Echapter 5: Answers to Questions and Problems

EChapter 5: Answers to Questions and Problems

5. Since MRTS KL ≠

w , the firm is not using the cost minimizing combination of r labor and capital. To minimize costs, the firm should use more labor and less capital since the marginal product per dollar spent is greater for labor: MPL 50 MPK 75 . = > = w r 6 12

6. See Table 5-2.

(1) (2) (3) Variable Cost VC 0 10,000 15,000 30,000 50,000 90,000 140,000 (4) (5) Average Fixed Cost AFC -100 50 33.33 25 20 16.67 (6) Average Variable Cost AVC -100 75 100 125 180 233.33 (7) Average Total Cost ATC -200 125 133.33 150 200 250 (8) Marginal Cost MC -100 50 150 200 400 500

Quantity Q 0 100 200 300 400 500 600

Fixed Cost FC 10,000 10,000 10,000 10,000 10,000 10,000 10,000

Total Cost TC 10,000 20,000 25,000 40,000 60,000 100,000 150,000

Table 5-2 13. The profit-maximizing level of labor and output is achieved where VMPL = w . Here, VMPL = 2 ( $100 ) ( 4 ) ( L ) = $400 ( L ) and w = $100 per day. Solving yields L = 16. The profit-maximizing level of output is 12 12 Q = 2(4 ) (16 ) = 16 units. The firm’s fixed costs are $10,000, its variable costs are $100(16) = $1,600, and its total revenues are $200(16) = $3,200. Profits are $3,200 – $11,600 = – $8,400. The firm is suffering a loss, but the loss is lower than the $10,000 that would be lost if the firm shut down its operation.

1/ 2 −1 2 −1/ 2

14. The higher wage rate in Europe induces Airbus to employ a more capital intensive input mix than Boeing. Since Airbus optimally uses fewer workers than Boeing, and profit-maximization entails input usage in the range of diminishing marginal product, it follows that the lower quantity of labor used by Airbus translates into a higher marginal product of labor at Airbus than at Boeing. 15. Table 5-3 provides some useful information for making your decision. According to the VMPL = w rule, you should hire five units of labor and produce 90 units of output to maximize profits. Your fixed costs are ($10)(5) = $50, your...