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# notes_2150a_Ch8_part+2.docx

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School
Western University
Department
Economics
Course
Economics 2150A/B
Professor
Prof
Semester
Fall

Description
Micro Chapter 8 part 2 Practice problems: 1 8.7 Afirm’s long-run total cost curve is TC(Q)=1000Q 2 . Derive the equation for the AC(Q). corresponding long-run average cost curve, Given the equation of the long-run average cost curve, which of the following statements is true: a. The long-run marginal cost curve MC(Q) lies below AC(Q) for all positive quantities Q. MC(Q) AC(Q) b. The long-run marginal cost curve is the same as the for all positive Q. quantities MC(Q) AC(Q) c. The long-run marginal cost curve lies above the for all positive Q. quantities d. The long-run marginal cost curve MC(Q) lies below AC(Q) for some positive quantities Q and above the AC(Q) for some positive quantities Q. ANSWER: a The equation of the AC curve is AC(Q) = TC(Q)/Q = 1000Q /Q = 1000Q -(1/. This is a decreasing function of Q. Given the relationship between AC and MC curves, the fact that the AC curve is decreasing means that the MC curve must lie below the AC curve. 8.9. Afirm’s long-run total cost curve is TC(Q) = 40Q − 10Q + Q , and its long-run 2 marginal cost curve is MC(Q) = 40 − 20Q + 3Q . Over what range of output does the production function exhibit economies of scale, and over what range does it exhibit diseconomies of scale? 2 AC(Q) = 40−10Q+Q From the total cost curve, we can derive the average cost curve, . The minimum point of theAC curve will be the point at which it intersects the marginal cost curve, 2 2 40−10Q+Q = 40−20Q+3Q i.e. . This implies that AC is minimized when Q = 5. By definition, there are economies of scale when the AC curve is decreasing (i.e. Q < 5) and diseconomies when it is rising (Q > 5). 8.10. For each of the total cost functions, write the expressions for the total fixed cost, average variable cost, and marginal cost (if not given), and draw the average total cost and marginal cost curves. a) TC(Q) = 10Q b) TC(Q) = 160 + 10Q 2 c) TC(Q) = 10Q , where MC(Q) = 20Q d) TC(Q) = 10√Q, where MC(Q) = 5/√Q e) TC(Q) = 160 + 10Q , where MC(Q) = 20Q a) TFC = 0, AVC = 10, MC = 10. MC = AC = 10 b) TFC = 160, AVC = 10, MC = 10. AC MC = 10 c) TFC = 0, AVC = 10Q. MC AC 10 Q d) TFC = 0, AVC = . AC MC e) TFC = 160, AVC = 10Q. MC AC 8.11. Afirm produces a product with labor and capital as inputs. The production function is described by Q = LK. The marginal products associated with this production function are MP = K and MP = L. Let w = 1 and r = 1 be the prices of labor and capital, respectively. L K a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q. b) Solve the firm’s short-run cost-minimization problem when capital is fixed at a quantity of 5 units (i.e., K = 5). Derive the equation for the firm’s short-run total cost curve as a function of quantity Q and graph it together with the long-run total cost curve. a) Cost-minimizing quantities of inputs are equal to L = √Q √(r/w) and K = √Q / √(r/w). Hence, in the long-run the total cost of producing Q units of output is equal to TC(Q) = 10 + 2√(Qrw). For w = 1 and r = 1 we have TC(Q) = 2√Q. b) When capital is fixed at a quantity of 5 units (i.e., K = 5) we have Q = K L = 5 L. Hence, in the short-run the total cost of producing Q units of output is equal to STC(Q) = 5 + Q/5. 8.14. Consider a production function of two inputs, labor and capital, given by Q = (√L + √K) . The marginal products associated with this production function are as follows: Let w = 2 and r = 1. a) Suppo
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