# Chapter 8: Theory of Cost

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1 Chapter 8: Theory of Input s Classification Minimization Shifts in Curves Explicit and Implicit s Fixed and Variable s Profit Long Run Short Run Input Price Change New Technologies Positive Feedback Normal Pure Isocost Isoquant Isocost Isoquant Least- Combination Least- Combination Long-Run Total Total Long-Run Marginal Long-Run Average Total Variable Total Fixed Average Total Returns to Scale Marginal Average Variable Average Fixed Increasing Returns Constant Returns Decreasing Returns Stages of Production Outline and Conceptual Inquiries Application: Stakeholder versus Shareholder and Management Ethics How to Classify s and Profits Explicit and Implicit s What is the cost of your time in completing a college degree? Fixed and Variable s Do you pay both a fixed and variable rate for your monthly cell-phone service? Profits Determining the -Minimizing Input Choice Long-Run s How do you produce a low-cost pizza? Application: Labor Unionization and of Production Is bigger better? Application: Economies of Scale in Electricity Production Is an additional driver s cost of road congestion the same as all the other current drives? s

2 Is marginal cost just some adjustment to average cost? Why will average costs rise with increases in output? Application: Shapes of the Average Variable Curves How are Short- and Long-run Curves Related? Shifting the Curves Input Price Change How will marginal cost shift with a change in fixed cost? New Technologies Summary 1. Under the assumptions that prices are fixed, profits are nonstochastic, and firm managers can be controlled by owners, the objective of a profit-maximizing firm is consistent with maximizing the utility of the firms owners. 2. Total cost may be divided into explicit and implicit costs. Explicit costs are costs of employing inputs not owned by the firm; implicit costs are costs charged to inputs owned by the firm. 3. Total cost may also be divided into fixed and variable costs. Fixed costs are costs associated with the fixed inputs; variable costs are costs that vary with output and are associated with variable inputs. 4. Normal profit is the minimum total return to the inputs necessary to keep a firm in some production activity. Pure profit is total revenue minus total cost. If pure profit is zero, the firm is earning a normal profit. A negative level of pure profit indicates the firm is operating at loss. 5. An isocost curve represents a locus of points where the total cost is the same for alternative input combinations. 6. The least-cost combination of inputs for a given level of output is determined where the marginal rate of technological substitution is equal to the economic rate of substitution. At this least-cost combination, the price per marginal product for each input is equal to the firm s marginal cost. 7. Increasing (decreasing) returns to scale results when total cost increases proportionally less (more) than an increase in output. Constant returns to scale corresponds to total cost increasing proportionally with output. 8. Short-run total cost is equal to short-run total variable plus total fixed costs. Dividing through by output results in short-run average total cost equaling short-run average variable plus average fixed costs. Short-run marginal cost is the slope of both the short-run total and total variable cost curves.

3 9. The Law of Diminishing Marginal Returns results in U-shaped short-run average total, average variable and marginal cost curves. Given diminishing marginal returns, Stage II of production corresponds to where short-run marginal cost is rising and above short-run average variable cost. A firm s profit-maximizing level of output will be somewhere within Stage II of production. 10. In the long run, an increase in the price of an input will tilt the long-run total cost curve upward. Similarly, an increase in the price of a variable input will tilt the short-run total variable and total cost curves upward. The tilt in the totals will shift the average and marginal curves upward. Only the curves solely associated with the fixed inputs (total fixed cost and average fixed cost curves) will not shift. 11. An increase in fixed costs shifts the short-run total cost curve upward. The short-run average total cost will then also shift upward; however, the short-run total variable cost, average variable cost, and marginal cost curves do not shift. Key Concepts allocative efficiency average fixed cost (AFC) economic profit entrepreneurial costs expenditure costs explicit costs implicit costs imputed costs isocost curves long-run average cost (LAC) long-run marginal cost (LMC) long-run total cost (LTC) necessary profit nonexpenditure costs normal profit opportunity-cost profit ordinary profit positive feedback pure profit short-run average total cost (SATC) short-run average variable cost (SAVC) short-run marginal cost (SMC) short-run total cost (STC) short-run total variable cost (STVC) total cost (TC) total fixed cost (TFC) Key Equations TC = wl + vk Isocost equation determined by equating the price per marginal product to marginal cost. λ * = w/mp L = v/mp K = LMC The least-cost combination of inputs is Marginal cost is equal to average cost plus an adjustment factor.

4 TEST YOURSELF Multiple Choice 1. The costs of employing inputs not owned by the firm are called costs. a. Variable b. Short-run c. Explicit d. Implicit. 2. Kala owns her own business. Her revenues for the year were \$200,000. Her explicit costs were \$150,000. To start her business, Kala gave up her job managing a store with a salary of \$40,000. She also used \$50,000 from her savings account that was earning 3 percent interest. Which of the following statements is correct? a. Kala is earning a negative pure profit b. Kala s implicit costs are \$90,000 c. Kala is just breaking even and earning a normal profit d. Kala is earning a positive pure profit. 3. The slope of the isocost line with capital on the vertical axis is a. TC/v b. w/v c. v/w d. (v/w)(k/l). 4. When the price of labor rises, the isocost line with labor on the horizontal axis a. Tilts output b. Shifts out c. Shifts inward d. Tilts inward. 5. Suppose the total cost of producing 12 units of output is \$120. The price of labor is \$8 and the price of capital is \$12. The equation for the isocost line is a. 12q 120 = 12L + 8K b. 120 = 12L + 8K c. 120 = 20(L + K) d. 30 = 2L + 3K.

5 6. The least-cost combination of inputs for capital and labor occurs where a. b. c. d. 7. The additional cost associated with an additional increase in output when all inputs are variable is known as cost. a. Long-run marginal b. Long-run total c. Short-run average total d. Short-run marginal. 8. Suppose long-run average cost falls as output rises. This implies the firm is experiencing a. Decreasing returns to scale b. Diminishing returns to labor c. Increasing returns to scale d. Diseconomies of scale. 9. At a production level of 100 units, long-run average cost is \$40 and long-run marginal cost is \$50. If another unit is produced, long-run a. Marginal cost and long-run average cost will both fall b. Average cost will rise c. Average cost will be unaffected d. None of the above. 10. In the short-run, a. All costs are explicit b. Some costs are fixed c. All costs are variable d. Output is constant. 11. When short-run average cost is equal to short-run marginal cost, short-run a. Marginal cost is maximized b. Average cost is maximized c. Marginal cost is minimized d. Average cost is minimized.

6 12. Stage I can be defined as the stage of production where short-run a. Marginal cost is rising b. Average variable cost is declining c. Marginal cost is declining d. Average variable cost is rising. 13. Which of the following is true? a. Short-run average variable cost can never be less than short-run average total cost b. Short-run average variable cost and short-run marginal cost are equal when short-run marginal cost is at its minimum c. Short-run total cost can never be less than long-run total cost d. Long-run marginal cost is minimized when it is equal to short-run marginal cost. 14. Which of the following shift up when the price of a fixed input rises? I. Short-run average variable cost II. Short-run average total cost III. Short-run marginal cost a. I b. II c. II and III d. I, II and III. 15. Suppose a firm discovers a new technology that alters its production function. This will result in a(n) a. Outward shift of the firm s isoquants b. Upward shift of the firm s short-run cost curves c. Drop in the firm s short-run total cost d. Change in the slope of the firm s isocost line.

7 Short Answer 1. Explain the difference between explicit and implicit costs. How are implicit costs related to normal profit? Explain. 2. Explain why the slope of the isocost line is called the economic rate of substitution. 3. With total cost is \$200, the price of labor is \$5 and the price of capital is \$10, state the firm s isocost equation and graph it. 4. Kelly produces barbecues. The marginal product of labor is 14 and the marginal product of capital is 20. If the price of labor is \$7 and the price of capital is \$12, is the firm producing at minimum cost? Explain. If not, how should the firm alter its input use to lower its costs? 5. What is an expansion path? Draw a graph illustrating how a firm s expansion path can be derived. 6. Explain how the shape of the firm s long-run average cost curve is related to returns to scale. 7. True, false, or uncertain? Short-run average variable cost and short-run marginal cost will be equal when short-run average total cost is at its minimum. Explain. 8. Describe the three stages of production in terms of short-run cost. Explain how diminishing marginal returns determines the shapes of the short-run cost curves. 9. Explain why short-run total cost can never be less than long-run total cost. 10. Graph the isoquants for two different levels of output employing capital and labor. Illustrate the expansion path between these outputs. If the price of labor falls, illustrate the shift in the expansion path.

8 Problems 1. Given the following data, find the firm s pure profit and normal profit: Fixed Explicit 100,000 Implicit 50,000 Variable Explicit 500,000 Implicit 150,000 Revenue 950, Suppose a firm s production function is q = 20K 2/5 L 3/5. If w = 12 and v = 8, find the least-cost combination of inputs to produce 40 units of output. 3. Suppose a firm s production function is q = 2K + 6L. If w = 6 and v = 10, find the least-cost combination of inputs to produce 60 units of output. 4. Suppose a firm s production function is q = 5KL. If w = 8 and v = 10, derive the equation for long-run cost (LTC). What is long-run marginal cost (LMC)? 5. Refer to Problem 4. Derive the firm s short-run total, average total and marginal cost curves assuming that capital is fixed. 6. Suppose a firm s production function is q = 2K 1/2 L 1/2. If w = 4 and v = 6, find the firm s expansion path. If w increases to 6, find the new expansion path. 7. Suppose a firm s short-run total cost curve is STC = 15q 2 + 8q Find the firm s a. Short-run total variable cost (STVC) b. Total fixed cost (TFC) c. Short-run average total cost (SATC) d. Short-run average variable cost (SAVC) e. Average fixed cost (AFC) f. Short-run marginal cost (SMC) g. Level of output where short-run average total cost is minimized. h. Level of output where short-run average variable cost is minimized. 8. Suppose the firm in Problem 7 experiences an increase in fixed costs of \$15 to \$60 from \$45. Show what happens to the firm s short-run average total cost, short-run average variable cost and short-run marginal cost

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