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Unformatted text preview: 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 189 PA RT FOUR Firms and Markets 9 Profit, Production, and Costs After studying this chapter, y ou will be able to: ■ Distinguish between the short run and the long run ■ Explain the relationship between a firm’s output and labor employed in the short run ■ Explain the relationship between a firm’s output and costs in the short run and derive a firm’s short-run cost curves ■ Explain the relationship between a firm’s output and costs in the long run and derive a firm’s long-run average cost curve What do the nation’s largest automaker, global warming. Why don’t they make more use of clean General Motors, a big electricity supplier in Pennsylvania, solar and wind technologies? PennPower, and a small (fictional) producer of knitwear, We are going to answer these questions in this chapter. Campus Sweaters, have in common? Like every firm, they must To explain the basic ideas as clearly as possible, we are decide how much to produce, how many people to employ, going to focus on the economic decisions of Campus and how much and what type of capital equipment to use. How Sweaters, Inc. Studying the way Cindy copes with her firm’s do firms make these decisions? economic problems will give us a clear view of the prob- GM and the other automakers in the United States could lems faced by all firms. We’ll then apply what we learn in produce more cars than they can sell. Why do automakers this chapter to the real-world costs of producing cars and have expensive equipment lying around that isn’t fully used? electricity. In Reading Between the Lines, we’ll look at the PennPower and the other electric utilities in the United States use technologies that contribute to climate change and effects of changing technologies that aim to lower the cost of clean electricity. 189 9160335_CH09_p189-212.qxd 190 7/2/09 CHAPTER 9 2:01 PM Page 190 Pr ofit, Production, and Costs ◆ The Firm and Its Economic Problem The 20 million firms in the United States differ in size and in the scope of what they do, but they all perform the same basic economic functions. Each firm is an institution that hires factors of production and organizes those factors to produce and sell goods and services. Our goal is to predict firms’ behavior. To do so, we need to know a firm’s goal and the constraints it faces. We start with the goal. Economic Profit vs. Accounting Profit The goal of any firm is to maximize profit, the difference between revenue and costs. Because the definition of an economic cost includes more than just monetary costs, we need to distinguish between two different measures of profit: accounting profit and economic profit. Accounting profit can be defined as the difference between revenues and explicit costs, where explicit costs refer to a firm’s monetary or “outof-pocket” expenses. On the other hand, economic profit is defined as the difference between revenues and economic costs. Remember, economic costs include both explicit (nonsunk) costs and implicit costs. As a result, accounting profit generally will be greater than economic profit. To see the difference, consider the table below that lists annual revenues and monetary expenses (explicit costs) for a printing company. Annual Sales Revenue $4,000,000 Wage costs of labor $1,500,000 Paper expense $500,000 Rental payments for printers $350,000 Rental payments for office space $150,000 Total Costs $2,500,000 Profit $1,500,000 Based on these numbers, the printing company is earning $1,500,000 more in revenues than it is paying out in expenses—$1,500,000 in accounting profit. But this example includes only the explicit monetary expenses of production and none of the implicit costs of production. There are monetary costs included for labor (wages), land (office space), and capital (printers), but what about the cost of the owner’s entrepreneurship resource? The profit earned in the business is the reward to the printing company owner, but just because the owner earns this monetary profit doesn’t mean owning the printing company is the best choice for this entrepreneur. Presumably, the owner of the printing company has other options available for his or her labor and entrepreneurial services. For example, what if the printing company owner’s best alternative to owning the printing company is working as an advertising executive for a local business at an annual salary of $800,000? By choosing to own the printing company, the owner of the printing company is sacrificing that $800,000 salary he or she would earn as an advertising executive. Even though this $800,000 is not paid by the owner of the printing company, it is still an opportunity the owner is sacrificing and must be included as an economic cost of production. The table of revenues and costs changes to the following: Annual Sales Revenue $4,000,000 Wage costs of labor $1,500,000 Paper expense $500,000 Rental payments for printers $350,000 Rental payments for office space $150,000 Forgone Salary as Advertising Executive $800,000 Total Costs Profit $3,300,000 $700,000 Notice that the printing company owner is still earning a positive economic profit of $700,000, even after including the opportunity cost of entrepreneurship. Anytime economic profit is positive, revenues are large enough to pay off all the economic costs and still leave some surplus. In other words, the revenues made in this business are greater than the opportunity costs, so the printing company owner is earning more by using resources in this business than he or she could in the best alternative. Accounting profit focuses only on the firm’s ability to pay off its expenses. When accounting profit is positive, the firm is earning enough to pay its bills. However, that does not imply that the firm is earning the highest level of profit it could. Economic profit identifies whether a firm is earning more or less than it could earn if the firm’s resources were used elsewhere. When economic profits are positive, firms recognize that the industry offers the best return for use of their resources and are attracted to that industry. 9160335_CH09_p189-212.qxd 7/1/09 3:45 PM Page 191 T he Firm and Its Economic Problem However, if revenues are not high enough to pay off all the economic costs of a business, economic profit will be negative. When economic profit is negative, the resources being used in an industry would have a higher value if they were moved to their best alternatives. In other words, opportunity costs are greater than revenues. With negative economic profits, firms have an incentive to leave an industry, as they recognize that their resources have higher value elsewhere. Normal Profit If economic profit is zero, a firm’s resources are earning revenues exactly equal to their opportunity costs. When a firm’s resources are earning the same value they would earn in their best alternative, we say a firm is earning normal profit. In that case, a firm is receiving no more and no less than what it would earn if the firm moved its resources to their best alternative uses. There is no incentive for a firm to leave an industry when it is earning normal profit, and there is no incentive for new firms to enter the industry either. In the table above, if the owner of the printing company could earn $1,500,000 as an advertising executive (instead of the $800,000), total economic costs would rise from $3,300,000 to $4,000,000. Now total economic costs equal total revenues, and economic profit is zero. This does not mean the printing company owner should get out of the printing business though. The printing company owner is making an accounting profit of $1,500,000 ($4,000,000 in revenues minus $2,500,000 in accounting costs), and that accounting profit is the same amount of money the owner would have if he or she worked as an advertising executive instead. The owner would be indifferent between making $1,500,000 in accounting profit as a printing company owner and making $1,500,000 as an advertising executive. Because the best alternative has the same value as the current use of resources, the firm cannot leave this market and do any better somewhere else. When the firm earns zero economic profit, the firm is earning a “normal” profit. More Implicit Costs and Benefits In the example above, rental expenses for printers ($350,000) and office space ($150,000) are included. But what if the company already owned its own printers or its own building? In that case, there are no explicit expenses associated with those rental payments for those resources. You don’t have to pay rent on a building or piece of equipment you already own. It may appear then 191 that $500,000 of cost disappears and profit increases by $500,000. However, we know that the true cost of a resource doesn’t include just what you pay for it. The true cost, or economic cost, of a resource is its opportunity cost—the value of the best alternative. Even though the company owns its own printers and its building, using the printers and the building as part of the printing business means those resources are not available for other potential uses. Printers, for example, could be rented out to other companies or sold to other companies. The economic cost of using those printers would be the value the owner of the printing company would receive in the best alternative use of those printers. For example, if printers can be rented out for $350,000 (the same price the company in the above example would have to pay to rent them), then the economic cost of using those printers in the printing company is still $350,000 (the value of the best alternative to owning the printers). The same is true for the building. If the company owns the building, it is not a “free” resource. There is still an economic cost of using the building, even if there is no explicit cost. The economic cost of using the building in the printing business would be the value of its best alternative—the value of income that could be earned from renting or selling the building to another business, for example. Just as economists include implicit costs in the economic costs of operating a business, there may be some implicit benefit to running a business that an accountant would not consider. For example, many entrepreneurs see value in being able to set their own work schedules without having to answer to anyone else. In that case, even if the difference between revenues and economic costs is negative, the printing company owner may decide to continue owning the printing company simply because there is enough intrinsic value to “being your own boss” that it is worthwhile to continue operating the business. The goal of measuring economic profit is to uncover the most valuable use of resources. The concept of economic profit should also include these “implicit benefits” as part of the value of running a company in addition to the monetary revenues. Because implicit benefits and implicit costs are determined by an individual entrepreneur’s alternatives and preferences, the economic profit earned from a business can vary with each entrepreneur. To simplify this, we will focus simply on revenue earned by a company as the benefit to running a business. However, you should keep in mind that true economic profit would include an individual entrepreneur’s implicit 9160335_CH09_p189-212.qxd 192 6/22/09 9:01 AM Page 192 CHAPTER 9 Output and Costs benefits as well. When we refer to the costs of production from now on, we will include all the relevant explicit (nonsunk) costs and implicit costs so that the “cost of production” will refer to the “economic cost of production.” ◆ Decision Time Frames People who operate firms make many decisions, and all of their decisions are aimed at achieving one overriding goal: maximum attainable profit. But not all decisions are equally critical. Some decisions are big ones. Once made, they are costly (or impossible) to reverse. If such a decision turns out to be incorrect, it might lead to the failure of the firm. Other decisions are small. They are easily changed. If one of these decisions turns out to be incorrect, the firm can change its actions and survive. The biggest decision that an entrepreneur makes is in what industry to establish a firm. For most entrepreneurs, their background knowledge and interests drive this decision. But the decision also depends on profit prospects—on the expectation that total revenue will exceed total cost. Cindy has already decided to set up Campus Sweaters. She has also decided the most effective method of organizing the firm. But she has not decided the quantity to produce, the factors of production to hire, or the price to charge for sweaters. Decisions about the quantity to produce and the price to charge depend on the type of market in which the firm operates. Perfect competition, monopolistic competition, oligopoly, and monopoly all confront the firm with their own special problems. But decisions about how to produce a given output do not depend on the type of market in which the firm operates. All types of firms in all types of markets make similar decisions about how to produce. The actions that a firm can take to influence the relationship between output and cost depend on how soon the firm wants to act. A firm that plans to change its output rate tomorrow has fewer options than one that plans to change its output rate six months or six years from now. To study the relationship between a firm’s output decision and its costs, we distinguish between two decision time frames: ■ The short run ■ The long run The Short Run The short run is a time frame in which the quantity of at least one factor of production is fixed. For most firms, capital, land, and entrepreneurship are fixed factors of production and labor is the variable factor of production. We call the fixed factors of production the firm’s plant : In the short run, a firm’s plant is fixed. For Campus Sweaters, the fixed plant is its factory building and its knitting machines. For an electric power utility, the fixed plant is its buildings, generators, computers, and control systems. To increase output in the short run, a firm must increase the quantity of a variable factor of production, which is usually labor. So to produce more output, Campus Sweaters must hire more labor and operate its knitting machines for more hours a day. Similarly, an electric power utility must hire more labor and operate its generators for more hours a day. Short-run decisions are easily reversed. The firm can increase or decrease its output in the short run by increasing or decreasing the amount of labor it hires. The Long Run The long run is a time frame in which the quantities of all factors of production can be varied. That is, the long run is a period in which the firm can change its plant. To increase output in the long run, a firm can change its plant as well as the quantity of labor it hires. Campus Sweaters can decide whether to install more knitting machines, use a new type of machine, reorganize its management, or hire more labor. Long-run decisions are not easily reversed. Once a plant decision is made, the firm usually must live with it for some time. To emphasize this fact, we call the past expenditure on a plant that has no resale value a sunk cost. A sunk cost is irrelevant to the firm’s current decisions. The only costs that influence its current decisions are the short-run cost of changing its labor inputs and the long-run cost of changing its plant. Review Quiz ◆ 1 2 Distinguish between the short run and the long run. Why is a sunk cost irrelevant to a firm’s current decisions? Work Study Plan 9.1 and get instant feedback. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 193 Short-Run Technology Constraint We’re going to study costs in the short run and the long run. We begin with the short run and describe a firm’s technology constraint. ◆ Short-Run Technology Constraint To increase output in the short run, a firm must increase the quantity of labor employed. We describe the relationship between output and the quantity of labor employed by using three related concepts: 1. Total product 2. Marginal product 3. Average product If you look closely at the numbers in Table 9.1, you can see some patterns. As Campus Sweaters hires more labor, marginal product increases initially, and then begins to decrease. For example, marginal product increases from 4 sweaters a day for the first worker to 6 sweaters a day for the second worker and then decreases to 3 sweaters a day for the third worker. Average product also increases at first and then decreases. You can see the relationships between the quantity of labor hired and the three product concepts more clearly by looking at the product curves. TABLE 9.1 These product concepts can be illustrated either by product schedules or by product curves. Let’s look first at the product schedules. Product Schedules Table 9.1 shows some data that describe Campus Sweaters’ total product, marginal product, and average product. The numbers tell us how the quantity of sweaters increases as Campus Sweaters employs more workers. The numbers also tell us about the productivity of the labor that Campus Sweaters employs. Focus first on the columns headed “Labor” and “Total product.” Total product is the maximum output that a given quantity of labor can produce. You can see from the numbers in these columns that as Campus Sweaters employs more labor, total product increases. For example, when 1 worker is employed, total product is 4 sweaters a day, and when 2 workers are employed, total product is 10 sweaters a day. Each increase in employment increases total product. The marginal product of labor is the increase in total product that results from a one-unit increase in the quantity of labor employed, with all other inputs remaining the same. For example, in Table 9.1, when Campus Sweaters increases employment from 2 to 3 workers and does not change its capital, the marginal product of the third worker is 3 sweaters—total product increases from 10 to 13 sweaters. Average product tells how productive workers are on average. The average product of labor is equal to total product divided by the quantity of labor employed. For example, in Table 9.1, the average product of 3 workers is 4.33 sweaters per worker— 13 sweaters a day divided by 3 workers. 193 Total Product, Marginal Product, and Average Product Labor Total product Marginal product Average product (workers per day) (sweaters per day) (sweaters per additional worker) (sweaters per worker) A 0 0 B 1 4 C 2 10 D 3 13 E 4 15 F 5 16 . . . . . . . . . . .4 . . . . . . . . . . .6 . . . . . . . . . . .3 . . . . . . . . . . . .2 . . . . . . . . . . .1 4.00 5.00 4.33 3.75 3.20 Total product is the total amount produced. Marginal product is the change in total product that results from a one-unit increase in labor. For example, when labor increases from 2 to 3 workers a day (row C to row D), total product increases from 10 to 13 sweaters a day. The marginal product of going from 2 to 3 workers is 3 sweaters. Average product is total product divided by the quantity of labor employed. For example, the average product of 3 workers is 4.33 sweaters per worker (13 sweaters a day divided by 3 workers). Product Curves The product curves are graphs of the relationships between employment and the three product concepts you’ve just studied. They show how total product, marginal product, and average product change as employment changes. They also show the relationships among the three concepts. Let’s look at the product curves. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 194 CHAPTER 9 Output and Costs 194 Total Product Curve Marginal Product Curve Figure 9.1 shows Campus Sweaters’ total product curve, TP, which is a graph of the total product schedule. Points A through F correspond to rows A through F in Table 9.1. To graph the entire total product curve, we vary labor by hours rather than whole days. Notice the shape of the total product curve. As employment increases from zero to 1 worker a day, the curve becomes steeper. Then, as employment increases to 3, 4, and 5 workers a day, the curve becomes less steep. The total product curve is similar to the production possibilities frontier (explained in Chapter 2). It separates the attainable output levels from those that are unattainable. All the points that lie above the curve are unattainable. Points that lie below the curve, in the orange area, are attainable, but they are inefficient—they use more labor than is necessary to produce a given output. Only the points on the total product curve are technologically efficient. Figure 9.2 shows Campus Sweaters’ marginal product of labor. Part (a) reproduces the total product curve from Fig. 9.1 and part (b) shows the marginal product curve, MP. In part (a), the orange bars illustrate the marginal product of labor. The height of a bar measures marginal product. Marginal product is also measured by the slope of the total product curve. Recall that the slope of a curve is the change in the value of the variable measured on the y-axis—output—divided by the change in the variable measured on the x-axis— labor—as we move along the curve. A one-unit increase in labor, from 2 to 3 workers, increases output from 10 to 13 sweaters, so the slope from point C to point D is 3 sweaters per additional worker, the same as the marginal product we’ve just calculated. Again varying the amount of labor in the smallest units possible, we can draw the marginal product curve shown in Fig. 9.2(b). The height of this curve measures the slope of the total product curve at a point. Part (a) shows that an increase in employment from 2 to 3 workers increases output from 10 to 13 sweaters (an increase of 3). The increase in output of 3 sweaters appears on the y-axis of part (b) as the marginal product of going from 2 to 3 workers. We plot that marginal product at the midpoint between 2 and 3 workers. Notice that the marginal product shown in Fig. 9.2(b) reaches a peak at 1.5 workers, and at that point, marginal product is 6 sweaters per additional worker. The peak occurs at 1.5 workers because the total product curve is steepest when employment increases from 1 worker to 2 workers. The total product and marginal product curves differ across firms and types of goods. GM’s product curves are different from those of PennPower, whose curves in turn are different from those of Campus Sweaters. But the shapes of the product curves are similar because almost every production process has two features: Total Product Curve Output (sweaters per day) FIGURE 9.1 TP 15 E D Unattainable 10 F C Attainable 5 B A 0 1 2 3 4 5 Labor (workers per day) The total product curve, TP, is based on the data in Table 9.1. The total product curve shows how the quantity of sweaters produced changes as the quantity of labor employed changes. For example, 2 workers can produce 10 sweaters a day (point C ). Points A through F on the curve correspond to the rows of Table 9.1. The total product curve separates attainable outputs from unattainable outputs. Points below the TP curve are inefficient. animation ■ ■ Increasing marginal returns initially Diminishing marginal returns eventually Increasing Marginal Returns Increasing marginal returns occur when the marginal product of an additional worker exceeds the marginal product of the previous worker. Increasing marginal returns arise from increased specialization and division of labor in the production process. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 195 Short-Run Technology Constraint Output (sweaters per day) FIGURE 9.2 Total Product and Marginal Product TP 15 D 13 10 C 5 4 0 2 1 3 4 5 Labor (workers per day) Marginal product (sweaters per additional worker) (a) Total product 6 4 3 2 MP 0 2 1 3 4 5 Labor (workers per day) (b) Marginal product Marginal product is illustrated by the orange bars. For example, when labor increases from 2 to 3 workers a day, marginal product is the orange bar whose height is 3 sweaters. (Marginal product is shown midway between the quantities of labor to emphasize that marginal product results from changing the quantity of labor.) The steeper the slope of the total product curve (TP ) in part (a), the larger is marginal product (MP ) in part (b). Marginal product increases to a maximum (in this example when 1.5 workers a day are employed) and then declines—diminishing marginal product. animation 195 For example, if Campus Sweaters employs one worker, that person must learn all the aspects of sweater production: running the knitting machines, fixing breakdowns, packaging and mailing sweaters, buying and checking the type and color of the wool. All these tasks must be performed by that one person. If Campus Sweaters hires a second person, the two workers can specialize in different parts of the production process and can produce more than twice as much as one worker. The marginal product of the second worker is greater than the marginal product of the first worker. Marginal returns are increasing. Diminishing Marginal Returns Most production processes experience increasing marginal returns initially, but all production processes eventually reach a point of diminishing marginal returns. Diminishing marginal returns occur when the marginal product of an additional worker is less than the marginal product of the previous worker. Diminishing marginal returns arise from the fact that more and more workers are using the same capital and working in the same space. As more workers are added, there is less and less for the additional workers to do that is productive. For example, if Campus Sweaters hires a third worker, output increases but not by as much as it did when it hired the second worker. In this case, after two workers are hired, all the gains from specialization and the division of labor have been exhausted. By hiring a third worker, the factory produces more sweaters, but the equipment is being operated closer to its limits. There are even times when the third worker has nothing to do because the machines are running without the need for further attention. Hiring more and more workers continues to increase output but by successively smaller amounts. Marginal returns are diminishing. This phenomenon is such a pervasive one that it is called a “law”—the law of diminishing returns. The law of diminishing returns states that As a firm uses more of a variable factor of production, with a given quantity of the fixed factor of production, the marginal product of the variable factor eventually diminishes. You are going to return to the law of diminishing returns when we study a firm’s costs. But before we do that, let’s look at the average product of labor and the average product curve. 9160335_CH09_p189-212.qxd 196 6/22/09 9:01 AM Page 196 CHAPTER 9 Output and Costs Average Product Curve Figure 9.3 illustrates Campus Sweaters’ average product of labor and shows the relationship between average product and marginal product. Points B through F on the average product curve AP correspond to those same rows in Table 9.1. Average product increases from 1 to 2 workers (its maximum value at point C ) but then decreases as yet more workers are employed. Notice also that average product is largest when average product and marginal product are equal. That is, the marginal product curve cuts the average product curve at the point of maximum average product. For the number of workers at which marginal product exceeds average product, average product is increasing. For the number of workers at which marginal product is less than average product, average product is decreasing. The relationship between the average product and marginal product is a general feature of the relationship between the average and marginal values of any variable—even your grades. Marginal Grades and Average Grades How to Pull Up Your Average Do you want to pull up your average grade? Then make sure that your next test is better than your current average! Your next test is your marginal test. If your marginal grade exceeds your average grade (like Economics in the graph), your average will rise. If your marginal grade equals your average grade (like English in the graph), your average won’t change. If your marginal grade is below your average grade (like History in the figure), your average will fall. The relationship between your marginal and average grades is exactly the same as that between marginal product and average product. 4 Average grade 3 Marginal grade 2 Average Product 6 1 Maximum average product C GPA Average product and marginal product (sweaters per day per worker) FIGURE 9.3 4 B 0 Calculus D Economics English History Course E Marginal and Average Grade Curves F AP Review Quiz ◆ 2 1 MP 0 1 2 3 4 5 Labor (workers per day) The figure shows the average product of labor and the connection between average product and marginal product. With 1 worker, marginal product exceeds average product, so average product is increasing. With 2 workers, marginal product equals average product, so average product is at its maximum. With more than 2 workers, marginal product is less than average product, so average product is decreasing. animation 2 3 Explain how the marginal product of labor and the average product of labor change as the quantity of labor employed increases (a) initially and (b) eventually. What is the law of diminishing returns? Why does marginal product eventually diminish? Explain the relationship between marginal product and average product. Work Study Plan 9.2 and get instant feedback. Campus Sweaters’ product curves influence its costs, as you are now going to see. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 197 Short-Run Cost ◆ Short-Run Cost ■ ■ ■ Total cost Marginal cost Average cost Cost (dollars per day) To produce more output in the short run, a firm must employ more labor, which means that it must increase its costs. We describe the relationship between output and cost by using three cost concepts: FIGURE 9.4 197 Total Cost Curves TC 150 TC = TFC + TVC TVC 100 75 50 Total Cost TFC A firm’s total cost (TC ) is the cost of all the factors of production it uses. We separate total cost into total fixed cost and total variable cost. Total fixed cost (TFC ) is the cost of the firm’s fixed factors. For Campus Sweaters, total fixed cost includes the cost of renting knitting machines and normal profit, which is the opportunity cost of Cindy’s entrepreneurship. The quantities of fixed factors don’t change as output changes, so total fixed cost is the same at all outputs. Total variable cost (TVC ) is the cost of the firm’s variable factors. For Campus Sweaters, labor is the variable factor, so this component of cost is its wage bill. Total variable cost changes as output changes. Total cost is the sum of total fixed cost and total variable cost. That is, TC = TFC + TVC. The table in Fig. 9.4 shows total costs. Campus Sweaters rents one knitting machine for $25 a day, so its TFC is $25. To produce sweaters, the firm hires labor, which costs $25 a day. TVC is the number of workers multiplied by $25. For example, to produce 13 sweaters a day, in row D, the firm hires 3 workers and TVC is $75. TC is the sum of TFC and TVC, so to produce 13 sweaters a day, TC is $100. Check the calculations in the other rows of the table. Figure 9.4 shows Campus Sweaters’ total cost curves, which graph total cost against output. The green TFC curve is horizontal because total fixed cost ($25 a day) does not change when output changes. The purple TVC curve and the blue TC curve both slope upward because to increase output, more labor must be employed, which increases total variable cost. Total fixed cost equals the vertical distance between the TVC and TC curves. Let’s now look at a firm’s marginal cost. 0 5 10 13 15 Output (sweaters per day) Total fixed cost ( TFC ) Total variable cost ( TVC ) Total cost ( TC) Labor Output (workers per day) (sweaters per day) A 0 0 25 0 25 B 1 4 25 25 50 C 2 10 25 50 75 D 3 13 25 75 100 E 4 15 25 100 125 F 5 16 25 125 150 (dollars per day) Campus Sweaters rents a knitting machine for $25 a day, so this cost is the firm’s total fixed cost. The firm hires workers at a wage rate of $25 a day, and this cost is its total variable cost. For example, in row D, Campus Sweaters employs 3 workers and its total variable cost is 3 × $25, which equals $75. Total cost is the sum of total fixed cost and total variable cost. For example, when Campus Sweaters employs 3 workers, total cost is $100—total fixed cost of $25 plus total variable cost of $75. The graph shows Campus Sweaters’ total cost curves. Total fixed cost is constant—the TFC curve is a horizontal line. Total variable cost increases as output increases, so the TVC curve and the TC curve increase as output increases. The vertical distance between the TC curve and the TVC curve equals total fixed cost, as illustrated by the two arrows. animation 9160335_CH09_p189-212.qxd 198 6/22/09 9:01 AM Page 198 CHAPTER 9 Output and Costs Marginal Cost Figure 9.4 shows that total variable cost and total cost increase at a decreasing rate at small outputs but eventually, as output increases, total variable cost and total cost increase at an increasing rate. To understand this pattern in the change in total cost as output increases, we need to use the concept of marginal cost. A firm’s marginal cost is the increase in total cost that results from a one-unit increase in output. We calculate marginal cost as the increase in total cost divided by the increase in output. The table in Fig. 9.5 shows this calculation. When, for example, output increases from 10 sweaters to 13 sweaters, total cost increases from $75 to $100. The change in output is 3 sweaters, and the change in total cost is $25. The marginal cost of one of those 3 sweaters is ($25 3), which equals $8.33. Figure 9.5 graphs the marginal cost data in the table as the red marginal cost curve, MC. This curve is U-shaped because when Campus Sweaters hires a second worker, marginal cost decreases, but when it hires a third, a fourth, and a fifth worker, marginal cost successively increases. At small outputs, marginal cost decreases as output increases because of greater specialization and the division of labor, but as output increases further, marginal cost eventually increases because of the law of diminishing returns. The law of diminishing returns means that the output produced by each additional worker is successively smaller. To produce an additional unit of output, ever more workers are required, and the cost of producing the additional unit of output—marginal cost—must eventually increase. Marginal cost tells us how total cost changes as output increases. The final cost concept tells us what it costs, on average, to produce a unit of output. Let’s now look at Campus Sweaters’ average costs. Average Cost Three average costs of production are 1. Average fixed cost 2. Average variable cost 3. Average total cost Average fixed cost (AFC ) is total fixed cost per unit of output. Average variable cost (AVC ) is total variable cost per unit of output. Average total cost (ATC ) is total cost per unit of output. The average cost con- cepts are calculated from the total cost concepts as follows: TC = TFV + TVC. Divide each total cost term by the quantity produced, Q, to get TFC TVC TC = + , Q Q Q or ATC = AFC + AVC. The table in Fig. 9.5 shows the calculation of average total cost. For example, in row C, output is 10 sweaters. Average fixed cost is ($25 10), which equals $2.50, average variable cost is ($50 10), which equals $5.00, and average total cost is ($75 10), which equals $7.50. Note that average total cost is equal to average fixed cost ($2.50) plus average variable cost ($5.00). Figure 9.5 shows the average cost curves. The green average fixed cost curve (AFC ) slopes downward. As output increases, the same constant total fixed cost is spread over a larger output. The blue average total cost curve (ATC ) and the purple average variable cost curve (AVC ) are U-shaped. The vertical distance between the average total cost and average variable cost curves is equal to average fixed cost—as indicated by the two arrows. That distance shrinks as output increases because average fixed cost declines with increasing output. Marginal Cost and Average Cost The marginal cost curve (MC ) intersects the average variable cost curve and the average total cost curve at their minimum points. When marginal cost is less than average cost, average cost is decreasing, and when marginal cost exceeds average cost, average cost is increasing. This relationship holds for both the ATC curve and the AVC curve. It is another example of the relationship you saw in Fig. 9.3 for average product and marginal product and in your average and marginal grades. Why the Average Total Cost Curve Is U-Shaped Average total cost is the sum of average fixed cost and average variable cost, so the shape of the ATC curve 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 199 Short-Run Cost Marginal Cost and Average Costs Cost (dollars per sweater) FIGURE 9.5 15 Marginal cost is calculated as the change in total cost divided by the change in output. When output increases from 4 to 10 sweaters, an increase of 6 sweaters, total cost increases by $25. Marginal cost is $25 ÷ 6, which is $4.17. Each average cost concept is calculated by dividing the related total cost by output. When 10 sweaters are produced, AFC is $2.50 ($25 ÷ 10), AVC is $5 ($50 ÷ 10), and ATC is $7.50 ($75 ÷ 10). The graph shows that the MC curve is U-shaped and intersects the AVC curve and the ATC curve at their minimum points. Average fixed cost curve (AFC ) is downward sloping. The ATC curve and AVC curve are U-shaped. The vertical distance between the ATC curve and the AVC curve is equal to average fixed cost, as illustrated by the two arrows. MC ATC = AFC + AVC ATC 10 AVC 5 AFC 0 199 10 15 Output (sweaters per day) 5 Total fixed cost ( TFC ) Total variable cost ( TVC ) Total cost ( TC ) Labor Output (workers (sweaters per day) per day) A 0 0 25 0 25 B 1 4 25 25 50 C 2 10 25 50 75 D 3 13 25 75 100 E 4 15 25 100 125 F 5 16 25 125 150 (dollars per day) Marginal cost ( MC ) (dollars per Average fixed cost ( AFC ) additional sweater) Average variable cost ( AVC ) Average total cost ( ATC ) (dollars per sweater) . . . . . . . 4.17 . . . . . . . 8.33 . . . . . . . 12.50 . . . . . . . 25.00 — — — 6.25 6.25 12.50 2.50 5.00 7.50 1.92 5.77 7.69 1.67 6.67 8.33 1.56 . . . . . . . 6.25 7.81 9.38 animation combines the shapes of the AFC and AVC curves. The U shape of the ATC curve arises from the influence of two opposing forces: 1. Spreading total fixed cost over a larger output 2. Eventually diminishing returns When output increases, the firm spreads its total fixed cost over a larger output and so its average fixed cost decreases—its AFC curve slopes downward. Diminishing returns means that as output increases, ever-larger amounts of labor are needed to produce an additional unit of output. So as output increases, average variable cost decreases initially but eventually increases, and the AVC curve slopes upward. The AVC curve is U shaped. The shape of the ATC curve combines these two effects. Initially, as output increases, both average fixed cost and average variable cost decrease, so average total cost decreases. The ATC curve slopes downward. But as output increases further and diminishing returns set in, average variable cost starts to increase. With average fixed cost decreasing more quickly than average variable cost is increasing, the ATC curve continues to slope downward. Eventually, average variable cost starts to increase more quickly than average fixed cost decreases, so average total cost starts to increase. The ATC curve slopes upward. 9160335_CH09_p189-212.qxd 200 6/22/09 9:01 AM Page 200 CHAPTER 9 Output and Costs Cost Curves and Product Curves Average product and marginal product 6 AP 4 MP 2 Rising MP and falling MC: rising AP and falling AVC 0 1.5 ■ Technology Prices of factors of production 2.0 Maximum AP and Minimum AVC Shifts in the Cost Curves ■ Falling MP and rising MC: falling AP and rising AVC Maximum MP and Minimum MC 12 9 The position of a firm’s short-run cost curves depends on two factors: Falling MP and rising MC: rising AP and falling AVC Labor Cost (dollars per unit) The technology that a firm uses determines its costs. Figure 9.6 shows the links between the firm’s product curves and its cost curves. The upper graph shows the average product curve, AP, and the marginal product curve, MP—like those in Fig. 9.3. The lower graph shows the average variable cost curve, AVC, and the marginal cost curve, MC—like those in Fig. 9.5. As labor increases up to 1.5 workers a day (upper graph), output increases to 6.5 sweaters a day (lower graph). Marginal product and average product rise and marginal cost and average variable cost fall. At the point of maximum marginal product, marginal cost is at a minimum. As labor increases to 2 workers a day, (upper graph) output increases to 10 sweaters a day (lower graph). Marginal product falls and marginal cost rises, but average product continues to rise and average variable cost continues to fall. At the point of maximum average product, average variable cost is at a minimum. As labor increases further, output increases. Average product diminishes and average variable cost increases. Product Curves and Cost Curves FIGURE 9.6 MC 6 AVC 3 Technology A technological change that increases productivity increases the marginal product and average product of labor. With a better technology, the same factors of production can produce more output, so the technological advance lowers the costs of production and shifts the cost curves downward. For example, advances in robot production techniques have increased productivity in the automobile industry. As a result, the product curves of Chrysler, Ford, and GM have shifted upward and their cost curves have shifted downward. But the relationships between their product curves and cost curves have not changed. The curves are still linked in the way shown in Fig. 9.6. Often, as in the case of robots producing cars, a technological advance results in a firm using more capital, a fixed factor, and less labor, a variable factor. 0 6.5 10 Output A firm’s MP curve is linked to its MC curve. If, as the firm increases its labor from 0 to 1.5 workers a day, the firm’s marginal product rises, its marginal cost falls. If marginal product is at a maximum, marginal cost is at a minimum. If, as the firm hires more labor, its marginal product diminishes, its marginal cost rises. A firm’s AP curve is linked to its AVC curve. If, as the firm increases its labor to 2 workers a day, its average product rises, its average variable cost falls. If average product is at a maximum, average variable cost is at a minimum. If, as the firm hires more labor, its average product diminishes, its average variable cost rises. animation 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 201 Short-Run Cost TABLE 9.2 201 A Compact Glossary of Costs Term Symbol Definition Equation Fixed cost Cost that is independent of the output level; cost of a fixed factor of production Variable cost Cost that varies with the output level; cost of a variable factor of production Total fixed cost TFC Cost of the fixed factors of production Total variable cost TVC Cost of the variable factors of production Total cost TC Cost of all factors of production Output (total product) TP Total quantity produced (output Q) Marginal cost MC Change in total cost resulting from a oneunit increase in total product MC = ΔTC ÷ ΔQ Average fixed cost AFC Total fixed cost per unit of output AFC = TFC ÷ Q Average variable cost AVC Total variable cost per unit of output AVC = TVC ÷ Q Average total cost ATC Total cost per unit of output ATC = AFC + AVC TC = TFC + TVC Another example is the use of ATMs by banks to dispense cash. ATMs, which are fixed capital, have replaced tellers, which are variable labor. Such a technological change decreases total cost but increases fixed costs and decreases variable cost. This change in the mix of fixed cost and variable cost means that at small outputs, average total cost might increase, while at large outputs, average total cost decreases. truck drivers’ wages or the price of gasoline increases, the variable cost and marginal cost of transportation services increase. You’ve now completed your study of short-run costs. All the concepts that you’ve met are summarized in a compact glossary in Table 9.2. Prices of Factors of Production An increase in the Review Quiz ◆ price of a factor of production increases the firm’s costs and shifts its cost curves. But how the curves shift depends on which factor price changes. An increase in rent or some other component of fixed cost shifts the TFC and AFC curves upward and shifts the TC curve upward but leaves the AVC and TVC curves and the MC curve unchanged. For example, if the interest expense paid by a trucking company increases, the fixed cost of transportation services increases. An increase in wages, gasoline, or another component of variable cost shifts the TVC and AVC curves upward and shifts the MC curve upward but leaves the AFC and TFC curves unchanged. For example, if 1 2 3 4 5 What relationships do a firm’s short-run cost curves show? How does marginal cost change as output increases (a) initially and (b) eventually? What does the law of diminishing returns imply for the shape of the marginal cost curve? What is the shape of the AFC curve and why does it have this shape? What are the shapes of the AVC curve and the ATC curve and why do they have these shapes? Work Study Plan 9.3 and get instant feedback. 9160335_CH09_p189-212.qxd 202 6/22/09 9:01 AM Page 202 CHAPTER 9 Output and Costs ◆ Long-Run Cost We are now going to study the firm’s long-run costs. In the long run, a firm can vary both the quantity of labor and the quantity of capital, so in the long run, all the firm’s costs are variable. The behavior of long-run cost depends on the firm’s production function, which is the relationship between the maximum output attainable and the quantities of both labor and capital. TABLE 9.3 The Production Function Output (sweaters per day) Labor Table 9.3 shows Campus Sweaters’ production function. The table lists total product schedules for four different quantities of capital. The quantity of capital identifies the plant size. The numbers for plant 1 are for a factory with 1 knitting machine—the case we’ve just studied. The other three plants have 2, 3, and 4 machines. If Campus Sweaters uses plant 2 with 2 knitting machines, the various amounts of labor can produce the outputs shown in the second column of the table. The other two columns show the outputs of yet larger quantities of capital. Each column of the table could be graphed as a total product curve for each plant. Diminishing Returns Diminishing returns occur with each of the four plant sizes as the quantity of labor increases. You can check that fact by calculating the marginal product of labor in each of the plants with 2, 3, and 4 machines. With each plant size, as the firm increases the quantity of labor employed, the marginal product of labor (eventually) diminishes. Diminishing Marginal Product of Capital Diminishing returns also occur with each quantity of labor as the quantity of capital increases. You can check that fact by calculating the marginal product of capital at a given quantity of labor. The marginal product of capital is the change in total product divided by the change in capital when the quantity of labor is constant—equivalently, the change in output resulting from a one-unit increase in the quantity of capital. For example, if Campus Sweaters has 3 workers and increases its capital from 1 machine to 2 machines, output increases from 13 to 18 sweaters a day. The marginal product of the second machine is 5 sweaters a day. If the firm increases the number of Plant 2 Plant 3 Plant 4 1 4 10 13 15 2 10 15 18 20 3 13 18 22 24 4 The Production Function Plant 1 15 20 24 26 5 16 21 25 27 1 2 3 4 (workers per day) Knitting machines (number) The table shows the total product data for four quantities of capital (plant sizes). The greater the plant size, the larger is the output produced by any given quantity of labor. But for a given plant size, the marginal product of labor diminishes as more labor is employed. For a given quantity of labor, the marginal product of capital diminishes as the quantity of capital used increases. machines from 2 to 3, output increases from 18 to 22 sweaters a day. The marginal product of the third machine is 4 sweaters a day, down from 5 sweaters a day for the second machine. Let’s now see what the production function implies for long-run costs. Short-Run Cost and Long-Run Cost As before, Campus Sweaters can hire workers for $25 a day and rent knitting machines for $25 a day. Using these factor prices and the data in Table 9.3, we can calculate the average total cost and graph the ATC curves for factories with 1, 2, 3, and 4 knitting machines. We’ve already studied the costs of a factory with 1 machine in Figs. 9.4 and 9.5. In Fig. 9.7, the average total cost curve for that case is ATC1. Figure 9.7 also shows the average total cost curve for a factory with 2 machines, ATC2, with 3 machines, ATC3, and with 4 machines, ATC4. You can see, in Fig. 9.7, that the plant size has a big effect on the firm’s average total cost. Two things stand out: 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 203 Long-Run Cost Average cost (dollars per sweater) FIGURE 9.7 Short-Run Costs of Four Different Plants 12.00 10.00 ATC1 ATC2 ATC3 ATC4 9.50 8.00 7.69 6.80 6.00 0 203 5 10 13 15 20 25 30 Output (sweaters per day) The figure shows short-run average total cost curves for four different quantities of capital at Campus Sweaters. The firm can produce 13 sweaters a day with 1 knitting machine on ATC1 or with 3 knitting machines on ATC3 for an average cost of $7.69 a sweater. The firm can produce 13 sweaters a day by using 2 machines on ATC2 for $6.80 a sweater or by using 4 machines on ATC4 for $9.50 a sweater. If the firm produces 13 sweaters a day, the least-cost method of production, the long-run method, is with 2 machines on ATC2. animation 1. Each short-run ATC curve is U-shaped. 2. For each short-run ATC curve, the larger the plant, the greater is the output at which average total cost is at a minimum. Each short-run ATC curve is U-shaped because, as the quantity of labor increases, its marginal product initially increases and then diminishes. This pattern in the marginal product of labor, which we examined in some detail for the plant with 1 knitting machine on pp. 194–195, occurs at all plant sizes. The minimum average total cost for a larger plant occurs at a greater output than it does for a smaller plant because the larger plant has a higher total fixed cost and therefore, for any given output, a higher average fixed cost. Which short-run ATC curve a firm operates on depends on the plant it has. But in the long run, the firm can choose its plant and the plant it chooses is the one that enables it to produce its planned output at the lowest average total cost. To see why, suppose that Campus Sweaters plans to produce 13 sweaters a day. In Fig. 9.7, with 1 machine, the average total cost curve is ATC1 and the average total cost of 13 sweaters a day is $7.69 a sweater. With 2 machines, on ATC2, average total cost is $6.80 a sweater. With 3 machines, on ATC3, average total cost is $7.69 a sweater, the same as with 1 machine. Finally, with 4 machines, on ATC4, average total cost is $9.50 a sweater. The economically efficient plant for producing a given output is the one that has the lowest average total cost. For Campus Sweaters, the economically efficient plant to use to produce 13 sweaters a day is the one with 2 machines. In the long run, Cindy chooses the plant that minimizes average total cost. When a firm is producing a given output at the least possible cost, it is operating on its long-run average cost curve. The long-run average cost curve is the relationship between the lowest attainable average total cost and output when the firm can change both the plant it uses and the quantity of labor it employs. The long-run average cost curve is a planning curve. It tells the firm the plant and the quantity of labor to use at each output to minimize average cost. Once the firm chooses a plant, the firm operates on the short-run cost curves that apply to that plant. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 204 CHAPTER 9 Output and Costs 204 The Long-Run Average Cost Curve GM produces 100 cars a week, each worker must perform many different tasks and the capital must be general-purpose machines and tools. But if GM produces 10,000 cars a week, each worker specializes in a small number of tasks, uses task-specific tools, and becomes highly proficient. Diseconomies of scale are features of a firm’s technology that make average total cost rise as output increases. When diseconomies of scale are present, the LRAC curve slopes upward. In Fig. 9.8, Campus Sweaters experiences diseconomies of scale at outputs greater than 15 sweaters a day. The challenge of managing a large enterprise is the main source of diseconomies of scale. Constant returns to scale are features of a firm’s technology that keep average total cost constant as output increases. When constant returns to scale are present, the LRAC curve is horizontal. Figure 9.8 shows how a long-run average cost curve is derived. The long-run average cost curve LRAC consists of pieces of the four short-run ATC curves. For outputs up to 10 sweaters a day, average total cost is the lowest on ATC1. For outputs between 10 and 18 sweaters a day, average total cost is the lowest on ATC2. For outputs between 18 and 24 sweaters a day, average total cost is the lowest on ATC3. And for outputs in excess of 24 sweaters a day, average total cost is the lowest on ATC4. The piece of each ATC curve with the lowest average total cost is highlighted in dark blue in Fig. 9.8. This dark blue scallop-shaped curve made up of the pieces of the four ATC curves is the LRAC curve. Economies and Diseconomies of Scale are features of a firm’s technology that make average total cost fall as output increases. When economies of scale are present, the LRAC curve slopes downward. In Fig. 9.8, Campus Sweaters has economies of scale for outputs up to 15 sweaters a day. Greater specialization of both labor and capital is the main source of economies of scale. For example, if Economies of scale Average cost (dollars per sweater) FIGURE 9.8 economies of scale and diseconomies of scale at Campus Sweaters arise from the firm’s production function in Table 9.3. With 1 machine and 1 worker, the firm produces 4 sweaters a day. With 2 machines and 2 workers, total cost doubles but output more Long-Run Average Cost Curve Economies of scale 12.00 Economies of Scale at Campus Sweaters The Least-cost plant is 1 Diseconomies of scale Least-cost plant is 2 10.00 Least-cost plant is 3 ATC1 ATC2 Least-cost plant is 4 ATC3 ATC4 8.00 LRAC curve Minimum efficient scale 6.00 0 5 animation 10 15 18 20 24 25 30 Output (sweaters per day) The long-run average cost curve traces the lowest attainable ATC when both labor and capital change. The green arrows highlight the output range over which each plant achieves the lowest ATC. Within each range, to change the quantity produced, the firm changes the quantity of labor it employs. Along the LRAC curve, economies of scale occur if average cost falls as output increases; diseconomies of scale occur if average cost rises as output increases. Minimum efficient scale is the output at which average cost is lowest, 15 sweaters a day. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 205 Long-Run Cost 205 Economies of Scale at an Auto Plant Why do GM, Ford, and the other automakers have expensive equipment lying around that isn’t fully used? You can answer this question with what you’ve learned in this chapter. The basic answer is that auto production enjoys economies of scale. A larger output rate brings a lower long-run average cost—the firm’s LRAC curve slopes downward. An auto producer’s average total cost curves look like those in the figure. To produce 20 vehicles an hour, the firm installs the plant with the short-run average total cost curve ATC1. The average cost of producing a vehicle is $20,000. Producing 20 vehicles an hour doesn’t use the plant at its lowest possible average total cost. If the firm could sell enough cars for it to produce 40 vehicles an hour, the firm could use its current plant and produce at an average cost of $15,000 a vehicle. But if the firm planned to produce 40 vehicles an hour, it would not stick with its current plant. The firm would install a bigger plant with the short-run average total cost curve ATC2, and produce 40 vehicles an hour for $10,000 a car. than doubles to 15 sweaters a day, so average cost decreases and Campus Sweaters experiences economies of scale. With 4 machines and 4 workers, total cost doubles again but output less than doubles to 26 sweaters a day, so average cost increases and the firm experiences diseconomies of scale. Average cost (thousands of dollars per vehicle) Produce More to Cut Cost is the smallest output at which long-run average cost reaches its lowest level. At Campus Sweaters, the minimum efficient scale is 15 sweaters a day. The minimum efficient scale plays a role in determining market structure. In a market in which the minimum efficient scale is small relative to market demand, the market has room for many firms, and the market is competitive. In a market in which the minimum efficient scale is large relative to market demand, only a small number of firms, and possibly only one firm, can make a profit and the market is either an oligopoly or monopoly. We will return to this idea in the next three chapters. 30 ATC1 ATC2 20 15 10 LRAC 0 20 40 60 80 Output (vehicles per hour) Automobile Plant Average Cost Curves Review Quiz ◆ 1 2 3 Minimum Efficient Scale A firm’s minimum efficient scale 40 4 5 What does a firm’s production function show and how is it related to a total product curve? Does the law of diminishing returns apply to capital as well as labor? Explain why or why not. What does a firm’s long-run average cost curve show? How is it related to the firm’s short-run average cost curves? What are economies of scale and diseconomies of scale? How do they arise? What do they imply for the shape of the long-run average cost curve? What is a firm’s minimum efficient scale? Work Study Plan 9.4 and get instant feedback. ◆ Reading Between the Lines on pp. 206–207 applies what you’ve learned about a firm’s cost curves. It looks at the cost curves for generating electricity using a variety of technologies and compares the total cost and marginal cost of traditional and new technologies. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 206 READING BETWEEN THE LINES Cutting the Cost of Clean Electricity Start-Up: Affordable Solar PowerPossible in a Year http://www.usatoday.com April 29, 2008 A Silicon Valley start-up says it has developed technology that can deliver solar power in about a year at prices competitive with coal-fired electricity. … SUNRGI’s “concentrated photovoltaic” system relies on lenses to magnify sunlight 2,000 times, letting it produce as much electricity as standard panels with a far smaller system. Craig Goodman, head of the National Energy Marketers Association, is expected to announce the breakthrough today. … Executives of the year-old company say they’ll start producing solar panels by mid-2009 that will generate electricity for about 7 cents a kilowatt hour, including installation. That’s roughly the price of cheap coal-fired electricity. … Solar power is acclaimed as free of greenhouse gas emissions and able to supply electricity midday when demand is highest. But its cost—20 cents to 30 cents a kilowatt hour—has inhibited broad adoption. Solar makes up less than 1% of U.S. power generation. An armada of solar technology makers aim to drive solar’s price to 10 to 18 cents a kilowatt hour by 2010, and 5 to 10 cents by 2015, at or below utility costs. … Copyright 2008 USA TODAY. Reprinted with permission. Further reproduction prohibited. Essence of the Story ■ A new Silicon Valley firm, SUNRGI, says it has developed technology that can deliver solar power for 7 cents a kilowatt hour. ■ 7 cents a kilowatt hour is roughly the price of electricity produced by coal. 206 ■ Solar power on current technology costs 20 cents to 30 cents a kilowatt hour. ■ A large number of solar technology makers aim to bring costs down to 10 to 18 cents a kilowatt hour by 2010 and to 5 to 10 cents by 2015. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 207 Economic Analysis 15 Figure 1 shows the average total cost (ATC) of producing electricity using seven alternative technologies. ■ The cost differences come from differences in fuel and capital costs. Hydro, wind, and solar have zero fuel costs. ■ Today’s solar technology has the highest average total cost at 15 cents per kilowatt hour. ■ ■ ■ The news article says that SUNRGI’s average total cost of 7 cents a kilowatt hour is “roughly the price of cheap coal-fired electricity.” Figure 1 shows the average total cost of coal-generated electricity at 4 cents per kilowatt hour. Based on this (correct) cost, it appears that SUNRGI cannot compete with coal (if we ignore the emission costs of coal). Remember, though, that average total cost varies with the output rate. The costs in Fig. 1 are those for operating plants at their most efficient level—80 percent of maximum capacity. (The closer a plant operates to its theoretical maximum output, the higher are the maintenance costs and so the higher is the average total cost.) MCCoal 12 8 6 3 0 Nuclear Coal Gas Hydro Solar ■ In Fig. 2, the average total cost of electricity generated by coal has a minimum at 4 cents per kilowatt hour at 80 percent plant capacity. ■ In Fig. 3, the average total cost of electricity generated by solar technology decreases as the plant is operated closer to capacity. ■ The marginal cost of producing electricity by using coal eventually rises (Fig. 2), but the marginal cost of solar electricity is zero (Fig.3). All the costs for solar power are fixed costs. 16 ATCSolar 12 8 ATCCoal 4 Wind SUNRGI Figure 1 Average total costs compared Figures 2 and 3 compare the ATC curves and MC curves for producing electricity by using coal and solar technologies. 16 9 Technology Cost (cents per kilowatt-hour) ■ The new SUNRGI technology slashes the average total cost of solar power, but the cost doesn’t get it down to a level that competes with the other technologies. Cost (cents per kilowatt-hour) ■ 12 ATC (cents per kilowatt-hour) ■ ATCSUNRGI 4 AFCCoal MC 0 20 40 60 80 100 Output (percentage of capacity) Figure 2 Cost curves for coal-generated electricity 0 20 40 60 80 100 Output (percentage of capacity) Figure 3 Cost curves for solar power 207 9160335_CH09_p189-212.qxd 208 6/22/09 9:01 AM Page 208 CHAPTER 9 Output and Costs SUMMARY ◆ Key Points Short-Run Cost (pp. 197–201) ■ Decision Time Frames (p. 192) ■ ■ In the short run, the quantity of at least one factor of production is fixed and the quantities of the other factors of production can be varied. In the long run, the quantities of all factors of production can be varied. ■ As output increases, total fixed cost is constant, and total variable cost and total cost increase. As output increases, average fixed cost decreases and average variable cost, average total cost, and marginal cost decrease at low outputs and increase at high outputs. These cost curves are U-shaped. Long-Run Cost (pp. 202–205) Short-Run Technology Constraint (pp. 193–196) ■ ■ ■ ■ A total product curve shows the quantity a firm can produce with a given quantity of capital and different quantities of labor. Initially, the marginal product of labor increases as the quantity of labor increases, because of increased specialization and the division of labor. Eventually, marginal product diminishes because an increasing quantity of labor must share a fixed quantity of capital—the law of diminishing returns. Initially, average product increases as the quantity of labor increases, but eventually average product diminishes. ■ ■ ■ A firm has a set of short-run cost curves for each different plant. For each output, the firm has one least-cost plant. The larger the output, the larger is the plant that will minimize average total cost. The long-run average cost curve traces out the lowest attainable average total cost at each output when both capital and labor inputs can be varied. With economies of scale, the long-run average cost curve slopes downward. With diseconomies of scale, the long-run average cost curve slopes upward. Key Figures and Table Figure 9.2 Figure 9.3 Figure 9.5 Figure 9.6 Total Product and Marginal Product, 195 Average Product, 196 Marginal Cost and Average Costs, 199 Product Curves and Cost Curves, 200 Figure 9.7 Figure 9.8 Table 9.2 Short-Run Costs of Four Different Plants, 203 Long-Run Average Cost Curve, 204 A Compact Glossary of Costs, 201 Key Terms Average fixed cost, 198 Average product, 193 Average total cost, 198 Average variable cost, 198 Constant returns to scale, 204 Diminishing marginal returns, 195 Diseconomies of scale, 204 Economies of scale, 204 Law of diminishing returns, 195 Long run, 192 Long-run average cost curve, 203 Marginal cost, 198 Marginal product, 193 Minimum efficient scale, 205 Short run, 192 Sunk cost, 192 Total cost, 197 Total fixed cost, 197 Total product, 193 Total variable cost, 197 9160335_CH09_p189-212.qxd 7/1/09 3:46 PM Page 209 Problems and Applications PROBLEMS and APPLICATIONS 209 ◆ Work problems 1–11 in Chapter 9 Study Plan and get instant feedback. Work problems 12–22 as Homework, a Quiz, or a Test if assigned by your instructor. 1. Which of the following news items involves a short-run decision and which involves a long-run decision? Explain. January 31, 2008: Starbucks will open 75 more stores abroad than originally predicted, for a total of 975. February 25, 2008: For three hours on Tuesday, Starbucks will shut down every single one of its 7,100 stores so that baristas can receive a refresher course. June 2, 2008: Starbucks replaces baristas with vending machines. July 18, 2008: Starbucks is closing 616 stores by the end of March. 2. The table sets out Sue’s Surfboards’ total product schedule. Labor Output (workers per week) (surfboards per week) 1 2 3 4 5 6 7 30 70 120 160 190 210 220 a. Draw the total product curve. b. Calculate the average product of labor and draw the average product curve. c. Calculate the marginal product of labor and draw the marginal product curve. d. Over what output range does the firm enjoy the benefits of increased specialization and division of labor? e. Over what output range does the firm experience diminishing marginal product of labor? f. Over what output range does this firm experience an increasing average product of labor but a diminishing marginal product of labor? g. Explain how it is possible for a firm to experience simultaneously an increasing average product but a diminishing marginal product. 3. Sue’s Surfboards, in problem 2, hires workers at $500 a week and its total fixed cost is $1,000 a week. a. Calculate total cost, total variable cost, and total fixed cost of each output in the table. Plot these points and sketch the short-run total cost curves passing through them. b. Calculate average total cost, average fixed cost, average variable cost, and marginal cost of each output in the table. Plot these points and sketch the short-run average and marginal cost curves passing through them. c. Illustrate the connection between Sue’s AP, MP, AVC, and MC curves in graphs like those in Fig. 9.6. 4. Sue’s Surfboards, in problems 2 and 3, rents a factory building and the rent is increased by $200 a week. If other things remain the same, how do Sue’s Surfboards’ short-run average cost curves and marginal cost curve change. 5. Workers at Sue’s Surfboards, in problems 2 and 3, negotiate a wage increase of $100 a week for each worker. If other things remain the same, explain how Sue’s Surfboards’ short-run average cost curves and marginal cost curve change. 6. Sue’s Surfboards, in problem 2, buys a second plant and the output produced by each worker increases by 50 percent. The total fixed cost of operating each plant is $1,000 a week. Each worker is paid $500 a week. a. Calculate the average total cost of producing 180 and 240 surfboards a week when Sue’s Surfboards operates two plants. Graph these points and sketch the ATC curve. b. To produce 180 surfboards a week, is it efficient to operate one or two plants? c. To produce 160 surfboards a week, is it efficient for Sue’s to operate one or two plants? 7. Airlines Seek Out New Ways to Save on Fuel as Costs Soar The financial pain of higher fuel prices is particularly acute for airlines because it is their single biggest expense. … [Airlines] pump about 7,000 gallons into a Boeing 737 and as much as 60,000 gallons into the bigger 747 jet. … Each generation of aircraft is more efficient. At Northwest, the Airbus A330 long-range jets use 38 percent less fuel than the DC-10s they replaced, while the Airbus A319 medium-range planes are 27 9160335_CH09_p189-212.qxd 210 6/22/09 9:01 AM Page 210 CHAPTER 9 Output and Costs percent more efficient than DC-9s. … The New York Times, June 11, 2008 a. Is the price of fuel a fixed cost or a variable cost for an airline? b. Explain how an increase in the price of fuel changes an airline’s total costs, average costs, and marginal cost. c. Draw a graph to show the effects of an increase in the price of fuel on an airline’s TFC, TVC, AFC, AVC, and MC curves. d. Explain how a technological advance that makes an airplane engine more fuel efficient changes an airline’s total product, marginal product, and average product. e. Draw a graph to illustrate the effects of a more fuel-efficient aircraft on an airline’s TP, MP, and AP curves. f. Explain how a technological advance that makes an airplane engine more fuel-efficient changes an airline’s average variable cost, marginal cost, and average total cost. g. Draw a graph to illustrate how a technological advance that makes an airplane engine more fuel efficient changes an airline’s AVC, MC, and ATC curves. 8. The table shows the production function of Jackie’s Canoe Rides. Labor (workers per day) 10 20 30 40 Canoes Output ( rides per day) Plant 1 Plant 2 Plant 3 Plant 4 20 40 65 75 10 40 60 75 85 20 55 75 90 100 30 65 85 100 110 40 Jackie’s pays $100 a day for each canoe it rents and $50 a day for each canoe operator it hires. a. Graph the ATC curves for Plant 1 and Plant 2. b. On your graph in a, plot the ATC curves for Plant 3 and Plant 4. c. On Jackie’s LRAC curve, what is the average cost of producing 40, 75, and 85 rides a week? d. What is Jackie’s minimum efficient scale? e. Explain how Jackie’s uses its LRAC curve to decide how many canoes to rent. f. Does Jackie’s production function feature economies of scale or diseconomies of scale? 9. Business Boot Camp At a footwear company called Caboots, sales rose from $160,000 in 2000 to $2.3 million in 2006. But in 2007 sales dipped to $1.5 million. Joey and Priscilla Sanchez, who run Caboots, blame the decline partly on a flood that damaged the firm’s office and sapped morale. Based on a Fortune article, CNN, April 23, 2008 If the Sanchezes are correct in their assumptions and the prices of footwear didn’t change a. Explain the effect of the flood on the total product curve and marginal product curve at Caboots. b. Draw a graph to show the effect of the flood on the total product curve and marginal product curve at Caboots. 10. No Need for Economies of Scale Illinois Tool Works Inc. might not seem like an incubator for innovation. The 93-year-old company manufactures a hodgepodge of mundane products, from automotive components and industrial fasteners to zip-strip closures for plastic bags … and dedicates production lines and resources to high-volume products. A line will run only those three or four products. … Runs are much longer and more efficient. By physically linking machines … they are able to eliminate work in process and storage areas. … All the material handling and indirect costs are reduced. BusinessWeek, October 31, 2005 a. How would you expect “physically linking machines” to affect the firm’s short-run product curves and short-run average cost curves? b. Draw a graph to show your predicted effects of “physically linking machines” on the firm’s short-run product curves and cost curves. c. Explain how concentrating “production lines and resources to high-volume products” can influence long-run average cost as the output rate increases. 11. Grain Prices Go the Way of the Oil Price Every morning millions of Americans confront the latest trend in commodities markets at their kitchen table. … Rising prices for crops … have begun to drive up the cost of breakfast. The Economist, July 21, 2007 Explain how the rising price of crops affects the average total cost and marginal cost of producing breakfast cereals. 9160335_CH09_p189-212.qxd 6/22/09 9:01 AM Page 211 Problems and Applications 12. Coffee King Starbucks Raises Its Prices Blame the sour news at Starbucks this week on soaring milk costs. … The wholesale price [of ] milk is up nearly 70% in the 12 months. …“There’s a lot of milk in those [Starbucks] lattes,” notes John Glass, CIBC World Markets restaurant analyst. USA Today, July 24, 2007 a. Is milk a fixed factor of production or a variable factor of production? b. Describe how the increase in the price of milk changes Starbucks’ short-run cost curves. 13. Bill’s Bakery has a fire and Bill loses some of his cost data. The bits of paper that he recovers after the fire provide the information in the following table (all the cost numbers are dollars). TP AFC AVC ATC 10 120 100 A B 150 30 40 90 130 40 30 C D 50 24 108 c. Explain why the gap between total cost and total variable cost is the same at all outputs. 15. ProPainters hires students at $250 a week to paint houses. It leases equipment at $500 a week. Suppose that ProPainters doubles the number of students it hires and doubles the amount of equipment it leases. ProPainters experiences diseconomies of scale. a. Explain how the ATC curve with one unit of equipment differs from that when ProPainters uses double the amount of equipment. b. Explain what might be the source of the diseconomies of scale that ProPainters experiences. 16. The table shows the production function of Bonnie’s Balloon Rides. Output ( rides per day) Labor (workers per day) 220 20 MC 211 Plant 1 Plant 2 Plant 3 Plant 4 132 80 90 130 E Bill asks you to come to his rescue and provide the missing data in the five spaces identified as A, B, C, D, and E. 14. ProPainters hires students at $250 a week to paint houses. It leases equipment at $500 a week. The table sets out its total product schedule. Labor Output (students) (houses painted per week) 1 2 2 5 3 9 4 12 5 14 6 15 a. If ProPainters paints 12 houses a week, calculate its total cost, average total cost, and marginal cost b. At what output is average total cost a minimum? 10 20 30 40 50 Balloons ( number) 4 10 13 15 16 1 10 15 18 20 21 2 13 18 22 24 25 3 15 20 24 26 27 4 Bonnie’s pays $500 a day for each balloon it rents and $25 a day for each balloon operator it hires. a. Graph the ATC curves for Plant 1 and Plant 2. b. On your graph in a, plot the ATC curves for Plant 3 and Plant 4. c. On Bonnie’s LRAC curve, what is the average cost of producing 18 rides and 15 rides a day? d. Explain how Bonnie’s uses its long-run average cost curve to decide how many balloons to rent. 17. A firm is producing at minimum average total cost with its current plant. Sketch the firm’s short-run average total cost curve and long-run average cost curve for each of the following situations and explain, using the concepts of economies of scale and diseconomies of scale, the circumstances in which the firm a. Can lower its average total cost by increasing its plant. b. Can lower its average total cost by decreasing its plant. c. Cannot lower its average total cost. 9160335_CH09_p189-212.qxd 212 6/22/09 9:01 AM Page 212 CHAPTER 9 Output and Costs 18. Starbucks Unit Brews Up Self-Serve Espresso Bars … automated, self-serve espresso kiosks are in grocery stores. … The machines, which grind their own beans, crank out lattes, … and drip coffees … take credit and debit cards, [and] cash. … Concordia Coffee, a small Bellevue coffee equipment maker, builds the self-serve kiosks and sells them to Coinstar for just under $40,000 per unit. Coinstar installs them … and provides maintenance. The kiosks use [Starbucks’] Seattle’s Best Coffee. … The selfserve kiosks remove the labor costs of having a barista. … Store personnel handle refills of coffee beans and milk. … MSNBC, June 1, 2008 a. What is Coinstar’s total fixed cost of operating one self-serve kiosk? b. What are Coinstar’s variable costs of providing coffee at a self-serve kiosk? c. Assume that a coffee machine operated by a barista costs less than $40,000. Explain how the fixed costs, variable costs, and total costs of barista-served and self-served coffee differ. d. Sketch the marginal cost and average cost curves implied by your answer to c. 19. A Bakery on the Rise Some 500 customers a day line up to buy Avalon’s breads, scones, muffins, and coffee. … Staffing and management are worries. Avalon now employs 35 … [and] it will hire 15 more. … Payroll will climb by 30% to 40%. … As new CEO, Victor has quickly executed an ambitious agenda that includes the move to a larger space. … Avalon’s costs will soar. … Its monthly rent, for example, will leap to $10,000, from $3,500. CNN, March 24, 2008 a. Which of Avalon’s decisions described in the news clip is a short-run decision and which is a long-run decision? b. Why is Avalon’s long-run decision riskier than its short-run decision? c. By how much will Avalon’s short-run decision increase its total variable cost? d. By how much will Avalon’s long-run decision increase its monthly total fixed cost? e. Draw a graph to illustrate Avalon’s short-run ATC curve before and after the events described in the news clip. 20. Gap Will Focus on Smaller Scale Stores Gap has too many stores that are 12,500 square feet … deemed too large. … “Stores are larger than we need.” … The target size of stores should be 6,000 square feet to 10,000 square feet. In addition, the company plans to combine previously separate concept stores. Some Gap body, adult, maternity, baby and kids stores will be combined in one, rather than in separate spaces as they have been previously. CNN, June 10, 2008 a. Thinking of a Gap store as a production plant, explain why Gap is making a decision to reduce the size of its stores. b. Is Gap’s decision a long-run decision or a short-run decision? Explain. c. How might combining Gap’s concept stores into one store help better take advantage of economies of scale? 21. The Sunk-Cost Fallacy You have good tickets to a basketball game an hour’s drive away. There’s a blizzard raging outside, and the game is being televised. You can sit warm and safe at home by a roaring fire and watch it on TV, or you can bundle up, dig out your car, and go to the game. What do you do? Slate, September 9, 2005 a. What type of cost is your expenditure on tickets? b. Why is the cost of the ticket irrelevant to your current decision about whether to stay at home or go to the game? 22. Study Reading Between the Lines on pp. 206-207 and then answer the following questions. a. Sketch the AFC, AVC, and ATC curves for electricity production using seven technologies: (i) nuclear, (ii) coal, (iii) gas, (iv) hydro (v) wind, (vi) SUNRGI’s new solar system, and (vii) today’s solar technology. b. Sketch the marginal cost curves for electricity production using seven technologies: (i) nuclear, (ii) coal, (iii) gas, (iv) hydro, (v) wind, (vi) SUNRGI’s new solar system, and (vii) today’s solar technology. c. Given the cost differences among the different methods of generating electricity, why do you think we use more than one method? If we could use only one method, which would it be? ...
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