13. The profit-maximizing level of

13. The profit-maximizing level of labor and output is achieved where VMP w L = . Here,
( )( ) ( ) ( ) 1/ 2 1 2 1/ 2 2 $100 4 $400 L VMP L L − − = = and w = $100 per day. Solving yields L
= 16. The profit-maximizing level of output is Q = 2(4)1 2 (16)1 2 = 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.
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 variable costs are
($50)(5) =$250, and your revenues are ($5)(90) = $450. Thus, your maximum profits
are $450 - $300 = $150
19. To maximize profits the firm should continue adding workers so long as the value
marginal product of labor exceeds the wage. The value marginal product of labor is
defined as the marginal product of labor times the price of output. Here, output sells
for $50 per panel, so the value marginal product of the third worker is $50(290) =
$14,500. Table 5-4 summarizes the VMPL for each choice of labor. Since the wage is
$7,000, the profit maximizing number of workers is 4.