microeconomics book solution 12

2 martys frozen yogurt is a small shop that sells

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2. Marty’s Frozen Yogurt is a small shop that sells cups of frozen yogurt in a university town. Marty owns three frozen-yogurt machines. His other inputs are refrigerators, frozen-yogurt mix, cups, sprinkle toppings, and, of course, workers. He estimates that his daily production function when he varies the number of workers employed (and at the same time, of course, yogurt mix, cups, and so on) is as shown in the accom- panying table. a. What are the fixed inputs and variable inputs in the production of cups of frozen yogurt? b. Draw the total product curve. Put the quantity of labor on the horizontal axis and the quantity of frozen yogurt on the vertical axis. c. What is the marginal product of the first worker? The second worker? The third worker? Why does marginal product decline as the number of workers increases? 2. a. The fixed inputs are those whose quantities do not change as the quantity of out- put changes: frozen-yogurt machines, refrigerators, and the shop. The variable inputs are those whose quantities do change as the quantity of output changes: frozen-yogurt mix, cups, sprinkle toppings, and workers. b. The accompanying diagram illustrates the total product curve. TP 5 6 4 3 2 1 0 350 300 250 200 150 100 50 Quantity of frozen yogurt (cups) Quantity of labor (workers) Quantity of labo r Quantity of f r ozen (wo r ke r s) yogu r t (cups) 0 0 1 110 2 200 3 270 4 300 5 320 6 330 S-172 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-172
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Solution c. The marginal product, MPL, of the first worker is 110 cups. The MPL of the sec- ond worker is 90 cups. The MPL of the third worker is 70 cups. The MPL of labor declines as more and more workers are added due to the principle of diminishing returns to labor. Since the number of frozen-yogurt machines is fixed, as workers are added there are fewer and fewer machines for each worker to work with, mak- ing each additional worker less and less productive. 3. The production function for Marty’s Frozen Yogurt is given in Problem 2. Marty pays each of his workers $80 per day. The cost of his other variable inputs is $0.50 per cup of yogurt. His fixed cost is $100 per day. a. What is Marty’s variable cost and total cost when he produces 110 cups of yogurt? 200 cups? Calculate variable and total cost for every level of output given in Problem 2. b. Draw Marty’s variable cost curve. On the same diagram, draw his total cost curve. c. What is the marginal cost per cup for the first 110 cups of yogurt? For the next 90 cups? Calculate the marginal cost for all remaining levels of output. 3. a. Marty’s variable cost, VC, is his wage cost ($80 per worker per day) and his other input costs ($0.50 per cup). His total cost, TC, is the sum of the variable cost and his fixed cost of $100 per day. The answers are given in the accompanying table.
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