# ECON 103, ANSWERS TO HOME WORK ASSIGNMENTS

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1 ECON 103, ANSWERS TO HOME WORK ASSIGNMENTS Due the Week of June 9 Chapter 6 WRITE [4] Gomez runs a small pottery firm. He hires one helper at \$12,000 per year, pays annual rent of \$5,000 for his shop, and spends \$20,000 per year on materials. He has \$40,000 of his own funds invested in equipment (pottery wheels, kilns, and so forth) that could earn him \$4,000 per year if alternatively invested. He has been offered \$15,000 per year to work as a potter for a competitor. He estimates his entrepreneurial talents are worth \$3,000 per year. annual revenue from pottery sales is \$72,000. Calculate the accounting profit and economic profit for Gomez s pottery firm. Explicit s: \$37,000 (= \$12,000 for the helper + \$5,000 of rent + \$20,000 of materials). Implicit s: \$22,000 (= \$4,000 of forgone interest + \$15,000 of forgone salary + \$3,000 of entreprenuership). Accounting profit = \$35,000 (= \$72,000 of revenue - \$37,000 of explicit s); Economic profit = \$13,000 (= \$72,000 - \$37,000 of explicit s - \$22,000 of implicit s). WRITE [6] (a) Complete the following table by calculating marginal product and average product from the data given. (b) Plot total, marginal, and average product and explain in detail the relationship between each pair of curves. (c) Explain why marginal product first rises, then declines, and ultimately becomes negative. (d) What bearing does the law of diminishing returns have on short-run s? Be specific. (e) When marginal product is rising, marginal is falling. And when marginal product is diminishing, marginal is rising. Illustrate and explain graphically. Inputs of Marginal Average labour product product product (a). See the table above. (b). Your diagram should have the same general characteristics as Figure 6-2 in the textbook. (c). MP is the slope the rate of change of the TP curve. When TP is rising at an increasing rate, MP is positive and rising. When TP is rising at a diminishing rate, MP is positive but falling. When TP is falling, MP is negative and falling. AP rises when MP is above it; AP falls when MP is below it. (d) MP first rises because the fixed capital gets used more productively as added workers are employed. Each added worker contributes more to output than the previous worker because the firm is better able to use its fixed plant and equipment. As still more labour is added, the law of diminishing returns takes hold. Labour becomes so abundant relative to the fixed capital that congestion occurs and marginal product falls. At the extreme, the addition of labour so overcrowds the plant that the marginal product of still more labour is negative total output falls. (e) This is illustrated by a diagram that looks like Figure 6-6. Because labour is the only variable input and its price (its wage rate) is constant, MC is found by dividing the wage rate by MP. When MP is rising, MC is falling; when MP reaches its maximum, MC is at its minimum; when MP is falling, MC is rising. page 1

2 WRITE [9] A firm has \$60 of fixed s, and variable s as indicated in the table below. Complete the table; check your calculations by referring to question 4 at the end of Chapter 7. product fixed variable AFC AVC ATC Marginal 0 \$60 \$0 \$60 1 \$60 \$45 \$105 \$60.00 \$45.00 \$ \$ \$60 \$85 \$145 \$30.00 \$42.50 \$72.50 \$ \$60 \$120 \$180 \$20.00 \$40.00 \$60.00 \$ \$60 \$150 \$210 \$15.00 \$37.50 \$52.50 \$ \$60 \$185 \$245 \$12.00 \$37.00 \$49.00 \$ \$60 \$225 \$285 \$10.00 \$37.50 \$47.50 \$ \$60 \$270 \$330 \$8.57 \$38.57 \$47.14 \$ \$60 \$325 \$385 \$7.50 \$40.63 \$48.13 \$ \$60 \$390 \$450 \$6.67 \$43.33 \$50.00 \$ \$60 \$465 \$525 \$6.00 \$46.50 \$52.50 \$75.00 a. Graph total fixed, total variable, and total. Explain how the law of diminishing returns influences the shapes of the total variable- and total- curves. b. Graph AFC, AVC, ATC, and MC. Explain the derivation and shape of each of these four curves and their relationships to one another. Specifically, explain in nontechnical terms why the MC curve intersects both the AVC and ATC curves at their minimum points. c. Explain how the locations of each of the four curves graphed in question 9b would be altered if (1) total fixed had been \$100 rather than \$60, and (2) total variable had been \$10 less at each level of output. (a) See the graph. Over the 0 to 4 range of output, the TVC and TC curves slope upward at a decreasing rate because of increasing marginal returns. The slopes of the curves then increase at an increasing rate as diminishing marginal returns occur.' (b) See the graph. AFC (= TFC/Q) falls continuously since a fixed amount of capital is spread over more units of output. The MC (= change in TC/change in Q), AVC (= TVC/Q), and ATC (= TC/Q) curves are U- shaped, reflecting the influence of first increasing and then diminishing returns. The ATC curve sums AFC and AVC vertically. The ATC curve falls when the MC curve is below it; the ATC curve rises when the MC curve is above it. This means the MC curve must intersect the ATC curve at its lowest point. The same logic holds for the minimum point of the AVC curve. Question 9-a page 2

3 Question 9-b (c1) If TFC has been \$100 instead of \$60, the AFC and ATC curves would be higher by an amount equal to \$40 divided by the specific output. Example: at 4 units, AFC = \$25.00 [= (\$60 + \$40)/4]; and ATC = \$62.50 [= (\$210 + \$40)/4]. The AVC and MC curves are not affected by changes in fixed s. (c2) If TVC has been \$10 less at each output, MC would be \$10 lower for the first unit of output but remain the same for the remaining output. The AVC and ATC curves would also be lower by an amount equal to \$10 divided by the specific output. Example: at 4 units of output, AVC = \$35.00 [= \$150 - \$10)/4], ATC = \$50 [= (\$210 - \$10)/4]. The AFC curve would not be affected by the change in variable s. WRITE [10] Indicate how each of the following would shift the (a) marginal curve, (b) average variable curve, (c) average fixed curve, and (d) average total curve of a manufacturing firm. In each case specify the direction of the shift. a. A reduction in business property taxes b. An increase in the nominal wages of production workers c. A decrease in the price of electricity d. An increase in the insurance rates on plant and equipment e. An increase in transportation s MC AVC AFC ATC a. business property tax reduction (fixed) down down b. wage increase (variable) up up up c. elec. price decrease (variable) down down down d. increase in insurance (fixed) up up e. increase in trans. (variable) up up up page 3

4 WRITE [11] Suppose a firm has only three possible plant size options as shown in the accompanying figure. What plant size will the firm choose in producing (a) 50, (b) 130, (c) 160, and (d) 250 units of output? Draw the firm s long-run average curve on the diagram and describe this curve. ATC ATC2 ATC3 ATC Q (a) To produce 50 units, the firm will choose plant size #1, since its ATC is lower for this size firm in producing less than 80 units. (b) To produce 130 units, the firm will choose plant size #2, since its ATC is lower for size #2 in producing between 80 and 240 units. (c) To produce 160 units, the firm will choose plant size #2, since its ATC is lowest for producing between 80 and 240 units. (d) To produce 250 units, the firm will choose plant size #3, since its ATC is lowest for production of more than 240 units. The long-run average- curve drawn on this diagram would trace ATC 1 as far as 80 units, then ATC 2 between 80 and 240 units, then finally trace ATC 3 from 240 units to the end of the graph. It would look kind of like the picture below (if you weren't trying to draw it with a lousy mouse). ATC ATC2 LR ATC ATC Q page 4

6 CONSIDER [7] Why can the distinction between fixed and variable s be made in the short run? Classify the following as fixed or variable s: advertising expenditures, fuel, interest on company-issued bonds, shipping charges, payments for raw materials, real estate taxes, executive salaries, insurance premiums, wage payments, depreciation and obsolescence charges, sales taxes, and rental payments on leased office machinery. There are no fixed s in the long run; all s are variable. Explain. The distinction can be made because there are some s that do not vary with total output. These are the fixed s which, fundamentally, are related to the scale or size of the plant. In the short run, by definition, the scale of the plant cannot change: The firm cannot bring in more machinery or move to a larger building. All s that are related to the scale of the plant s that continue to be incurred even though the firm s output may be zero are fixed s. On the other hand, the firm can increase its output by using its plant its fixed capital more intensively, that is, by hiring more labour, or by using more materials. But by doing so, it will increase its operating s, its variable s. Advertising expenditures: variable s (although it may be reasonable to argue a fixed component). Fuel: variable s. Interest on company-issued bonds: fixed s. Shipping charges: variable s. Payments for raw materials: variable s. Real estate taxes: fixed s. Executive salaries: fixed s. Insurance premiums: fixed s. Wage payments: variable s. Depreciation and obsolescence charges: fixed s. Sales taxes: variable s. Rental payments on leased office machinery: fixed s (although it is possible that short-term lease arrangements on some types of office equipment may rise or fall with output). In the long run, the firm can, by definition, get out of paying all of its short-run fixed s; its lease is up, it can fire its executives without penalty, the insurance has run out, and so on. All of its s at this moment, then, are variable. It can decide to continue producing at the same scale and thus reassume all its previous fixed s for the next short-run period; or it can decide to increase its scale and thus increase its fixed s; or it can decide to go out of business and thus have no s at all. CONSIDER [12] Use the concepts of economies and diseconomies of scale to explain the shape of a firm s long-run ATC curve. What is the concept of minimum efficient scale? What bearing can the shape of the long-run ATC curve have on the structure of an industry? The long-run ATC curve is U-shaped. At first, long-run ATC falls as the firm expands and realizes economies of scale from labour and managerial specialization and the use of more efficient capital. The long-run ATC curve later turns upward when the enlarged firm experiences diseconomies of scale, usually resulting from managerial inefficiencies. The MES (minimum efficient scale) is the smallest level of output needed to attain all economies of scale and minimum long-run ATC. If long-run ATC drops quickly to its minimum, which then extends over a long range of output, the industry will likely be composed of both large and small firms. If long-run ATC descends slowly to its minimum over a long range of output, the industry will likely be composed of a few large firms. If long-run ATC drops quickly to its minimum point and then rises abruptly, the industry will likely be composed of many small firms. page 6

7 Write: Fill in the blanks in the following table Output Fixed Cost Var. Cost Cost AFC AVC ATC MC page 7

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