Problem_Set_7_Firm's_Technologies_&_Costs

Problem_Set_7_Firm's_Technologies_&_Costs - 153...

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153 Problems on Firm’s Technologies, Production Costs and Supply Decisions. Problem 7.1. A firm produces a fine Western New York delicacy, the cardboard hamburger. Table 7.8 shows how the firm’s production of burgers varies with the quantity of labor hired. Table 7.8: The Firm’s Technology. Output Labor Marginal Average Level Input Productivity Productivity Of Labor Of Labor (burgers) (hours) (burgers/labor hour) (burgers/labor hour) 0 0 50 1 120 2 186 3 246 4 295 5 342 6 385 7 416 8 432 9 440 10 440 11 420 12 (i) Compute the marginal physical productivities of the firm’s labor units and enter the values into the “Marginal Productivity of Labor” column of Table 7.8. (ii) In what unit is the marginal labor productivity measured? (iii) Where on a graph of total output versus labor used do you see the marginal physical productivities of labor represented or measured? (iv) If you add up the marginal productivities of the first three labor hours, what do you get? (v) Your answer to part (iv) is a special case of the general statement that “If you add up the marginal physical productivities of the first L labor hours, then you get the total quantity of output produced when L labor hours are used. (vi) Now compute the average physical productivities of the firm’s labor units and enter the values into the “Average Productivity of Labor” column of Table 7.8.
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154 CHAPTER 7. TECHNOLOGIES, COSTS AND SUPPLY (vii) In what unit is the average labor productivity measured? (vii) What do you notice about the units in which the marginal and average produc- tivities of labor are measured? (ix) Look at the Marginal and Average Productivity of Labor columns of Table 7.8. Does adding an extra labor hour increase the average labor productivity only if the marginal productivity of the extra labor hour is larger than the average labor pro- ductivity without the extra labor hour? (x) Does adding an extra labor hour decrease the average labor productivity only if the marginal productivity of the extra labor hour is smaller than the average labor productivity without the extra labor hour? (xi) Explain your answers to parts (ix) and (x). Problem 7.2. Labor is an input essential to a firm ( i.e. if the firm uses no labor then it produces no output). If the marginal physical productivities of the first, second and third units of labor used by the firm are, respectively, 20, 18 and 15 units of extra output, then what is the firm’s output level when it uses 0 units of labor, 1 unit of labor, 2 units of labor, and 3 units of labor? Problem 7.3. When a firm hired 4 workers, the average labor productivity of these workers was 2 · 5 pianos per worker. The firm then hired a 5 th worker and found that the average productivity of its workers changed to 2 · 6 pianos per worker. (i) What is the firm’s output level when it uses 4 workers?
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