microeconomics book solution 12

B the accompanying diagram shows the variable cost

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b. The accompanying diagram shows the variable cost and total cost curves. c. Marginal cost, MC, per cup of frozen yogurt is shown in the table in part a; it is the change in total cost divided by the change in quantity of output. TC VC 150 100 250 200 350 300 50 0 $800 600 400 200 Cost Quantity of frozen yogurt (cups) Quantity of f r ozen Quantity yogu r t of labo r (cups) (wo r ke r s) VC TC MC of cup 0 0 $ 0 $ 100 $ 1.23 110 1 1 × 8 0 + 110 × 0.5 = 135 235 1.39 200 2 2 × 8 0 + 200 × 0.5 = 260 360 1.64 270 3 3 × 8 0 + 270 × 0.5 = 375 475 3.17 300 4 4 × 8 0 + 300 × 0.5 = 470 570 4.50 320 5 5 × 8 0 + 320 × 0.5 = 560 660 8 .50 330 6 6 × 8 0 + 330 × 0.5 = 645 745 C H A P T E R 1 2 B E H I N D T H E S U P P LY C U R V E : I N P U T S A N D C O S T S S-173 S171-S184_Krugman2e_PS_Ch12.qxp 9/16/08 9:22 PM Page S-173
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Solution 4. The production function for Marty’s Frozen Yogurt is given in Problem 2. The costs are given in Problem 3. a. For each of the given levels of output, calculate the average fixed cost ( AFC ), aver- age variable cost ( AVC ), and average total cost ( ATC ) per cup of frozen yogurt. b. On one diagram, draw the AFC, AVC, and ATC curves. c. What principle explains why the AFC declines as output increases? What principle explains why the AVC increases as output increases? Explain your answers. d. How many cups of frozen yogurt are produced when average total cost is minimized? 4. a. The average fixed cost, average variable cost, and average total cost per cup of yogurt are given in the accompanying table. (Numbers are rounded.) b. The accompanying diagram shows the AFC, AVC, and ATC curves. c. AFC declines as output increases due to the spreading effect. The fixed cost is spread over more and more units of output as output increases. AVC increases as output increases due to the diminishing returns effect. Due to diminishing returns to labor, it costs more to produce each additional unit of output. d. Average total cost is minimized when 270 cups of yogurt are produced. At lower quantities of output, the fall attributable to the spreading effect dominates changes in average total cost. At higher quantities of output, the rise attributable to the diminishing returns effect dominates changes in average total cost. 150 100 250 200 350 300 0 $2.50 2.00 1.50 1.00 0.50 Cost of cup Quantity of frozen yogurt (cups) ATC AFC AVC Quantity of f r ozen yogu r t (cups) VC TC AFC of cup AVC of cup ATC of cup 0 $ 0 $ 100 110 135 235 $ 0.91 $ 1.23 $ 2.14 200 260 360 0.50 1.30 1. 8 0 270 375 475 0.37 1.39 1.76 300 470 570 0.33 1.57 1.90 320 560 660 0.31 1.75 2.06 330 645 745 0.30 1.95 2.26 S-174 C H A P T E R 1 2 B E H I N D T H E S U P P LY C U R V E : I N P U T S A N D C O S T S S171-S184_Krugman2e_PS_Ch12.qxp 9/16/08 9:22 PM Page S-174
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Solution 5. The accompanying table shows a car manufacturer’s total cost of producing cars. a. What is this manufacturer’s fixed cost? b. For each level of output, calculate the variable cost ( VC ). For each level of output except zero output, calculate the average variable cost ( AVC ), average total cost ( ATC ), and average fixed cost ( AFC ). What is the minimum-cost output?
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