Economics: Output and Costs PDF

After studying this chapter, you will be able to: 䉬 Distinguish between the short run and the long run 䉬 Explain the relationship between a firm’s output and labor...

After studying this chapter, you will be able to: 䉬 Distinguish between the short run and the long run 䉬 Explain the relationship between a firm’s output and labor employed in the short run 䉬 Explain the relationship between a firm’s output and costs in the short run and derive a firm’s short-run cost curves 䉬 Explain the relationship between a firm’s output and costs in the long run and derive a firm’s long-run average cost curve W hat does a big electricity supplier in Pennsylvania, PennPower, and Campus 11 Sweaters, a small (fictional) producer of knitwear have in common? Like every firm, they must decide how much to produce, how many people to employ, and how much and what type of capital equipment to use. How do firms make these decisions? PennPower and the other electric utilities in the United States face a demand for electricity that fluctuates across the day and that fluctuates from day to day depending on the temperature. How do electric utilities cope with these demand fluctuations? We are going to answer these questions in this chapter. OUTPUT AND COSTS To explain the basic ideas as clearly as possible, we focus on the economic decisions of Campus Sweaters, Inc. Studying the way this firm copes with its economic problems will give us a clear view of the problems faced by all firms. We’ll then apply what we learn in this chapter to the real-world costs of producing cars and electricity. In Reading Between the Lines, we’ll look at the effects of a new generation of ‘smart’ meters that encourage users to even out electricity consumption across the day. 251 252 CHAPTER 11 Output and Costs ◆ Decision Time Frames production. We call the fixed factors of production the firm’s plant : In the short run, a firm’s plant is fixed. People who operate firms make many decisions, and For Campus Sweaters, the fixed plant is its factory all of their decisions are aimed at achieving one over- building and its knitting machines. For an electric riding goal: maximum attainable profit. But not all power utility, the fixed plant is its buildings, genera- decisions are equally critical. Some decisions are big tors, computers, and control systems. ones. Once made, they are costly (or impossible) to To increase output in the short run, a firm must reverse. If such a decision turns out to be incorrect, it increase the quantity of a variable factor of production, might lead to the failure of the firm. Other decisions which is usually labor. So to produce more output, are small. They are easily changed. If one of these Campus Sweaters must hire more labor and operate its decisions turns out to be incorrect, the firm can knitting machines for more hours a day. Similarly, an change its actions and survive. electric power utility must hire more labor and operate The biggest decision that an entrepreneur makes is its generators for more hours a day. in what industry to establish a firm. For most entre- Short-run decisions are easily reversed. The firm preneurs, their background knowledge and interests can increase or decrease its output in the short run by drive this decision. But the decision also depends on increasing or decreasing the amount of labor it hires. profit prospects—on the expectation that total rev- enue will exceed total cost. Cindy has already decided to set up Campus The Long Run Sweaters. She has also decided the most effective The long run is a time frame in which the quantities of method of organizing the firm. But she has not all factors of production can be varied. That is, the long decided the quantity to produce, the factors of pro- run is a period in which the firm can change its plant. duction to hire, or the price to charge for sweaters. To increase output in the long run, a firm can Decisions about the quantity to produce and the change its plant as well as the quantity of labor it hires. price to charge depend on the type of market in Campus Sweaters can decide whether to install more which the firm operates. Perfect competition, knitting machines, use a new type of machine, reorgan- monopolistic competition, oligopoly, and monopoly ize its management, or hire more labor. Long-run deci- all confront the firm with their own special problems. sions are not easily reversed. Once a plant decision is Decisions about how to produce a given output do made, the firm usually must live with it for some not depend on the type of market in which the firm time. To emphasize this fact, we call the past expendi- operates. All types of firms in all types of markets ture on a plant that has no resale value a sunk cost. A make similar decisions about how to produce. sunk cost is irrelevant to the firm’s current decisions. The actions that a firm can take to influence the The only costs that influence its current decisions are relationship between output and cost depend on how the short-run cost of changing its labor inputs and soon the firm wants to act. A firm that plans to the long-run cost of changing its plant. change its output rate tomorrow has fewer options than one that plans to change its output rate six months or six years from now. REVIEW QUIZ To study the relationship between a firm’s output decision and its costs, we distinguish between two 1 Distinguish between the short run and the long decision time frames: run. The short run 2 Why is a sunk cost irrelevant to a firm’s current The long run decisions? You can work these questions in Study Plan 11.1 and get instant feedback. 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 We’re going to study costs in the short run and the firms, capital, land, and entrepreneurship are fixed fac- long run. We begin with the short run and describe a tors of production and labor is the variable factor of firm’s technology constraint.  Short-Run Technology Constraint 253 ◆ Short-Run Technology TABLE 11.1 Total Product, Marginal Product, Constraint and Average Product To increase output in the short run, a firm must Total Marginal Average increase the quantity of labor employed. We describe Labor product product product (workers (sweaters (sweaters per (sweaters the relationship between output and the quantity of per day) per day) additional worker) per worker) labor employed by using three related concepts: A 0 0 1. Total product..........4 2. Marginal product B 1 4 4.00 3. Average product..........6 C 2 10 5.00 These product concepts can be illustrated either by..........3 product schedules or by product curves. Let’s look D 3 13 4.33 first at the product schedules...........2 E 4 15 3.75..........1 Product Schedules F 5 16 3.20 Table 11.1 shows some data that describe Campus Sweaters’ total product, marginal product, and aver- Total product is the total amount produced. Marginal age product. The numbers tell us how the quantity of product is the change in total product that results from a sweaters produced increases as Campus Sweaters one-unit increase in labor. For example, when labor employs more workers. The numbers also tell us increases from 2 to 3 workers a day (row C to row D), about the productivity of the labor that Campus total product increases from 10 to 13 sweaters a day. Sweaters employs. The marginal product of going from 2 to 3 workers is Focus first on the columns headed “Labor” and 3 sweaters. Average product is total product divided by “Total product.” Total product is the maximum output the quantity of labor employed. For example, the average that a given quantity of labor can produce. You can see product of 3 workers is 4.33 sweaters per worker from the numbers in these columns that as Campus (13 sweaters a day divided by 3 workers). Sweaters employs more labor, total product increases. For example, when 1 worker is employed, total prod- uct 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 then begins to decrease. For example, marginal prod- total product that results from a one-unit increase in uct increases from 4 sweaters a day for the first worker the quantity of labor employed, with all other inputs to 6 sweaters a day for the second worker and then remaining the same. For example, in Table 11.1, decreases to 3 sweaters a day for the third worker. when Campus Sweaters increases employment from 2 Average product also increases at first and then to 3 workers and does not change its capital, the mar- decreases. You can see the relationships between the ginal product of the third worker is 3 sweaters—total quantity of labor hired and the three product con- product increases from 10 to 13 sweaters. cepts more clearly by looking at the product curves. 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 Product Curves employed. For example, in Table 11.1, the average The product curves are graphs of the relationships product of 3 workers is 4.33 sweaters per worker— between employment and the three product concepts 13 sweaters a day divided by 3 workers. you’ve just studied. They show how total product, mar- If you look closely at the numbers in Table 11.1, ginal product, and average product change as employ- you can see some patterns. As Campus Sweaters hires ment changes. They also show the relationships among more labor, marginal product increases initially, and the three concepts. Let’s look at the product curves. 254 CHAPTER 11 Output and Costs Total Product Curve Marginal Product Curve Figure 11.1 shows Campus Sweaters’ total product Figure 11.2 shows Campus Sweaters’ marginal prod- curve, TP, which is a graph of the total product uct of labor. Part (a) reproduces the total product schedule. Points A through F correspond to rows A curve from Fig. 11.1 and part (b) shows the marginal through F in Table 11.1. To graph the entire total product curve, MP. product curve, we vary labor by hours rather than In part (a), the orange bars illustrate the marginal whole days. product of labor. The height of a bar measures mar- Notice the shape of the total product curve. As ginal product. Marginal product is also measured by employment increases from zero to 1 worker a day, the slope of the total product curve. Recall that the the curve becomes steeper. Then, as employment slope of a curve is the change in the value of the vari- increases to 3, 4, and 5 workers a day, the curve able measured on the y-axis—output—divided by the becomes less steep. change in the variable measured on the x-axis— The total product curve is similar to the produc- labor—as we move along the curve. A one-unit tion possibilities frontier (explained in Chapter 2). It increase in labor, from 2 to 3 workers, increases out- separates the attainable output levels from those that put from 10 to 13 sweaters, so the slope from point are unattainable. All the points that lie above the C to point D is 3 sweaters per additional worker, the curve are unattainable. Points that lie below the curve, same as the marginal product we’ve just calculated. in the orange area, are attainable, but they are ineffi- Again varying the amount of labor in the smallest cient—they use more labor than is necessary to pro- units possible, we can draw the marginal product duce a given output. Only the points on the total curve shown in Fig. 11.2(b). The height of this curve product curve are technologically efficient. 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 FIGURE 11.1 Total Product Curve sweaters (an increase of 3). The increase in output of TP 3 sweaters appears on the y-axis of part (b) as the Output (sweaters per day) 15 E F marginal product of going from 2 to 3 workers. We plot that marginal product at the midpoint between D Unattainable 2 and 3 workers. Notice that the marginal product shown in Fig. 11.2(b) reaches a peak at 1.5 workers, 10 C 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 Attainable employment increases from 1 worker to 2 workers. 5 The total product and marginal product curves B differ across firms and types of goods. GM’s product curves are different from those of PennPower, whose A curves in turn are different from those of Campus 0 1 2 3 4 5 Sweaters. But the shapes of the product curves are Labor (workers per day) similar because almost every production process has two features: The total product curve, TP, is based on the data in Table Increasing marginal returns initially 11.1. The total product curve shows how the quantity of sweaters produced changes as the quantity of labor Diminishing marginal returns eventually employed changes. For example, 2 workers can produce 10 sweaters a day (point C ). Points A through F on the Increasing Marginal Returns Increasing marginal curve correspond to the rows of Table 11.1. The total prod- returns occur when the marginal product of an addi- uct curve separates attainable outputs from unattainable out- tional worker exceeds the marginal product of the puts. Points below the TP curve are inefficient. previous worker. Increasing marginal returns arise from increased specialization and division of labor in animation the production process.  Short-Run Technology Constraint 255 For example, if Campus Sweaters employs one FIGURE 11.2 Total Product and Marginal Product worker, that person must learn all the aspects of sweater production: running the knitting machines, Output (sweaters per day) TP fixing breakdowns, packaging and mailing sweaters, 15 buying and checking the type and color of the wool. D All these tasks must be performed by that one person. 13 If Campus Sweaters hires a second person, the two workers can specialize in different parts of the pro- 10 C duction 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. 5 4 Diminishing Marginal Returns Most production processes experience increasing marginal returns ini- tially, but all production processes eventually reach a 0 1 2 3 4 5 point of diminishing marginal returns. Diminishing Labor (workers per day) marginal returns occur when the marginal product of (a) Total product an additional worker is less than the marginal prod- uct of the previous worker. Diminishing marginal returns arise from the fact that more and more workers are using the same capi- Marginal product (sweaters per additional worker) 6 tal 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 4 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 divi- 3 sion of labor have been exhausted. By hiring a third worker, the factory produces more sweaters, but the 2 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 MP without the need for further attention. Hiring more 0 1 2 3 4 5 and more workers continues to increase output but Labor (workers per day) by successively smaller amounts. Marginal returns are (b) Marginal product diminishing. This phenomenon is such a pervasive one that it is called a “law”—the law of diminishing Marginal product is illustrated by the orange bars. For exam- returns. The law of diminishing returns states that ple, when labor increases from 2 to 3 workers a day, mar- ginal product is the orange bar whose height is 3 sweaters. (Marginal product is shown midway between the quantities As a firm uses more of a variable factor of production of labor to emphasize that marginal product results from with a given quantity of the fixed factor of production, changing the quantity of labor.) The steeper the slope of the the marginal product of the variable factor eventually total product curve (TP ) in part (a), the larger is marginal diminishes. product (MP ) in part (b). Marginal product increases to a maximum (in this example when 1.5 workers a day are You are going to return to the law of diminishing employed) and then declines—diminishing marginal product. returns when we study a firm’s costs, but before we do that, let’s look at the average product of labor and animation the average product curve. 256 CHAPTER 11 Output and Costs Average Product Curve Figure 11.3 illustrates Campus Sweaters’ average Economics in Action product of labor and shows the relationship between How to Pull Up Your Average average product and marginal product. Points B through F on the average product curve AP corre- Do you want to pull up your average grade? Then spond to those same rows in Table 11.1. Average make sure that your grade this semester is better than product increases from 1 to 2 workers (its maximum your current average! This semester is your marginal value at point C ) but then decreases as yet more semester. If your marginal grade exceeds your average workers are employed. Notice also that average prod- grade (like the second semester in the figure), your uct is largest when average product and marginal average will rise. If your marginal grade equals your product are equal. That is, the marginal product average grade (like the third semester in the figure), curve cuts the average product curve at the point of your average won’t change. If your marginal grade is maximum average product. For the number of work- below your average grade (like the fourth semester in ers at which marginal product exceeds average prod- the figure), your average will fall. uct, average product is increasing. For the number of The relationship between your marginal and aver- workers at which marginal product is less than aver- age grades is exactly the same as that between mar- age product, average product is decreasing. ginal product and average product. The relationship between the average product and 4 marginal product is a general feature of the relation- Average ship between the average and marginal values of any grade variable—even your grades. 3 Marginal 2 FIGURE 11.3 Average Product grade Average product and marginal product (sweaters per day per worker) 6 Maximum 1 average C product GPA D 0 First Second Third Fourth 4 B E Semester F AP Marginal and Average Grade Curves 2 REVIEW QUIZ MP 1 Explain how the marginal product and average 0 1 2 3 4 5 product of labor change as the labor employed Labor (workers per day) increases (a) initially and (b) eventually. The figure shows the average product of labor and the con- 2 What is the law of diminishing returns? Why nection between average product and marginal product. does marginal product eventually diminish? With 1 worker, marginal product exceeds average product, 3 Explain the relationship between marginal so average product is increasing. With 2 workers, marginal product and average product. product equals average product, so average product is at its You can work these questions in Study maximum. With more than 2 workers, marginal product is Plan 11.2 and get instant feedback. less than average product, so average product is decreasing. Campus Sweaters’ product curves influence its animation costs, as you are now going to see.  Short-Run Cost 257 ◆ Short-Run Cost FIGURE 11.4 Total Cost Curves To produce more output in the short run, a firm must Cost (dollars per day) 150 TC employ more labor, which means that it must increase its costs. We describe the relationship between output TC = TFC + TVC TVC and cost by using three cost concepts: Total cost 100 Marginal cost 75 Average cost 50 Total Cost A firm’s total cost (TC ) is the cost of all the factors of TFC production it uses. We separate total cost into total fixed cost and total variable cost. 0 5 10 13 15 Total fixed cost (TFC ) is the cost of the firm’s fixed Output (sweaters per day) factors. For Campus Sweaters, total fixed cost includes the cost of renting knitting machines and normal profit, which is the opportunity cost of Total Total Cindy’s entrepreneurship (see Chapter 10, p. 229). fixed variable Total cost cost cost The quantities of fixed factors don’t change as out- Labor Output ( TFC ) ( TVC ) ( TC ) put changes, so total fixed cost is the same at all (workers (sweaters outputs. per day) per day) (dollars per day) Total variable cost (TVC ) is the cost of the firm’s A 0 0 25 0 25 variable factors. For Campus Sweaters, labor is the B 1 4 25 25 50 variable factor, so this component of cost is its wage bill. Total variable cost changes as output changes. C 2 10 25 50 75 Total cost is the sum of total fixed cost and total D 3 13 25 75 100 variable cost. That is, E 4 15 25 100 125 TC = TFC + TVC. F 5 16 25 125 150 The table in Fig. 11.4 shows total costs. Campus Sweaters rents one knitting machine for $25 a day, so Campus Sweaters rents a knitting machine for $25 a day, its TFC is $25. To produce sweaters, the firm hires so this cost is the firm’s total fixed cost. The firm hires work- labor, which costs $25 a day. TVC is the number of ers at a wage rate of $25 a day, and this cost is its total workers multiplied by $25. For example, to produce variable cost. For example, in row D, Campus Sweaters 13 sweaters a day, in row D, the firm hires 3 workers employs 3 workers and its total variable cost is 3 × $25, and TVC is $75. TC is the sum of TFC and TVC, so which equals $75. Total cost is the sum of total fixed cost to produce 13 sweaters a day, TC is $100. Check the and total variable cost. For example, when Campus calculations in the other rows of the table. Sweaters employs 3 workers, total cost is $100—total fixed Figure 11.4 shows Campus Sweaters’ total cost cost of $25 plus total variable cost of $75. curves, which graph total cost against output. The The graph shows Campus Sweaters’ total cost curves. green TFC curve is horizontal because total fixed Total fixed cost is constant—the TFC curve is a horizontal cost ($25 a day) does not change when output line. Total variable cost increases as output increases, so changes. The purple TVC curve and the blue TC the TVC curve and the TC curve increase as output curve both slope upward because to increase output, increases. The vertical distance between the TC curve and more labor must be employed, which increases total the TVC curve equals total fixed cost, as illustrated by the variable cost. Total fixed cost equals the vertical dis- two arrows. tance between the TVC and TC curves. animation Let’s now look at a firm’s marginal cost. 258 CHAPTER 11 Output and Costs Marginal Cost cepts are calculated from the total cost concepts as Figure 11.4 shows that total variable cost and total follows: cost increase at a decreasing rate at small outputs TC = TFV + TVC. but eventually, as output increases, total variable cost and total cost increase at an increasing rate. To Divide each total cost term by the quantity produced, understand this pattern in the change in total cost Q, to get as output increases, we need to use the concept of TC TFC TVC marginal cost. = + , Q Q Q A firm’s marginal cost is the increase in total cost that results from a one-unit increase in output. We or calculate marginal cost as the increase in total cost ATC = AFC + AVC. divided by the increase in output. The table in Fig. 11.5 shows this calculation. When, for example, out- The table in Fig. 11.5 shows the calculation of put increases from 10 sweaters to 13 sweaters, total average total cost. For example, in row C, output is cost increases from $75 to $100. The change in out- 10 sweaters. Average fixed cost is ($25  10), which put is 3 sweaters, and the change in total cost is equals $2.50, average variable cost is ($50  10), $25. The marginal cost of one of those 3 sweaters which equals $5.00, and average total cost is is ($25  3), which equals $8.33. ($75  10), which equals $7.50. Note that average Figure 11.5 graphs the marginal cost data in the total cost is equal to average fixed cost ($2.50) plus table as the red marginal cost curve, MC. This curve average variable cost ($5.00). is U-shaped because when Campus Sweaters hires a Figure 11.5 shows the average cost curves. The second worker, marginal cost decreases, but when it green average fixed cost curve (AFC ) slopes down- hires a third, a fourth, and a fifth worker, marginal ward. As output increases, the same constant total cost successively increases. fixed cost is spread over a larger output. The blue At small outputs, marginal cost decreases as output average total cost curve (ATC ) and the purple average increases because of greater specialization and the variable cost curve (AVC ) are U-shaped. The vertical division of labor. But as output increases further, distance between the average total cost and average marginal cost eventually increases because of the law variable cost curves is equal to average fixed cost—as of diminishing returns. The law of diminishing returns indicated by the two arrows. That distance shrinks as means that the output produced by each additional output increases because average fixed cost declines worker is successively smaller. To produce an addi- with increasing output. tional unit of output, ever more workers are required, and the cost of producing the additional unit of out- Marginal Cost and Average Cost put—marginal cost—must eventually increase. The marginal cost curve (MC ) intersects the average Marginal cost tells us how total cost changes as variable cost curve and the average total cost curve at output increases. The final cost concept tells us what their minimum points. When marginal cost is less it costs, on average, to produce a unit of output. Let’s than average cost, average cost is decreasing, and now look at Campus Sweaters’ average costs. when marginal cost exceeds average cost, average cost is increasing. This relationship holds for both the Average Cost ATC curve and the AVC curve. It is another example Three average costs of production are of the relationship you saw in Fig. 11.3 for average product and marginal product and in your average 1. Average fixed cost and marginal grades. 2. Average variable cost 3. Average total cost Why the Average Total Cost Curve Average fixed cost (AFC ) is total fixed cost per unit of output. Average variable cost (AVC ) is total vari- Is U-Shaped able cost per unit of output. Average total cost (ATC ) Average total cost is the sum of average fixed cost and is total cost per unit of output. The average cost con- average variable cost, so the shape of the ATC curve  Short-Run Cost 259 FIGURE 11.5 Marginal Cost and Average Costs Marginal cost is calculated as the change in total cost divided Cost (dollars per sweater) 15 MC by the change in output. When output increases from 4 to 10 sweaters, an increase of 6 sweaters, total cost increases by ATC = AFC + AVC $25. Marginal cost is $25 ÷ 6, which is $4.17. Each average cost concept is calculated by dividing the 10 ATC related total cost by output. When 10 sweaters are produced, AVC 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 5 intersects the AVC curve and the ATC curve at their minimum points. The average fixed cost curve (AFC ) is downward slop- ing. The ATC curve and AVC curve are U-shaped. The vertical AFC distance between the ATC curve and the AVC curve is equal to 0 5 10 15 average fixed cost, as illustrated by the two arrows. Output (sweaters per day) Total Total Marginal Average Average Average fixed variable Total cost fixed variable total Labor Output cost cost cost ( MC ) cost cost cost ( TFC ) ( TVC ) ( TC ) ( AFC ) ( AVC ) ( ATC ) (workers (sweaters (dollars per per day) per day) (dollars per day) additional sweater) (dollars per sweater) A 0 0 25 0 25 — — —....... 6.25 B 1 4 25 25 50 6.25 6.25 12.50....... 4.17 C 2 10 25 50 75 2.50 5.00 7.50....... 8.33 D 3 13 25 75 100 1.92 5.77 7.69.......12.50 E 4 15 25 100 125 1.67 6.67 8.33.......25.00 F 5 16 25 125 150 1.56 7.81 9.38 animation combines the shapes of the AFC and AVC curves. eventually increases, and the AVC curve slopes The U shape of the ATC curve arises from the influ- upward. The AVC curve is U shaped. ence of two opposing forces: The shape of the ATC curve combines these two 1. Spreading total fixed cost over a larger output effects. Initially, as output increases, both average fixed cost and average variable cost decrease, so average total 2. Eventually diminishing returns cost decreases. The ATC curve slopes downward. When output increases, the firm spreads its total But as output increases further and diminishing fixed cost over a larger output and so its average returns set in, average variable cost starts to increase. fixed cost decreases—its AFC curve slopes With average fixed cost decreasing more quickly than downward. average variable cost is increasing, the ATC curve Diminishing returns means that as output continues to slope downward. Eventually, average increases, ever-larger amounts of labor are needed to variable cost starts to increase more quickly than produce an additional unit of output. So as output average fixed cost decreases, so average total cost increases, average variable cost decreases initially but starts to increase. The ATC curve slopes upward. 260 CHAPTER 11 Output and Costs Cost Curves and Product Curves FIGURE 11.6 Product Curves and The technology that a firm uses determines its costs. Cost Curves Figure 11.6 shows the links between the firm’s prod- Average product and marginal product uct curves and its cost curves. The upper graph shows the average product curve, AP, and the marginal 6 product curve, MP—like those in Fig. 11.3. The lower graph shows the average variable cost curve, AP AVC, and the marginal cost curve, MC—like those in Fig. 11.5. 4 MP 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 2 the point of maximum marginal product, marginal Rising MP and Falling MP and Falling MP and cost is at a minimum. falling MC: rising MC: rising MC: rising AP and rising AP and falling AP and As labor increases from 1.5 workers to 2 workers a falling AVC falling AVC rising AVC day, (upper graph) output increases from 6.5 sweaters to 10 sweaters a day (lower graph). Marginal product 0 1.5 2.0 Labor falls and marginal cost rises, but average product con- Cost (dollars per unit) tinues to rise and average variable cost continues to fall. At the point of maximum average product, aver- Maximum MP and age variable cost is at a minimum. As labor increases 12 Minimum MC further, output increases. Average product diminishes and average variable cost increases. Maximum AP and 9 Minimum AVC Shifts in the Cost Curves MC The position of a firm’s short-run cost curves depends 6 AVC on two factors: Technology Prices of factors of production 3 Technology A technological change that increases productivity increases the marginal product and aver- 0 6.5 10 age product of labor. With a better technology, the Output same factors of production can produce more output, A firm’s MP curve is linked to its MC curve. If, as the firm so the technological advance lowers the costs of pro- increases its labor from 0 to 1.5 workers a day, the firm’s duction and shifts the cost curves downward. marginal product rises, its marginal cost falls. If marginal For example, advances in robot production tech- product is at a maximum, marginal cost is at a minimum. If, niques have increased productivity in the automobile as the firm hires more labor, its marginal product dimin- industry. As a result, the product curves of Chrysler, ishes, its marginal cost rises. Ford, and GM have shifted upward and their cost A firm’s AP curve is linked to its AVC curve. If, as the curves have shifted downward. But the relationships firm increases its labor to 2 workers a day, its average between their product curves and cost curves have product rises, its average variable cost falls. If average not changed. The curves are still linked in the way product is at a maximum, average variable cost is at a mini- shown in Fig. 11.6. mum. If, as the firm hires more labor, its average product Often, as in the case of robots producing cars, a diminishes, its average variable cost rises. technological advance results in a firm using more cap- ital, a fixed factor, and less labor, a variable factor. animation  Short-Run Cost 261 TABLE 11.2 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 TC = TFC + TVC Output (total product) TP Total quantity produced (output Q) Marginal cost MC Change in total cost resulting from a one- MC = ΔTC ÷ ΔQ unit increase in total product 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 Another example is the use of ATMs by banks to dis- truck drivers’ wages or the price of gasoline increases, pense cash. ATMs, which are fixed capital, have the variable cost and marginal cost of transportation replaced tellers, which are variable labor. Such a tech- services increase. nological change decreases total cost but increases fixed You’ve now completed your study of short-run costs and decreases variable cost. This change in the costs. All the concepts that you’ve met are summa- mix of fixed cost and variable cost means that at small rized in a compact glossary in Table 11.2. outputs, average total cost might increase, while at large outputs, average total cost decreases. Prices of Factors of Production An increase in the REVIEW QUIZ price of a factor of production increases the firm’s 1 What relationships do a firm’s short-run cost costs and shifts its cost curves. How the curves shift curves show? depends on which factor price changes. An increase in rent or some other component of 2 How does marginal cost change as output fixed cost shifts the TFC and AFC curves upward and increases (a) initially and (b) eventually? shifts the TC curve upward but leaves the AVC and 3 What does the law of diminishing returns TVC curves and the MC curve unchanged. For imply for the shape of the marginal cost curve? example, if the interest expense paid by a trucking 4 What is the shape of the AFC curve and why company increases, the fixed cost of transportation does it have this shape? services increases. 5 What are the shapes of the AVC curve and the An increase in wages, gasoline, or another compo- ATC curve and why do they have these shapes? nent of variable cost shifts the TVC and AVC curves You can work these questions in Study upward and shifts the MC curve upward but leaves Plan 11.3 and get instant feedback. the AFC and TFC curves unchanged. For example, if 262 CHAPTER 11 Output and Costs ◆ Long-Run Cost TABLE 11.3 The Production Function We are now going to study the firm’s long-run costs. Output In the long run, a firm can vary both the quantity of Labor (sweaters per day) labor and the quantity of capital, so in the long run, (workers per day) Plant 1 Plant 2 Plant 3 Plant 4 all the firm’s costs are variable. The behavior of long-run cost depends on the 1 4 10 13 15 firm’s production function, which is the relationship 2 10 15 18 20 between the maximum output attainable and the quantities of both labor and capital. 3 13 18 22 24 4 15 20 24 26 5 16 21 25 27 The Production Function Table 11.3 shows Campus Sweaters’ production Knitting machines 1 2 3 4 function. The table lists total product schedules for (number) four different quantities of capital. The quantity of capital identifies the plant size. The numbers for The table shows the total product data for four quantities plant 1 are for a factory with 1 knitting machine— of capital (plant sizes). The greater the plant size, the the case we’ve just studied. The other three plants larger is the output produced by any given quantity of have 2, 3, and 4 machines. If Campus Sweaters uses labor. For a given plant size, the marginal product of plant 2 with 2 knitting machines, the various labor diminishes as more labor is employed. For a given amounts of labor can produce the outputs shown in quantity of labor, the marginal product of capital dimin- the second column of the table. The other two columns ishes as the quantity of capital used increases. 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 and increases the number of machines from 2 to 3, each of the four plant sizes as the quantity of labor output increases from 18 to 22 sweaters a day. The increases. You can check that fact by calculating the marginal product of the third machine is 4 sweaters marginal product of labor in each of the plants with a day, down from 5 sweaters a day for the second 2, 3, and 4 machines. With each plant size, as the machine. firm increases the quantity of labor employed, the Let’s now see what the production function marginal product of labor (eventually) diminishes. implies for long-run costs. Diminishing Marginal Product of Capital Diminishing returns also occur with each quantity Short-Run Cost and Long-Run Cost of labor as the quantity of capital increases. You can As before, Campus Sweaters can hire workers for $25 check that fact by calculating the marginal product a day and rent knitting machines for $25 a day. of capital at a given quantity of labor. The marginal Using these factor prices and the data in Table 11.3, product of capital is the change in total product we can calculate the average total cost and graph the divided by the change in capital when the quantity ATC curves for factories with 1, 2, 3, and 4 knitting of labor is constant—equivalently, the change in machines. We’ve already studied the costs of a factory output resulting from a one-unit increase in the with 1 machine in Figs. 11.4 and 11.5. In Fig. 11.7, quantity of capital. For example, if Campus the average total cost curve for that case is ATC1. Sweaters has 3 workers and increases its capital Figure 11.7 also shows the average total cost curve for from 1 machine to 2 machines, output increases a factory with 2 machines, ATC2, with 3 machines, from 13 to 18 sweaters a day. The marginal product ATC3, and with 4 machines, ATC4. of the second machine is 5 sweaters a day. If You can see, in Fig. 11.7, that the plant size has a Campus Sweaters continues to employ 3 workers big effect on the firm’s average total cost.  Long-Run Cost 263 FIGURE 11.7 Short-Run Costs of Four Different Plants The figure shows short-run Average cost (dollars per sweater) average total cost curves for 12.00 four different quantities of capital at Campus Sweaters. The firm can produce 13 sweaters a day with 1 knit- 10.00 ATC1 ATC2 ATC3 ATC4 ting machine on ATC1 or with 9.50 3 knitting machines on ATC3 for an average cost of $7.69 a sweater. The firm can pro- 8.00 duce 13 sweaters a day by 7.69 using 2 machines on ATC2 for $6.80 a sweater or by using 6.80 4 machines on ATC4 for 6.00 $9.50 a sweater. If the firm produces 13 sweaters a day, the least-cost method of production, the 0 5 10 13 15 20 25 30 long-run method, is with 2 Output (sweaters per day) machines on ATC2. animation In Fig. 11.7, two things stand out: average total cost of 13 sweaters a day is $7.69 a 1. Each short-run ATC curve is U-shaped. sweater. With 2 machines, on ATC2, average total cost is $6.80 a sweater. With 3 machines, on ATC3, 2. For each short-run ATC curve, the larger the average total cost is $7.69 a sweater, the same as with plant, the greater is the output at which average 1 machine. Finally, with 4 machines, on ATC4, aver- total cost is at a minimum. age total cost is $9.50 a sweater. Each short-run ATC curve is U-shaped because, as The economically efficient plant for producing a the quantity of labor increases, its marginal product given output is the one that has the lowest average initially increases and then diminishes. This pattern total cost. For Campus Sweaters, the economically in the marginal product of labor, which we examined efficient plant to use to produce 13 sweaters a day is in some detail for the plant with 1 knitting machine the one with 2 machines. on pp. 254–255, occurs at all plant sizes. In the long run, Cindy chooses the plant that min- The minimum average total cost for a larger plant imizes average total cost. When a firm is producing a occurs at a greater output than it does for a smaller given output at the least possible cost, it is operating plant because the larger plant has a higher total fixed on its long-run average cost curve. cost and therefore, for any given output, a higher The long-run average cost curve is the relationship average fixed cost. between the lowest attainable average total cost and Which short-run ATC curve a firm operates on output when the firm can change both the plant it depends on the plant it has. In the long run, the firm uses and the quantity of labor it employs. can choose its plant and the plant it chooses is the The long-run average cost curve is a planning one that enables it to produce its planned output at curve. It tells the firm the plant and the quantity of the lowest average total cost. labor to use at each output to minimize average To see why, suppose that Campus Sweaters plans cost. Once the firm chooses a plant, the firm oper- to produce 13 sweaters a day. In Fig. 11.7, with 1 ates on the short-run cost curves that apply to that machine, the average total cost curve is ATC1 and the plant. 264 CHAPTER 11 Output and Costs The Long-Run Average Cost Curve GM produces 100 cars a week, each worker must per- Figure 11.8 shows how a long-run average cost curve form many different tasks and the capital must be gen- is derived. The long-run average cost curve LRAC eral-purpose machines and tools. But if GM produces consists of pieces of the four short-run ATC curves. 10,000 cars a week, each worker specializes in a small For outputs up to 10 sweaters a day, average total cost number of tasks, uses task-specific tools, and becomes is the lowest on ATC1. For outputs between 10 and highly proficient. Diseconomies of scale are features of a firm’s tech- 18 sweaters a day, average total cost is the lowest on ATC2. For outputs between 18 and 24 sweaters a day, nology that make average total cost rise as output average total cost is the lowest on ATC3. And for out- increases. When diseconomies of scale are present, puts in excess of 24 sweaters a day, average total cost the LRAC curve slopes upward. In Fig. 11.8, is the lowest on ATC4. The piece of each ATC curve Campus Sweaters experiences diseconomies of scale with the lowest average total cost is highlighted in at outputs greater than 15 sweaters a day. dark blue in Fig. 11.8. This dark blue scallop-shaped The challenge of managing a large enterprise is the curve made up of the pieces of the four ATC curves is main source of diseconomies of scale. Constant returns to scale are features of a firm’s tech- the LRAC curve. nology that keep average total cost constant as output increases. When constant returns to scale are present, Economies and Diseconomies of Scale the LRAC curve is horizontal. Economies of scale are features of a firm’s technology that make average total cost fall as output increases. Economies of Scale at Campus Sweaters The When economies of scale are present, the LRAC curve economies of scale and diseconomies of scale at slopes downward. In Fig. 11.8, Campus Sweaters has Campus Sweaters arise from the firm’s production economies of scale for outputs up to 15 sweaters a day. function in Table 11.3. With 1 machine and 1 Greater specialization of both labor and capital is worker, the firm produces 4 sweaters a day. With 2 the main source of economies of scale. For example, if machines and 2 workers, total cost doubles but out- FIGURE 11.8 Long-Run Average Cost Curve The long-run average cost Average cost (dollars per sweater) Economies of scale Diseconomies of scale curve traces the lowest attain- Least-cost plant is 1 Least-cost plant is 2 Least-cost plant is 3 Least-cost plant is 4 able ATC when both labor 12.00 and capital change. The green arrows highlight the output range over which each plant achieves the lowest 10.00 ATC1 ATC2 ATC3 ATC4 ATC. Within each range, to change the quantity pro- duced, the firm changes the quantity of labor it employs. 8.00 Along the LRAC curve, LRAC curve economies of scale occur if average cost falls as output increases; diseconomies of Minimum 6.00 scale occur if average cost efficient scale rises as output increases. Minimum efficient scale is the 0 5 10 15 18 20 24 25 30 output at which average cost Output (sweaters per day) is lowest, 15 sweaters a day. animation  Long-Run Cost 265 Economics in Action Produce More to Cut Cost 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 Average cost (thousands of dollars per vehicle) 40 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 30 ATC1 hour, the firm installs the plant with the short-run average total cost curve ATC1. The average cost of ATC2 producing a vehicle is $20,000. 20 Producing 20 vehicles an hour doesn’t use the 15 plant at its lowest possible average total cost. If the firm could sell enough cars for it to produce 40 vehi- 10 cles an hour, the firm could use its current plant and produce at an average cost of $15,000 a vehicle. LRAC But if the firm planned to produce 40 vehicles an hour, it would not stick with its current plant. The 0 20 40 60 80 firm would install a bigger plant with the short-run Output (vehicles per hour) average total cost curve ATC2, and produce 40 vehi- Automobile Plant Average Cost Curves cles an hour for $10,000 a car. put more than doubles to 15 sweaters a day, so aver- age cost decreases and Campus Sweaters experiences REVIEW QUIZ economies of scale. With 4 machines and 4 workers, 1 What does a firm’s production function show total cost doubles again but output less than doubles and how is it related to a total product curve? to 26 sweaters a day, so average cost increases and the 2 Does the law of diminishing returns apply to firm experiences diseconomies of scale. capital as well as labor? Explain why or why not. Minimum Efficient Scale A firm’s minimum efficient 3 What does a firm’s LRAC curve show? How is it scale is the smallest output at which long-run average related to the firm’s short-run ATC curves? cost reaches its lowest level. At Campus Sweaters, the 4 What are economies of scale and diseconomies minimum efficient scale is 15 sweaters a day. of scale? How do they arise? What do they imply The minimum efficient scale plays a role in deter- for the shape of the LRAC curve? mining market structure. In a market in which the 5 What is a firm’s minimum efficient scale? minimum efficient scale is small relative to market demand, the market has room for many firms, and You can work these questions in Study Plan 11.4 and get instant feedback. 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 ◆ Reading Between the Lines on pp. 266–267 applies only one firm, can make a profit and the market is what you’ve learned about a firm’s cost curves. It looks either an oligopoly or monopoly. We will return to at the cost of producing electricity and explains how this idea in the next three chapters. the use of smart meters can lower average variable cost.  READING BETWEEN THE LINES Cutting the Cost of Producing Electricity Here Come the “Smart” Meters http://www.wsj.com May 21, 2010 One of modern life’s most durable features—fixed-price electricity—is slowly being pushed to the sidelines, a creeping change that will influence such things as what time millions of Ameri- cans cook dinner and what appliances they buy. Driving the change is the rollout of so-called smart meters, which can transmit data on how much power is being used at any given time. That gives utilities the ability to charge more for electricity at peak times and less during lulls. Spreading out electricity consumption more evenly across the day leads to more efficient use of power plants and lower emissions.... The new system uses digital meters to charge prices that vary during the day. Though fewer than 10 percent of U.S. homes have smart ESSENCE OF THE STORY meters now, the Department of Energy is funding efforts that will boost that number to nearly a third by 2015. Fixed-price electricity is being replaced by The majority of homes in California and Texas, the two time-of-day pricing. most populous states, will have smart meters by 2013. Smart meters make it possible for utilities to charge more for electricity at peak times and Smart meters lie at the heart of efforts to get Americans less at off-peak times. to use less electricity. Power generation accounts for Fewer than 10 percent of U.S. homes had about 40 percent of greenhouse-gas emissions in the smart meters in 2010, but the majority of United States. A 2009 federal study found that smart homes in California and Texas will have them meters could help cut peak electricity use by 20 percent. by 2013 and almost a third of all U.S. homes will have them by 2015. In California, power plants totaling 30,000 to 35,000 Time-of-day pricing makes electricity megawatts of capacity are needed on a typical day. But consumption more even across the day. 50,000 megawatts or more are needed on hot days. A 2009 federal study found that smart meters That forces generators to turn on their least efficient could help cut peak electricity use by 20 and most polluting plants to meet demand. In New percent. York, average demand is 42 percent less than peak-time Making electricity consumption more even demand. Flatten peak use, experts say, and system costs across the day lowers the cost of electricity drop, as does pollution.... generation. Wall Street Journal, excerpted from “Here Come the ‘Smart’ Meters: ‘Smart' Meters In California, power plants produce 30,000 Know When You’re Cooking, Cleaning; How About Dinner at 4?” by Rebecca Smith. to 35,000 megawatts on a typical day and Copyright 2010 by Dow Jones & Company, Inc. Reproduced with permission of Dow 50,000 megawatts or more on a hot day. Jones & Company, Inc. via Copyright Clearance Center. In New York, average production is 42 percent less than peak-time production. 266  ECONOMIC ANALYSIS The average variable cost of producing electricity de- pends on the technology used and on the quantity of electricity produced. Figure 1 shows some of the cost differences that arise from using different technologies. The variable cost of using wind power is zero; nuclear is the next least costly; and a turbine has the highest cost. Electric power utilities use the lowest-cost technologies to meet normal demand and where possible to meet peak demand. At very high peak demand, they also use turbines that burn a high-cost gasoline fuel. For a given technology, average variable cost depends on the quantity produced, and Fig. 2 illustrates this re- lationship. In the example in Fig. 2 the plant is designed to have A smart meter being installed minimum AVC when it produces 60 percent of its phys- ical maximum output. If production could be held steady at 60 percent of the plant’s physical maximum output, the cost of producing By introducing smart meters that enable time-of-day electricity is minimized. pricing of electricity, consumers can be confronted with But if production increases to meet peak demand at the the marginal cost of their choices. physical limit of the plant, the cost of production in- By raising the price during the peak hours and lower- creases along the rising AVC curve and MC curve. ing the price during off-peak hours, electricity consump- When electricity is sold for a single price, consumers tion can be kept more even over the day and closer to have no incentive to limit their peak-hour usage. the quantity at minimum average variable cost. Cost (cents per kilowatt-hour) 0.75 MC Wind 0.70 Peak load power Nuclear costs more to produce 0.50 Gas-oil AVC 0.40 Hydro 0.25 Coal Turbine Normal load Peak load 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0 20 40 60 80 100 Average variable cost (cents per kWh) Output (percentage of maximum) Figure 1 Average variable costs of alternative technologies Figure 2 Cost curves for generating electricity 267 268 CHAPTER 11 Output and Costs SUMMARY Key Points Short-Run Cost (pp. 257–261) As output increases, total fixed cost is constant, Decision Time Frames (p. 252) and total variable cost and total cost increase. In the short run, the quantity of at least one factor As output increases, average fixed cost decreases of production is fixed and the quantities of the and average variable cost, average total cost, and other factors of production can be varied. marginal cost decrease at low outputs and increase In the long run, the quantities of all factors of at high outputs. These cost curves are U-shaped. production can be varied. Working Problems 9 to 14 will give you a better under- Working Problems 1 and 2 will give you a better under- standing of a firm’s short-run cost. standing of a firm’s decision time frames. Long-Run Cost (pp. 262–265) Short-Run Technology Constraint (pp. 253–256) A firm has a set of short-run cost curves for each A total product curve shows the quantity a firm different plant. For each output, the firm has one can produce with a given quantity of capital and least-cost plant. The larger the output, the larger is different quantities of labor. the plant that will minimize average total cost. Initially, the marginal product of labor increases The long-run average cost curve traces out the as the quantity of labor increases, because of lowest attainable average total cost at each output increased specialization and the division of labor. when both capital and labor inputs can be varied. Eventually, marginal product diminishes because an With economies of scale, the long-run average cost increasing quantity of labor must share a fixed quan- curve slopes downward. With diseconomies of tity of capital—the law of diminishing returns. scale, the long-run average cost curve slopes Initially, average product increases as the quantity upward. of labor increases, but eventually average product Working Problems 15 to 20 will give you a