tables and Production Functions How a firm combines factors of production to produce goods and services can be pre- sented in a production table (a table showing the output resulting from various com- binations of factors of production or inputs). Real-world production tables are complicated. They often involve hundreds of inputs, hundreds of outputs, and millions of possible combinations of inputs and outputs. Studying these various combinations and determining which is best requires expertise and ex perience. Business schools devote entire courses to it (operations research and produc- tion analysis); engineering schools devote entire specialties to it (industrial engineering). Studying the problems and answering the questions that surround production is much of what a firm does: What combination of outputs should it produce? What com- bination of inputs should it use? What combination of techniques should it use? What new techniques should it explore? To answer these questions, the managers of a firm look at a production table. Production tables are so complicated that in introductory economics we concentrate on short-run production analysis in which one of the factors is fixed. Doing so allows us to capture some important technical relationships of production without getting too tied up in numbers. The relevant part of a production table of earrings appears in Figure 11-1(c). In it the number of the assumed fixed inputs (machines) has already been determined. Columns 1 and 2 of the table tell us how output of earrings varies as the variable input (the number of workers) changes. For example, you can see that with 3 workers the firm can produce 17 pairs of earrings. Column 3 tells us workers’ marginal product (the additional output that will be forthcoming from an additional worker, other inputs constant). Column 4 tells us workers’ average product (output per worker). It is important to distinguish marginal product from average product. Workers’ average product is the total output divided by the number of workers. For example, let’s consider the case of 5 workers. Total output is 28, so average product is 5.6 (28 divided by 5). To find the marginal product, we must ask how much additional output will be forthcoming if we change the number of workers. For example, if we change from 4 to 5 workers, the additional worker’s marginal product will be 5; if we change from 5 to 6, the additional worker’s marginal product will be 3. That’s why the mar- ginal products are written between each level of output. The information in a production table is often summarized in a production function. A production function is the relationship between the inputs (factors of production) and outputs. Specifically, the production function tells the maximum amount of output that

A long-run decision is a decision in which the firm can choose among all possible production techniques.

A short-run decision is a decision in which the firm is constrained in regard to what production decisions it can make.

The marginal product is the additional output forthcoming from an additional input, other inputs constant; the average product is the total output divided by the quantity of the input.

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Chapter 11 ■ Production and Cost Analysis I 229

can be derived from a given number of inputs. Figure 11-1(a) is the production function that displays the information in the production table in Figure 11-1(c). The number of workers is on the horizontal axis and the output of earrings is on the vertical axis.

The Law of Diminishing Marginal Productivity Figure 11-1(b) graphs the workers’ average and marginal productivities from the produc- tion function in Figure 11-1(a). [Alternatively you can determine those graphs by plotting columns 3 and 4 from the table in Figure 11-1(c).] Notice that both marginal and average productivities are initially increasing, but that eventually they both decrease. Between 7 and 8 workers, the marginal productivity of workers actually becomes negative. This means that initially this production function exhibits increasing marginal pro- ductivity and then it exhibits diminishing marginal productivity. Eventually it exhibits negative marginal productivity. The same information can be gathered from Figure 11-1(a), but it’s a bit harder to interpret.1 Notice that initially the production function is bowed upward. Where it’s bowed upward there is increasing marginal productivity, as you can see if you extend

Q-2 What are the normal shapes of marginal productivity and average productivity curves?

FIGURE 11-1 (A, B, AND C) A Production Table and Production Function

The production function in (a) is a graph of the production table in (c). Its shape reflects the underlying production technology. The graph in (b) shows the marginal and average product. Notice that when marginal product is increasing, the production function is bowed upward; when marginal product is decreasing, the production function is bowed downward; when marginal product is zero, the production function is at its highest point. Firms are interested in producing where both average product and marginal product are positive and falling, which starts at 4 workers and ends at 7.5 workers.

O u

tp u

t O

u tp

u t

p e

r w

o rk

e r

(a)

(b)

Highest output possible

Diminishing marginal

productivity

Diminishing absolute

productivity

32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

1 2 3 4 5 6 7 8 9 10

Increasing marginal

productivity

Number of workers

Increasing marginal productivity

Diminishing marginal productivity

Diminishing absolute productivity

4 6 7 6 5 3 1 0 −2 −5

(1 ) (2) (3) (4) Average Marginal Product Product (total product/ Number of Total (change in number of Workers Output total output) workers)

1 4 4 2 10 5 3 17 5.7 4 23 5.8 5 28 5.6 6 31 5.2 7 32 4.6 8 32 4.0 9 30 3.3 10 25 2.5

(c)

1Technically the marginal productivity curve is a graph of the slope of the total product curve.

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230 Microeconomics ■ Production and Cost Analysis

a line down to Figure 11-1(b). Then, between 2.5 and 7.5 workers, the production function is bowed downward but is still rising. In this range, there’s diminishing mar- ginal productivity, as you can see by extending a line down to Figure 11-1(b). Finally marginal productivity is negative. The most important area of these relationships is the area of diminishing marginal productivity (between 2.5 and 7.5 workers). Why? Because a firm is most likely to oper- ate in that area. If it’s in the first range and marginal productivity is increasing, a firm can increase its existing workers’ output by hiring more workers; it will have a strong incen- tive to do so and get out of that range. Similarly, if hiring an additional worker actually cuts total output (as it does when marginal productivity is negative), the firm would be crazy to hire that worker. So it stays out of that range. This range of the relationship between fixed and variable inputs is so important that economists have formulated a law that describes what happens in production processes when firms reach this range—when more and more of one input is added to a fixed amount of another input. The law of diminishing marginal productivity states that as more and more of a variable input is added to an existing fixed input, eventually the additional output one gets from that additional input is going to fall. The law of diminishing marginal productivity is sometimes called the flowerpot law because if it didn’t hold true, the world’s entire food supply could be grown in one flowerpot. In the absence of diminishing marginal productivity, we could take a flow- erpot and keep adding seeds to it, getting more and more food per seed until we had enough to feed the world. In reality, however, a given flowerpot is capable of producing only so much food no matter how many seeds we add to it. At some point, as we add more and more seeds, each additional seed will produce less food than did the seed before it. That’s the law of diminishing marginal productivity in action. Eventually the pot reaches a stage of diminishing absolute productivity, in which the total output, not simply the output per unit of input, decreases as inputs are increased.

The Costs of Production In any given firm, owners and managers probably discuss costs far more than anything else. Invariably costs are too high and the firm is trying to figure out ways to lower them. But the concept costs is ambiguous; there are many different types of costs and it’s important to know what they are. Let’s consider some of the most important cate- gories of costs in reference to Table 11-1, which shows costs associated with making between 3 and 32 pairs of earrings.

Fixed Costs, Variable Costs, and Total Costs Fixed costs are costs that are spent and cannot be changed in the period of time under consideration. There are no fixed costs in the long run since all inputs are variable and hence their costs are variable. In the short run, however, a number of costs will be fixed. For example, say you make earrings. You buy a machine for working with silver, but suddenly there’s no demand for silver earrings. Assuming that machine can’t be modified and used for other purposes, the money you spent on it is a fixed cost. So within this model, all fixed costs are assumed to be sunk costs. Fixed costs are shown in column 2 of Table 11-1. Notice that fixed costs remain the same ($50) regardless of the level of production. As you can see, it doesn’t matter whether output is 3 or 32; fixed costs are always $50. Besides buying the machine, the silversmith must also hire workers. These workers are the earring firm’s variable costs—costs that change as output changes. The earring firm’s variable costs are shown in column 3. Notice that as output increases,

Q-3 Firms are likely to operate on what portion of the marginal productivity curve?

The law of diminishing marginal productivity states that as more and more of a variable input is added to an existing fixed input, after some point the additional output one gets from the additional input will fall.

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Chapter 11 ■ Production and Cost Analysis I 231

variable costs increase. For example, when the firm produces 9 pairs of earrings, vari- able costs are $100; when it produces 10, variable costs rise to $108. All costs are either fixed or variable in the standard model, so the total cost is the sum of the fixed and variable costs:

TC = FC + VC

The earring firm’s total costs are presented in column 4. Each entry in column 4 is the sum of the entries in columns 2 and 3 in the same row. For example, to produce 16 pairs of earrings, fixed costs are $50 and variable costs are $150, so total cost is $200.

Average Costs Total cost, fixed cost, and variable cost are important, but much of a firm’s discussion is about average cost. So the next distinction we want to make is between total cost and average cost. To arrive at the earring firm’s average cost, we simply divide the total amount of whatever cost we’re talking about by the quantity produced. Each of the three costs we’ve discussed has a corresponding average cost. For example, average total cost (often called average cost) equals total cost divided by the quantity produced. Thus:

ATC = TC/Q

Average fixed cost equals fixed cost divided by quantity produced:

AFC = FC/Q

Average variable cost equals variable cost divided by quantity produced:

AVC = VC/Q

TC = FC + VC

To arrive at the earring firm’s average cost, we simply divide the total amount of whatever cost we’re talking about by the quantity produced.

Q-4 If total costs are $400, fixed costs are 0, and output is 10, what are average variable costs?

TABLE 11-1 The Cost of Producing Earrings

(1) (2) (3) (4) (5) (6) (7) (8) Marginal Costs (MC) (change in total costs/ Average Average Variable Average Total Fixed Variable Total Costs (TC) change in Fixed Costs (AFC) Costs (AVC) Costs (ATC) Output Costs (FC) Costs (VC) (FC + VC) output) (FC/Output) (VC/Output) (AFC + AVC)

3 $50 $ 38 $ 88 $12

$16.67 $12.66 $29.33 4 50 50 100 12.50 12.50 25.00

9 50 100 150 8

5.56 11.11 16.67 10 50 108 158 5.00 10.80 15.80 16 50 150 200

7 3.12 9.38 12.50

17 50 157 207 2.94 9.24 12.18 22 50 200 250

10 2.27 9.09 11.36

23 50 210 260 2.17 9.13 11.30 27 50 255 305

15 1.85 9.44 11.29

28 50 270 320 1.79 9.64 11.43 32 50 400 450 1.56 12.50 14.06

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232 Microeconomics ■ Production and Cost Analysis

Average fixed cost and average variable cost are shown in columns 6 and 7 of Table 11-1. The most important average cost concept, average total cost, is shown in column 8. Average total cost also can be thought of as the sum of average fixed cost and average variable cost:

ATC = AFC + AVC

As you can see, the average total cost of producing 16 pairs of earrings is $12.50. It can be calculated by dividing total cost ($200) by output (16).

Marginal Cost All these costs are important to our earring firm, but they are not the most important costs it considers when deciding how many pairs of earrings to produce. That distinction goes to marginal cost, which appears in column 5.2 Marginal cost is the increase

Marginal cost is the increase (decrease) in total cost from increasing (decreasing) the level of output by 1 unit.

2Since only selected output levels are shown, not all entries have marginal costs. For a marginal cost to exist, there must be a marginal change, a change by only 1 unit.

Thinking Like a Modern Economist What “Goods” Do Firms Produce? The Costs of Producing Image

The textbook economic models are implicitly struc- tured around the production of physical goods that require physical inputs. Such physical goods have become less important in the modern economy. In today’s economy, many of the goods that firms pro- duce involve intangibles such as image and percep- tion. For example, Starbucks is not only producing coffee; it is also producing an image of luxury, so when you buy a Frappuccino, you are actually buying something that makes you feel good about yourself—you see yourself as a quality person. Or when you buy a car—you are not just buying a car—you are buying an image for yourself. Modern firms spend enormous time and effort trying to associate whatever they are selling with an image that people want to associate with themselves. Image is real, and has real effects. For example, experimental economists have shown that people re- spond better to medicine with a high price than to that same medicine with a low price. (This is a varia- tion of the well-known placebo effect in medicine; people get better from taking a sugar pill if they think it is a medicine that is going to help them.) Producing “image” rather than physical products affects both the structure of costs and how costs are analyzed. Specifically, producing image tends to require large expenditures not directly related to

production of any specific good that the firm pro- duces. It might involve:

• Advertising that has little to do with the product. (“Just do it” could apply to any number of goods, not just sneakers.)

• Buying only the highest-price coffee beans even though lower-price coffee might taste just as good, or better. (Do you buy Dunkin’ Donuts, Starbucks, or Blue Bottle brand?)

• Associating the firm’s name with something positive, for example, underwriting the cost of a stadium. (Think of Busch Stadium in St. Louis.)

• Supporting a local sports team or public radio station. (According to one study, 88 percent of public radio listeners say their opinion of a company is more positive when they discover the company supports public radio.)

These expenditures might seem inconsistent with profit maximizing until one recognizes that the firm is selling its image. These indirect costs of creating image are not quite fixed costs—since they must be made continually if the firm is to maintain its good’s image—but they are not variable costs either, since they do not vary with output of the product. Modern economists’ more advanced models of costs capture these distinctions.

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Chapter 11 ■ Production and Cost Analysis I 233

(decrease) in total cost from increasing (decreasing) the level of output by 1 unit. Let’s find marginal cost by considering what happens if our earring firm increases production by 1 unit—from 9 to 10. Looking again at Table 11-1, we see that the total cost rises from $150 to $158. In this case, the marginal cost of producing the 10th unit is $8.

Graphing Cost Curves Let’s say that the owner of the earring firm sees things better in pictures and asks you (an economic consultant) to show her what all those numbers in Table 11-1 mean. To do so, you first draw a graph, putting quantity on the horizontal axis and a dollar mea- sure of various costs on the vertical axis.

Total Cost Curves Figure 11-2(a) graphs the total cost, total fixed cost, and total variable cost for all the levels of output given in Table 11-1.3 The total cost curve is determined by plotting the entries in column 1 and the corresponding entries in column 4. For example, point L corresponds to a quantity of 10 and a total cost of $158. Notice that the total cost curve is upward-sloping: Increasing output increases total cost. The total fixed cost curve is determined by plotting column 1 and column 2 on the graph. The total variable cost curve is determined by plotting column 1 and column 3. As you can see, the total variable cost curve has the same shape as the total cost curve: Increasing output increases variable cost. This isn’t surprising, since the total cost curve is the vertical summation of total fixed cost and total variable cost. For example,

3To keep the presentation simple, we focus only on the most important part of the total cost curve, that part that follows the simplest rules. Other areas of the total cost curve can be bowed downward rather than bowed upward.

To ta

l c o

108

158

400

$450

(TC = VC + FC ) TC

10 32 Quantity of earrings

(a) Total Cost Curves (b) Per-Unit Output Cost Curves

C o

ATC AVC

AFC

Quantity of earrings 10 20 30

$30

FIGURE 11-2 (A AND B) Total and Per-Unit Output Cost Curves

Total fixed costs, shown in (a), are always constant; they don’t change with output. All other total costs increase with output. As output gets high, the rate of increase has a tendency to increase. The average fixed cost curve, shown in (b), is downward-sloping; the average variable cost curve and average total cost curve are U-shaped. The U-shaped MC curve goes through the minimum points of the AVC and ATC curves. (The AFC curve is often not drawn since AFC is also represented by the distance between the AVC and ATC.)

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234 Microeconomics ■ Production and Cost Analysis

at output 10, total fixed cost equals $50 (point M); total variable cost equals $108 (point O); and total cost equals $158 (point L).

Average and Marginal Cost Curves Figure 11-2(b) presents the average fixed cost curve, average total cost curve (or average cost curve, as it’s generally called), average variable cost curve, and marginal cost curve associated with the cost figures in Table 11-1. As was the case with the total cost curves, all the firm’s owner needs to do is look at this graph to find the various costs associated with different levels of output, since the graphical visualization of cost curves provides a good sense of what happens to costs as we change output. Let’s start our consideration with average fixed cost. Average fixed cost is decreasing throughout.

DownwarD-Sloping Shape of the average fixeD CoSt Curve The average fixed cost curve looks like a child’s slide: It starts out with a steep decline; then it becomes flatter and flatter. What this tells us about production is straightfor- ward: As output increases, the same fixed cost can be spread over a wider range of output, so average fixed cost falls. Average fixed cost initially falls quickly but then falls more and more slowly. As the denominator gets bigger while the numerator stays the same, the increase has a smaller and smaller effect.

the u Shape of the average CoSt CurveS Let’s now move on to the average cost curves. Why do they have the shapes they do? Or, expressed another way, how does our analysis of production relate to our analysis of costs? You may have already gotten an idea of how production and costs relate if you remembered Figure 11-1 and recognized the output numbers that we presented were similar output numbers to those that we used in the cost analysis. Cost analysis is simply another way of consid- ering production analysis. The laws governing costs are the same laws governing productivity. In the short run, output can be raised only by increasing the variable input. But as more and more of a variable input is added to a fixed input, the law of diminishing marginal productivity enters in. Marginal and average productivities fall. The key insight here is that when marginal productivity falls, marginal cost must rise, and when average productivity falls, average variable cost must rise. So to say that productivity falls is equivalent to saying that cost rises. It follows that if eventually the law of diminishing marginal productivity holds true, then eventually both the marginal cost curve and the average cost curve must be upward-sloping. And, indeed, in our examples they are. It’s also generally assumed that at low levels of production, marginal and average productivities are increasing. This means that marginal cost and average variable cost are initially falling. If they’re falling initially and rising eventually, at some point they must be neither rising nor fall- ing. This means that both the marginal cost curve and the average variable cost curve are U-shaped. As you can see in Figure 11-2(b), the average total cost curve has the same general U shape as the average variable cost curve. It has the same U shape because it is the vertical summation of the average fixed cost curve and the average vari- able cost curve. Its minimum, however, is to the right of the minimum of the aver- age variable cost curve. We’ll discuss why after we cover the shape of the average variable cost curve.

The marginal cost curve goes through the minimum point of the average total cost curve and average variable cost curve; each of these curves is U-shaped. The average fixed cost curve slopes down continuously.

Q-5 Draw a graph of both the marginal cost curve and the average cost curve.

As more and more of a variable input is added to a fixed input, the law of diminishing marginal productivity causes marginal and average productivities to fall. As these fall, marginal and average costs rise.

Q-6 What determines the distance between the average total cost and the average variable cost?

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Chapter 11 ■ Production and Cost Analysis I 235

Average total cost initially falls faster and then rises more slowly than average variable cost. If we increased output enormously, the average variable cost curve and the average total cost curve would almost meet. Average total cost is of key importance to the firm’s owner. She wants to keep it low.

the relationShip between the Marginal proDuCtivity anD Mar- ginal CoSt CurveS Let’s now consider the relationship between marginal prod- uct and marginal cost. In Figure 11-3(a), I draw a marginal cost curve and average variable cost curve. Notice their U shape. Initially costs are falling. Then there’s some minimum point. After that, costs are rising. In Figure 11-3(b), I graph the average and marginal productivity curves similar to those that I presented in Figure 11-1(b), although this time I relate average and marginal productivities to output, rather than to the number of workers. This allows us to relate output per worker and output. Say, for example, that we know that the average

If MP > AP, then AP is rising. If MP < AP, then AP is falling.

FIGURE 11-3 (A AND B) The Relationship between Productivity and Costs

The shapes of the cost curves are mirror-image reflections of the shapes of the corresponding productivity curves. (The corresponding productivity curve is an implicit function in which marginal productivity is related to output rather than inputs. At each output there is an implicit number of workers who would supply that output.) When one is increasing, the other is decreasing; when one is at a minimum, the other is at a maximum.

When marginal cost exceeds average cost, average cost must be rising. When marginal cost is less than average cost, average cost must be falling. This relationship explains why marginal cost curves always intersect the average cost curve at the minimum of the average cost curve.

C o

st s

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r u

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O u

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w o

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(a)

(b)

$16

2112

2110 12

Output

AVC

AP of workers

MP of workers

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236 Microeconomics ■ Production and Cost Analysis

product of 2 workers is 5, and that 2 workers can produce an output of 10. This means that when output is 10, the workers’ average productivity is 5. By continuing this reasoning, we can construct the curves. Point A corresponds to an output of 10 and average productivity of 5. Now let’s compare the graphs in Figure 11-3 (a and b). If you look at the two graphs carefully, you’ll see that one is simply the mirror image of the other. The minimum point of the average variable cost curve (output = 21) is at the same level of output as the maximum point of the average productivity curve; the minimum point of the marginal cost curve (output = 12) is at the same level of output as the maximum point on the marginal productivity curve. When the productivity curves are falling, the corresponding cost curves are rising. Why is that the case? Because as productivity falls, costs per unit increase; and as productivity increases, costs per unit decrease.

the relationShip between the Marginal CoSt anD average CoSt CurveS Now that we’ve considered the shapes of each cost curve, let’s consider some of the important relationships among them—specifically the relationships between the marginal cost curve on the one hand and the average variable cost and average total cost curves on the other. These general relationships are shown graphi- cally in Figure 11-4. Let’s first look at the relationship between marginal cost and average total cost. In the green shaded and yellow shaded areas (areas A and B) at output below Q1, even though marginal cost is rising, average total cost is falling. Why? Because, in areas A and B, the marginal cost curve is below the average total cost curve. At point B, where average total cost is at its lowest, the marginal cost curve intersects the average total cost curve. In area C, above output Q1, where average total cost is rising, the marginal cost curve is above the ATC curve.

Q-7 When marginal cost equals the minimum point of average variable cost, what is true about the average productivity and marginal productivity of workers?

When the productivity curves are falling, the corresponding cost curves are rising.

FIGURE 11-4 The Relationship of Marginal Cost Curve to Average Variable Cost and Average Total Cost Curves

The marginal cost curve goes through the minimum points of both the average variable cost curve and the average total cost curve. Thus, there is a small range where average total costs are falling and average variable costs are rising. C

o st

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Output

Q1Q0

ATC

AVC

Area A Area C

A re

a B

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Chapter 11 ■ Production and Cost Analysis I 237

The positioning of the marginal cost curve is not happenstance. The position of marginal cost relative to average total cost tells us whether average total cost is rising or falling.

If MC > ATC, then ATC is rising. If MC = ATC, then ATC is at its low point. If MC < ATC, then ATC is falling.

To understand why this is, think of it in terms of your grade point average. If you have a B average and you get a C on the next test (that is, your marginal grade is a C), your grade point average will fall below a B. Your marginal grade is below your aver- age grade, so your average grade is falling. If you get a C+ on the next exam (that is, your marginal grade is a C+), even though your marginal grade has risen from a C to a C+, your grade point average will fall. Why? Because your marginal grade is still below your average grade. To make sure you understand the concept, explain the next two cases:

1. If your marginal grade is above your average grade, your average grade will rise.

2. If your marginal grade and average grade are equal, the average grade will remain unchanged.

Marginal and average reflect a general relationship that also holds for marginal cost and average variable cost.

If MC > AVC, then AVC is rising. If MC = AVC, then AVC is at its low point. If MC < AVC, then AVC is falling.

This relationship is best seen in the yellow shaded area (area B) of Figure 11-4, when output is between Q0 and Q1. In this area, the marginal cost curve is above the average variable cost curve, so average variable cost is rising; but the MC curve is below the average total cost curve, so average total cost is falling. The intuitive expla- nation for the relationship in this area is that average total cost includes average vari- able cost, but it also includes average fixed cost, which is falling. As long as short-run marginal cost is only slightly above average variable cost, the average total cost will continue to fall. Put another way: Once marginal cost is above average variable cost, as long as average variable cost doesn’t rise by more than average fixed cost falls, average total cost will still fall.

Intermission At this point I’m going to cut off the chapter, not because we’re finished with the sub- ject, but because there’s only so much that anyone can absorb in one chapter. It’s time for a break. Those of you with significant others, go out and do something significant. Those of you with parents bearing the cost of this education, give them a call and tell them that you appreciate their expenditure on your education. Think of the opportunity cost of that education to them; it’s not peanuts. Those of you who are married should go out and give your spouse a big kiss; tell him or her that the opportunity cost of being away for another minute was so high that you couldn’t control yourself. Those of you with kids, go out and read them a Dr. Seuss book. (My favorite is about Horton.) Let’s face it—Seuss is a bet- ter writer than I, and if you’ve been conscientious about this course, you may not have paid your kids enough attention. We’ll return to the grind in the next chapter.

Q-8 If marginal costs are increasing, what is happening to average total costs?

Q-9 If marginal costs are decreasing, what must be happening to average variable costs?

Q-10 Why does the marginal cost curve intersect the average variable cost curve at the minimum point?

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A REMINDER

A Review of Costs

Average variable cost AVC = VC/Q

Average total cost ATC = AFC + AVC = TC/Q

AFC = FC/Q

Fixed cost Cost that is already spent and cannot be recovered. It exists only in the short run.

Average fixed cost Fixed costs per unit of production.

Variable cost Costs that vary with production.

Variable costs per unit of production.

Total cost The sum of all costs of inputs used by a firm in production.

Total cost per unit of production.

TC = FC + VC

Marginal cost The additional cost resulting from a 1-unit increase in output.

MC = ΔTC

Term Definition Equation

• Accounting profit is explicit revenue less explicit cost. Economists include implicit revenue and cost in their determination of profit. (LO11-1)

• Implicit revenue includes the increases in the value of assets owned by the firm. Implicit costs include the opportunity cost of time and capital provided by the owners of the firm. (LO11-1)

Summary • In the long run, a firm can choose among all possible

production techniques; in the short run, the firm is constrained in its choices. (LO11-2)

• The law of diminishing marginal productivity states that as more and more of a variable input is added to a fixed input, the additional output the firm gets will eventually be decreasing. (LO11-2)

238

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Chapter 11 ■ Production and Cost Analysis I 239

• Costs are generally divided into fixed costs, variable costs, and total costs. (LO11-3)

• TC = FC + VC; MC = Change in TC; AFC = FC/Q; AVC = VC/Q; ATC = AFC + AVC.

(LO11-3) • The average variable cost curve and marginal cost curve

are mirror images of the average product curve and the marginal product curve, respectively. (LO11-4)

• The law of diminishing marginal productivity causes marginal and average costs to rise. (LO11-4)

• If MC > ATC, then ATC is rising. If MC = ATC, then ATC is constant. If MC < ATC, then ATC is falling. (LO11-4) • The marginal cost curve goes through the minimum

points of the average variable cost curve and average total cost curve. (LO11-4)

Key Terms

average fixed cost average product average total cost average variable cost economic profit

firm fixed cost law of diminishing

marginal productivity long-run decision

marginal cost marginal product production production function production table

profit short-run decision total cost total revenue variable cost

Questions and Exercises

1. What costs and revenues do economists include when calculating profit that accountants don’t include? Give an example of each. (LO11-1)

2. Peggy-Sue’s cookies are the best in the world, or so I hear. She has been offered a job by Cookie Monster, Inc., to come to work at $125,000 per year. Currently, she is producing her own cookies, and she has revenues of $260,000 per year. Her costs are $40,000 for labor, $10,000 for rent, $35,000 for ingredients, and $5,000 for utilities. She has $100,000 of her own money invested in the operation, which, if she leaves, can be sold for $400,000 that she can invest at 1 percent per year. (LO11-1) a. Calculate her accounting and economic profits. b. Advise her as to what she should do.

3. Economan has been infected by the free enterprise bug. He sets up a firm on extraterrestrial affairs. The rent of the building is $4,000, the cost of the two secretaries is $40,000, and the cost of electricity and gas comes to $5,000. There’s a great demand for his information, and his total revenue amounts to $100,000. By working in the firm, though, Economan forfeits the $50,000 he could earn by working for the Friendly Space Agency and the $4,000 he could have earned as interest had he

saved his funds instead of putting them in this business. (LO11-1) a. What is his profit or loss by an accountant’s definitions? b. What is his profit or loss by an economist’s definitions?

4. What distinguishes the short run from the long run? (LO11-2)

5. What is the difference between marginal product and average product? (LO11-2)

6. Explain how studying for an exam is subject to the law of diminishing marginal productivity. (LO11-2)

7. Find TC, AFC, AVC, AC, and MC from the following table. (LO11-3)

Units FC VC

0 $100 $ 0 1 100 40 2 100 60 3 100 70 4 100 85 5 100 130

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240 Microeconomics ■ Production and Cost Analysis

8. For each of the following indicate what costs are being calculated: (LO11-3) a. FC + VC b. TC/Q c. FC/Q d. VC/Q e. AFC + AVC

9. Classify each of the following as fixed or variable costs: (LO11-3) a. Outsourced payroll services. b. Leased offices. c. Company-owned building. d. Payroll taxes.

10. Which of the costs discussed in the chapter is the most important when a firm is deciding how much to produce? (LO11-3)

11. Explain how each of the following will affect the average fixed cost, average variable cost, average total cost, and marginal cost curves faced by a steel manufacturer: (LO11-3) a. New union agreement increases hourly pay. b. Local government imposes an annual lump-sum tax

per plant. c. Federal government imposes a “stack tax” on emission

of air pollutants by steel mills. d. New steelmaking technology increases productivity of

every worker. 12. Graph the following table. (LO11-4)

14. If marginal cost is increasing, what do we know about average cost? (LO11-4)

15. A firm has fixed costs of $100 and variable costs of the following: (LO11-4)

Output 1 2 3 4 5 6 7 8 9 Variable costs $35 75 110 140 175 215 260 315 390

a. Show AFC, ATC, AVC, and MC in a table. b. Graph the AFC, ATC, AVC, and MC curves. c. Explain the relationship between the MC curve and the

AVC and ATC curves. d. Say fixed costs dropped to $50. Which curves shifted?

Why? 16. If average productivity falls, will marginal cost necessarily

rise? How about average cost? (LO11-4) 17. An economic consultant is presented with the following total

product table and asked to derive a table for average variable costs. The price of labor is $15 per hour. (LO11-4)

Number of Total Workers Output

0 0 1 20 2 60 3 150 4 260 5 350 6 420 7 455 8 420 9 375 10 300

a. What is marginal product and average product at each level of production?

b. Graph marginal product and average product. c. Label the areas of increasing marginal productivity,

diminishing marginal productivity, and diminishing absolute productivity.

13. If average product is falling, what is happening to short- run average variable cost? (LO11-4)

Labor TP

1 5 2 15 3 30 4 36 5 40

a. Help him do so. b. Show that the graphs of the average productivity curve

and average variable cost curve are mirror images of each other.

c. Show the marginal productivity curve for labor inputs between 1 and 5.

d. Show that the marginal productivity curve and mar- ginal cost curve are mirror images of each other.

18. Say that a firm has fixed costs of $100 and constant average variable costs of $25. (LO11-4) a. Show AFC, VC, AVC, and MC in a table. b. Graph the AFC, ATC, AVC, and MC curves. c. Explain why the curves have the shapes they do. d. What law is not operative for this firm?

19. Say a firm has $100 in fixed costs and its average variable costs increase by $5 for each unit, so that the cost of 1 is $25, the cost of 2 is $30, the cost of 3 is $35, and so on. (LO11-4) a. Show VC, AFC, AVC, and MC in a table. b. Graph the AFC, ATC, AVC, and MC curves associated

with these costs. c. Explain how costs would have to increase in order for

the curves to have the “normal” shapes of the curves presented in the text.

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Chapter 11 ■ Production and Cost Analysis I 241

Questions from Alternative Perspectives

1. The text presents very detailed cost tables when it considers the decisions of firms. a. Do entrepreneurs have such cost tables available to

them when they enter a business? b. If not, how do they gather such information? c. If such information is gathered through trial and error,

what implications does that have for government intervention in the marketplace? (Austrian)

2. Say that a drug firm could increase its profit by marketing a drug that it knows might have serious side effects. Say also that it knows that it can never be prosecuted for doing so. a. Would it? b. Should it? (Religious)

3. The analysis in the book suggests that firms hire inputs so that they hold costs as low as possible. Yet, as Gloria Steinem has pointed out, looking at reality one sees men selling refrigerators and women selling men’s underwear. a. Do you believe that that allocation of jobs reflects

firms trying to minimize costs because of the relative expertise of women and men?

b. If not, what does it reflect? (Feminist)

4. The text does not emphasize firms’ role in shaping the tastes and preferences of consumers even though this is a very important role with firms spending about $150 bil- lion a year on advertising. If it is true that firms are shaping consumer preferences, whose welfare are people maximizing when they make consumption decisions? (Institutionalist)

5. Walmart, the nation’s largest retailer, has perfected a “just-in-time competitive strategy.” This retail giant relies on bar codes for instant inventory, distribution centers that purchase supplies at the last minute and deliver only when needed, a small core of suppliers that Walmart can pres- sure for large discounts, routinized work that requires on average seven hours of training, and part-time workers who often work full-time hours without getting corre- sponding benefits. How does this “just-in-time” approach change the mix of fixed and variable costs to the advan- tage of Walmart? (Radical)

Issues to Ponder

1. “There is no long run; there are only short and shorter runs.” Evaluate that statement.

2. If you increase production to an infinitely large level, the average variable cost and the average total cost will merge. Why?

3. The following cell phone offer by Sprint is typical of what one can get on a cell phone plan: 4,000 free minutes for $39.99 a month. The fine print says that only 350 of those minutes are anytime minutes; the remaining are restricted to evening and weekend usage. If you go over your allot- ted time, you are charged 35 cents per minute for any ad- ditional minutes. a. What is your marginal cost? Graph it. b. What would your average variable cost curve for peak

time usage look like?

c. If you do not keep track of your usage, how would you figure your marginal cost?

d. Why do firms offer such confusing plans? e. Were firms that charged this way in favor of or

against portability of phone numbers? 4. Say that neither labor nor machines are fixed but that

there is a 50 percent quick-order premium paid for both workers and machines for their delivery in the short run. Once you buy them, they cannot be returned, however. What do your short-run marginal cost and short-run aver- age total cost curves look like?

5. If machines are variable and labor fixed, how will the general shapes of the short-run average cost curve and marginal cost curve change?

Answers to Margin Questions

1. Accounting profit measures explicit costs and revenues; economic profit includes implicit costs and revenues as well. ( LO11-1)

2. Normally the marginal productivity curve and average productivity curve are both inverted U shapes. ( LO11-2)

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242 Microeconomics ■ Production and Cost Analysis

3. Firms are likely to operate on the downward-sloping portion of the marginal productivity curve because on the upward-sloping portion, firms could increase workers’ output by hiring more workers. A firm will continue to hire more workers at least to the point where diminishing marginal productivity sets in. (LO11-2)

4. Average variable costs would be $40. (LO11-3) 5. As you can see in the graph, both these curves are

U-shaped and the marginal cost curve goes through the average cost curve at the minimum point of the average cost curve. (LO11-4)

C o

Quantity

Minimum point

6. The distance between the average total cost and the aver- age variable cost is determined by the average fixed cost

at that quantity. As quantity increases, the average fixed cost decreases, so the two curves get closer and closer together. (LO11-4)

7. Since the average productivity and marginal productivity of workers are the mirror images of average costs and marginal costs, and when the marginal costs and average costs intersect the two are equal, it follows that the average productivity and marginal productivity of workers must also be equal at that point. ( LO11-4)

8. It is impossible to say what is happening to average total costs on the basis of what is happening to marginal costs. It is the magnitude of marginal costs relative to average total costs that is important. (LO11-4)

9. It is impossible to say because it is the magnitude of marginal cost relative to average variable cost that determines what is happening to average variable cost. (LO11-4)

10. The marginal cost curve intersects the average variable cost curve at the minimum point because once the marginal cost exceeds average variable costs, the aver- age variable costs must necessarily begin to rise, and vice versa. ( LO11-4)