# OUTPUT AND COSTS. Chapter. Key Concepts. Decision Time Frames

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1 Chapter 10 OUTPUT AND COSTS Key Concepts Decision Time Frames Firms have two decision time frames: Short run is the time frame in which the quantity of at least one factor of production is fixed. Long run is the time frame in which the quantities of all factors of production can be varied. A sunk cost is a past cost. Sunk costs do not affect a firm s decisions. Short-Run Technology Constraint Three product concepts are important: Total product (TP )is the maximum output that a given quantity of labor can produce. The total product schedule shows the maximum attainable output with a fixed quantity of capital as the quantity of labor is varied. product of labor (MP ) is the increase in the total product resulting from a one-unit increase in the quantity of labor. product of labor (AP ) is equal to the total product divided by the quantity of labor employed. Figure 10.1 illustrates the MP and AP curves for labor. The product curves have the shapes shown because production initially has increasing marginal returns (another worker s marginal product is higher than the previous worker s) followed by diminishing marginal returns (when an additional worker s marginal product is less than the previous worker). The law of diminishing returns states that as a firm uses more of a variable factor of production, with a given quantity of fixed factors of production, the marginal product of the variable factor eventually diminishes. This figure also shows the (general) relationship between the marginal product and average product When the MP > AP, the AP rises. When the MP < AP, the AP falls. When MP = AP, the AP is at its maximum. Short-Run Cost Several important cost concepts are Total cost (TC ): cost of all factors of production used, including the normal profit. total cost (ATC ) is TC Q. 163

2 164 CHAPTER 10 Total fixed cost (TFC ): cost of the firm s fixed factors. fixed cost (AFC ) is TFC Q. Total variable cost (TVC ): cost of the firm s variable factors. variable cost (AVC ) is TVC Q. cost (MC ): the increase in total cost that results from one-unit increase in output or, in terms of a formula, MC = ΔTC ΔQ. Two relationships between these costs are: TC = TFC + TVC and ATC = AFC + AVC. Figure 10.2 shows typical AVC, ATC, and MC curves. The AVC, ATC, and MC curves are U-shaped. The MC crosses the AVC and ATC curves where the AVC and ATC are at their minimums. As output initially increases, both AFC and AVC fall, so ATC falls. As output increases still more, returns will diminish. AVC increases as output increases, so eventually ATC rises when output increases. The MC and MP curves are related. Over the range of output where the MP curve slopes upward, the MC curve slopes downward. At the level of output where the MP curve is at its maximum, the MC curve is at its minimum. Over the range of output where the MP curve slopes downward, the MC curve slopes upward. The AP and ATC curves are similarly related. An increase in technology shifts the firm s product curves upward and shifts its cost curves downward. A rise in factor prices shifts the firm s cost curves upward. Long-Run Cost The long-run cost is the cost of production when all factors of production are adjusted to their economically efficient levels. There are no fixed costs in the long run. The production function shows the relationship between the maximum attainable output and the quantities of all factors of production. In the long run, because all factors can be varied, all costs are variable costs. The long-run average cost curve (LRAC ) traces a U-shaped relationship between the lowest attainable average total cost and output when both the plant size and labor are varied. The long-run average cost curve is derived from the many different (short-run) average total cost curves that reflect different quantities of capital. The long-run average cost for any quantity is the lowest average cost of all the (short run) average costs of producing that quantity. The ranges of the long-run average cost (LRAC) are: Economies of scale features of a firm s technology that lead to falling long-run average cost as output increases. With factor prices not changing, economies of scale occur if a change in all factors leads to a larger percentage change in output. Diseconomies of scale features of a firm s technology that lead to rising long-run average cost as output increases. With factor prices not changing, diseconomies of scale occur if a change in all factors leads to a smaller change in output. Constant returns to scale features of a firm s technology that lead to constant long-run average cost as output increases. This can occur when a change in all factors leads to an equal percentage change in the firm s output. When a firm has constant returns to scale, the long-run average cost curve is horizontal. The minimum efficient scale is the smallest quantity of output at which the long-run average cost reaches its lowest level

3 OUTPUT AND COSTS 165 Helpful Hints 1. THE MOST IMPORTANT COST CONCEPTS : Be sure you understand Figure 10.3 thoroughly. Not only is it is the most important graph in the chapter, it is one of the most important graphs in all of microeconomics. You will see it repeatedly in the next several chapters. You need to know three important points about Figure First, both the ATC and AVC curves are U-shaped. The MC curve also is U-shaped, but the portion that slopes upward is the most important. Second, the MC curve intersects the ATC and AVC curves at their minimum points. In other words, when the MC equals the ATC, the ATC is at its minimum. Third, following the relationship between a marginal and an average, when the MC curve is below the ATC or AVC curves, the ATC or AVC slope downward. Similarly, when the MC curve is above the ATC or AVC curves, the ATC or AVC curves slope upward. 2. MEANING OF THE WORD MARGINAL : Be certain that you understand the difference between marginal cost and average cost. These are very different concepts. One way to remember that they are different is to keep in mind that the word marginal always means additional. Economists use the word marginal this way a lot. In this chapter, you already have seen it used in marginal product and marginal cost. You might also have seen it in Chapter 7 in the discussion of marginal utility, the additional utility from consuming another unit of a product. In the next few chapters you will encounter the term marginal revenue, which means additional revenue when output is increased by one unit. In all these examples, the word marginal means additional! 3. THE DIFFERENCE BETWEEN ECONOMIES OF SCALE AND DIMINISHING RETURNS : The last section of the chapter explains the long-run production function and cost function when the plant size that is, the capital stock varies. As the law of diminishing returns is the key to understanding short-run costs, the concept of economies and diseconomies of scale is the key to understanding long-run costs. In the long run, we explore the increase in output relative to the increase in factors when all factors of production are increased by the same percentage; diminishing returns are what happens when only one factor is changed, with the rest of the factors being kept constant. Questions True/False and Explain Decision Time Frames 11. The short run is the period of time over which only one factor of production is variable. 12. In the long run, all factors are variable. Short-Run Technology Constraint 13. If the marginal product of another worker exceeds the marginal product of the previous worker hired, the firm is experiencing economies of scale. 14. The law of diminishing returns implies that the marginal product of a factor of production eventually falls as more of the factor is used. 15. If the marginal product of labor exceeds the average product of labor, the average product of labor rises when more workers are hired. Short-Run Cost 16. Total cost equals fixed cost plus variable cost. 17. Total costs first fall and then, as diminishing returns sets in, total costs rise as the firm expands its output.

4 166 CHAPTER Total variable costs are always greater than total fixed costs. 19. cost equals total cost divided by total output. 10. cost is always greater than average total cost. 11. The average total cost curve, like the average product of labor curve, has an upside-down U-shape. 12. The ATC curve always passes through the minimum point of the MC curve. Long-Run Cost 13. In the long run, all costs are variable costs and no costs are fixed cost. 14. No part of any short-run average total cost curve lies below the long-run average total cost curve. 15. Economies of scale occur when an increase in the number of workers employed increases total output. 16. When the long-run average cost (LRAC ) curve slopes upward, the firm is experiencing economies of scale. Multiple Choice Decision Time Frames 11. The short run is a time period in which a. one year or less elapses. b. all factors are variable. c. all factors are fixed. d. there is at least one fixed factor and the other factors can be varied. 12. In the long run, a. only the amount of capital the firm uses is fixed. b. all factors are variable. c. all factors are fixed. d. a firm must experience diseconomies of scale. Short-Run Technology Constraint 13. Total product divided by the total quantity of labor employed equals the a. average product of labor. b. marginal product of labor. c. average total cost. d. average variable cost. 14. Diminishing marginal returns occurs when a. all factors are increased and output decreases. b. all factors are increased and output increases by a smaller proportion. c. a variable factor is increased and output decreases. d. a variable factor is increased and its marginal product falls. 15. The marginal product of labor equals the average product of labor when the a. average product of labor is at its maximum. b. average product of labor is at its minimum. c. marginal product of labor is at its maximum. d. None of the above answers are correct because the marginal product of labor never equals the average product of labor. 16. When the marginal product of labor curve is below the average product of labor curve, a. the average product of labor curve has a positive slope. b. the average product of labor curve has a negative slope. c. the total product curve has a negative slope. d. the firm experiences diseconomies of scale. Short-Run Costs 17. Pat s Catering finds that when it caters 10 meals a week, its total cost is \$3,000. If, at this level of output, Pat has a total variable cost of \$2,500, what is Pat s fixed cost? a. \$250 b. \$300 c. \$500 d. \$3,000

5 OUTPUT AND COSTS 167 Use Table 10.1 for the next three questions. Use Figure 10.4 for the next four questions. TABLE 10.1 Multiple Choice Questions 8, 9, 10 Output Total variable cost Total cost 3 \$15 \$21 4 \$18 \$ The marginal cost of producing the fourth unit is a. \$6. b. \$5. c. \$3. d. \$ The average total cost of the fourth unit is a. \$6. b. \$5. c. \$3. d. \$ The average fixed cost of the third unit is a. \$6. b. \$5. c. \$3. d. \$ If the company produces no output, it must pay a. no costs. b. a small amount of variable cost. c. its fixed cost. d. its owners a normal profit. 12. The change in total cost from producing another unit of output equals the a. average total cost. b. variable cost. c. average variable cost. d. marginal cost. 13. A farmer discovers that the total cost of growing 50 acres of eggplant is \$50,000 and that the total cost of growing 51 acres of eggplant is \$52,000. The marginal cost of the 51st acre of eggplant is a. \$52,000. b. \$50,000. c. \$2,000. d. \$1, In Figure 10.4 the MC curve is curve a. a. b. b. c. c. d. None of the curves is the MC curve. 15. In Figure 10.4 the ATC curve is curve a. a. b. b. c. c. d. None of the curves is the ATC curve. 16. In Figure 10.4 the AVC curve is curve a. a. b. b. c. c. d. None of the curves is the AVC curve. 17. In Figure 10.4 the AFC is curve a. a. b. b. c. c. d. None of the curves is the AFC curve.

6 168 CHAPTER Which curve intersects the minimum point of the average total cost curve, that is, minimum point of the ATC curve? a. The marginal cost (MC ) curve b. The average variable cost (AVC ) curve c. The average fixed cost (AFC ) curve d. The marginal product (MP ) curve 19. If the average total cost (ATC ) curve slopes downward, then at that level of output the marginal cost (MC ) curve must be a. sloping upward. b. sloping downward. c. above the ATC curve. d. below the ATC curve. 20. Over the range of output where the MP curve slopes upward, the a. MC curve slopes downward. b. AFC curve slopes upward. c. firm is experiencing economies of scale. d. total cost curve slopes downward. 21. A technological advance a. shifts the firm s total product curve upward. b. does not shift the firm s total product curve. c. shifts the firm s total product curve downward. d. cannot occur without raising the firm s average total costs and hence shifts the average total cost curve upward. 22. The cost of a variable factor, such as the wage paid to workers, rises. This change shifts the a. total fixed cost curve upward. b. marginal product of labor curve downward. c. average variable cost curve upward. d. marginal product of labor curve upward. Long-Run Cost 23. The concept of diminishing returns a. applies to both labor and capital. b. applies to labor but does not apply to capital. c. applies to capital but does not apply to labor. d. does not apply to either labor or capital. 24. The LRAC curve a. equals the minimum points on all the short-run ATC curves. b. equals the lowest possible marginal cost of producing the different levels of output. c. equals the lowest attainable average total cost for all levels of output when all factors can be varied. d. generally lies above the short-run ATC curves. 25. The LRAC curve generally is a. shaped as an upside-down U. b. U-shaped. c. upward sloping. d. downward sloping. 26. When a firm is experiencing economies of scale, a. the MP curve slopes upward. b. the LRAC curve slopes downward. c. diminishing returns to labor have been suspended. d. the MC curve slopes downward. 27. Constant returns to scale means that as all factors of production are increased, a. total output remains constant. b. average total cost rises. c. average total cost rises at the same rate as the factors. d. total output increases in the same proportion as the factors. Short Answer Problems 1. Where does the marginal product curve intersect the average product curve? Why? 2. a. Table 10.2 (on the next page) gives the total weekly product of turkeys at Al s Turkey Town. Complete this table. (The marginal product is entered midway between rows to emphasize that it is the result of changing factors moving from one row to the next. product corresponds to a fixed quantity of labor and so is entered on the appropriate row.) b. In Figure 10.5 (on the next page) label the axes and draw a graph of the total product curve (TP). c. In Figure 10.6 (on the next page) label the axes and draw a graph of the marginal product (MP ) and the average product (AP ). (As in Table 10.2,

7 OUTPUT AND COSTS 169 TABLE 10.2 Short Answer Problem 2 (a) product of labor (AP) product of labor (MP) 0 0 XX a. Let s examine Al s short-run cost of growing turkeys. The first two columns of Table 10.2 are reproduced in the first two columns of Table The cost of 1 worker (the only variable factor) is \$2,000 per month. Total fixed cost is \$4,000 per month. Complete Table 10.3 by using your answers from Table 10.2 and by computing total variable cost and total cost. TABLE 10.3 Total Cost of Growing Turkeys plot the marginal products midway between the units of labor and the average products directly above the units of labor.) Where do the AP and MP curves cross? Total variable cost (TVC ) Total cost (TC ) 0 0 \$4, , , ,000

8 170 CHAPTER 10 b. In Figure 10.7 label the axes and draw the TC and TVC curves. What is the relationship between these two curves? c. Table 10.4 contains spaces for some of Al s other costs, the average total cost (ATC ), average variable cost (AVC ), and marginal cost (MC ). Complete this table by using your answers from Table 10.3 and calculating the new costs called for in Table TABLE 10.4 Other Costs of Growing Turkeys variable cost (AVC ) total cost (ATC ) 0 XX XX 100 \$ cost (MC ) \$ d. In Figure 10.8 label the axes and draw the ATC, AVC, and MC curves. Be sure to plot the values for the MC between the relevant levels of output. What is the relationship between the ATC and AVC curves? Between the MC and AVC curves? 4. a. Suppose Al discovers new technology that boosts the productivity of his workers so that more turkeys can be grown than before. Complete Table 10.5, which presents production data with the new technology. TABLE 10.5 New Technology product of labor (AP ) 0 0 XX product of labor (MP ) 120

9 OUTPUT AND COSTS 171 b. Al s fixed cost remains at \$4,000 and he can continue to hire workers at a wage rate of \$2,000. Use the new technology production data to complete Table 10.6, which has the total cost, and Table 10.7, which has (some of) the average costs and the marginal cost. How do the old and new ATC curves compare? The old and new MC curves? TABLE 10.6 New Technology and Total Costs Total variable cost (TVC ) Total cost (TC ) TABLE 10.7 New Technology and Other Costs variable cost (AVC ) total cost (ATC ) 0 XX XX cost (MC ) c. In Figure 10.9, plot the ATC and MC curves you have just entered in Table Also draw the ATC and MC curves you have already plotted in Figure 10.8 (before the technology changed). Label the old ATC curve ATC 1 and the old MC curve MC 1 ; label the new ATC curve ATC 2 and the new MC curve MC a. Return to the old technology for growing turkeys, which you studied and worked out in problems 2 and 3. Suppose that the cost of Al s fixed factors remain at \$4,000. Now the cost of his variable factor, labor, rises. Specifically, suppose that a worker now receives \$3,000 per month. Complete Table For the two missing quantities, copy your answers from Table TABLE 10.8 A Change in Variable Costs Total variable cost (TVC ) Total cost (TC ) 0 0 \$4, , , ,000

10 172 CHAPTER 10 TABLE 10.9 Comparison of Costs Before increase total cost (ATC ) 0 XX cost (MC ) After increase total cost (ATC ) XX cost (MC ) b. To compare the effect of the rise in the variable cost on the average total cost and marginal cost, complete Table (Hint: As before, copy the before increase ATC and MC values from Table 10.4; work out the after increase ATC and MC values from Table 10.8.) From Table 10.9, how did the rise in variable costs affect the average total cost? The marginal cost? 6. What is the difference between diminishing returns and diseconomies of scale? You re the Teacher 1. This chapter has a lot to say about firms: production, costs, and stuff like that. But I don t really see the purpose. In real life, businesses are a lot more complicated than this chapter says. Workers are different, different companies make different goods, Intel s factory sure isn t the same as what we see at Krispy Kreme and what have you. What s the use of this chapter? This student is missing an essential point about economic theories. Can you help straighten out the student? 2. I get the idea that marginal cost is important, but I don t know why. You have any ideas about it? Your friend is asking you for your ideas; you have a chance to help your friend, so explain why you think marginal cost is important.

11 OUTPUT AND COSTS 173 True/False Answers Decision Time Frames Answers 11. F In the short run, at least one factor is fixed. 12. T The question presents the definition of the long run. Short-Run Technology Constraint 13. F The firm has increasing marginal returns because only one factor has been changed. 14. T The question presents the definition of diminishing returns. 15. T This result is a reflection of the relationship between marginals and averages. Short-Run Cost 16. T Total cost is the sum of fixed cost and variable cost. 17. F As output increases, total cost always rises. 18. F The amount of variable cost and the amount of fixed cost are not necessarily related, except that in the long run all costs are variable costs. 19. F cost equals the additional total cost divided by the additional output. 10. F cost usually starts below the average total cost and then rises above it. 11. F The average total cost curve has a right-sideup U shape. 12. F The MC curve always passes through the minimum point of the ATC curve. Long-Run Cost 13. T In the long run, all factors of production can be varied so all costs are variable costs. 14. T The long-run average cost curve shows the least possible cost to produce any level of output. 15. F Economies of scale occur when an increase in all factors increases output by a larger proportion. 16. F When the LRAC curve slopes upward, average cost increases when output increases, so over this range of output the firm is experiencing diseconomies of scale. Multiple Choice Answers Decision Time Frames 11. d This is the definition of the short run. 12. b The long run is the amount of time until all factors of production become variable. Short-Run Technology Constraint 13. a The average product of labor is total product (output) per worker. 14. d Answer (d) is the definition of diminishing returns. 15. a When MP > AP, the average product rises when employment increases; when MP < AP, the average product falls; and when MP = AP, the average product is at its maximum. 16. b This answer reflects the average/marginal relationship that when the marginal is below the average, the average falls. Short-Run Cost 17. c Total cost equals fixed cost plus variable cost, so fixed cost equals total cost minus variable cost. 18. c The marginal cost equals the difference in total cost (\$24 \$21 = \$3) divided by the change in output (4 3 = 1) so the marginal cost is \$ a total cost equals total cost divided by total output, that is, \$24 4, or \$ d Because total cost equals total fixed cost plus total variable cost, total fixed cost equals \$6. Then, average fixed cost is total fixed cost divided by total output, so average fixed cost equals \$6 3 = \$ c Fixed cost remains the same regardless of the level of output, that is, whether the firm produces a million units of output or no units of output. 12. d cost shows the added cost from producing an added unit of output. 13. c The marginal cost equals the change in total cost (\$52,000 \$50,000, or \$2,000) divided by the change in output (51 acres of eggplant 50 acres of eggplant, or 1 acre of eggplant). Therefore the marginal cost equals \$2,000 per acre of eggplant.

13 OUTPUT AND COSTS 175 product exceeds the average product, which is the case at any point left of the intersection point, the average product increases with output; whenever the marginal product is less than the average product, which is true for any point right of the intersection point, the average product falls. Hence when the marginal product equals the average product, the average product does not change. Left of this point the average product is rising and right it is falling. Therefore at this point the average product is at its maximum. 2. a. Table completes Table The average product of labor column is calculated by dividing the total product by the total amount of labor; that is, APL = Q L. So, the AP when 2 workers are employed is 300 2, or 150. The marginal product of labor is the extra output produced by an extra worker. In terms of a formula, the MP equals the change in total product divided by the change in labor, so that MP = ΔQ ΔL. So, between 2 and 1 workers the MP is ( ) (2 1) = 200. Because the MP equals the additional output when another unit of labor is employed, the quantity of output produced when 4 workers are employed equals the total quantity produced when 3 workers are employed (450) plus the additional amount the 4th worker produces, 110, or 560. TABLE Short Answer Problem 2 (a) (turkeys per product of labor (AP) product of labor (MP) 0 0 XX Finally, for the total quantity when 6 workers are used, multiply the average product of labor, 110, by the total number of workers employed, 6, to get the total product of 660. b. Figure shows the graph of the firm s total product curve. c. Figure shows the firm s AP and MP curves. The MP curve crosses the AP curve when the AP is at its maximum.

14 176 CHAPTER a. Table shows the total cost for each quantity of labor. Total variable cost equals the number of workers (the variable factor) multiplied by \$2,000 per worker. Total cost then equals the total variable cost plus the total fixed cost, which is given in the problem as \$4,000. TABLE Short Answer Problem 3 (a) c. Table completes Table In Table the average variable cost column was calculated by dividing total variable cost by the total quantity produced. So the AVC when 300 turkeys are produced is \$4, = \$ Similarly, the average total cost column is calculated by dividing total cost by the total quantity produced. Finally, marginal cost equals the change in total cost divided by the change in quantity, that is, MC = ΔTC ΔQ. Hence the MC between 300 and 100 turkeys per week is (\$8,000 \$6,000) ( ), or \$ TABLE Short Answer Problem 3 (c) Total variable cost (TVC ) Total cost (TC ) 0 0 \$0 \$4, ,000 6, ,000 8, ,000 10, ,000 12, ,000 14, ,000 16,000 b. Figure shows the firm s total cost (TC ) and total variable cost (TVC ) curves. The TC curve always lies \$4,000 above the TVC curve. variable cost (AVC ) total cost (ATC ) 0 XX XX 100 \$20.00 \$ cost (MC ) \$ d. Figure shows the ATC, AVC, and MC curves. The AVC curve lies below the ATC curve, but the vertical distance between the two (which equals AFC ) shrinks as output expands. The MC curve crosses the AVC curve where the

17 OUTPUT AND COSTS 179 duce, we can ask whether it wants to increase its production. By increasing its production, the firm will incur some additional costs its marginal cost. We ll then compare this cost to the added benefit from increasing production. So you re right: cost really is important because it s basically half the marginal analysis we ll be doing in the chapters ahead.

18 180 CHAPTER 10 Chapter Quiz 11. In the short run, a. at least one factor is fixed. b. all factors are fixed. c. at least one factor is variable. d. all factors are variable. 12. In the long run, a. at least one factor is fixed. b. all factors are fixed. c. at least one factor is variable. d. all factors are variable. 13. The marginal product of labor is the a. inverse of the marginal product of capital when the firm is in the long run. b. slope of the curve showing the average product of labor. c. change in total product divided by the change in labor. d. total product divided by total labor. 14. The average product of labor curve is at its maximum when the a. marginal product of labor curve is below it. b. marginal product of labor curve crosses it. c. marginal product of labor curve is above it. d. level of output is at its maximum. 15. The more shallow is a firm s total product curve, the a. greater is the marginal product of labor. b. smaller is the marginal product of labor. c. lower is the total cost curve. d. lower is the variable cost curve. 16. Variable cost is sum of all the a. costs associated with variable factors. b. costs associated with the production of the product. c. explicit costs but not all the implicit costs. d. costs that do not change when the amount produced increases. 17. A firm s average variable cost is \$10, its total fixed costs are \$50 and the firm produces 25 units of output. Hence its average total cost is a. more than \$50. b. \$12. c. \$4. d. \$ When producing 99 units, the total cost is \$595. The marginal cost of the 100th unit is \$5. The total cost of producing 100 units is a. \$600. b. \$590. c. \$6. d. an amount that cannot be calculated without additional information. 19. The average total cost curve is lowest when the a. marginal cost curve is below it. b. marginal cost curve crosses it. c. marginal cost curve is above it. d. level of output is at its maximum. 10. When long-run average costs increase when output increases, there definitely are a. economies of scale. b. diseconomies of scale. c. diminishing returns. d. constant returns to scale. The answers for this Chapter Quiz are on page 359

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