4. Consider a firm with the additive production function we discussed in

class: f(K, L) = 2L+ 2K

(a) Derive the firm's long run demand curve for labor, as well as the

firm's long run demand curve for capital.

(b) Notice that the firm's long run labor and capital demand curves

do not exhibit any substitution effects. That is, if the price of

labor increases, the firm's use of capital does not change. Why

do you think this is the case?

5. Suppose a firm has a production function that relies only on labor, not

capital. The firm's production function is

f(L) = 200L4L² . The firm is a price-taker in the market for labor,

and has to pay a wage of $20 for each hour of labor hired.

(a) A fellow economist tells you that he thinks it is optimal for the

firm to hire 25 hours of labor, since this maximizes the firm's

level of production. Is your fellow economist's reasoning correct?

(b) Please derive the firm's short-run labor demand curve if the firm

is also a price-taker in the output market.

(c) Explain briefly how your process for finding the demand curve

would have to change if the firm had market power in the output

market.

(d) If the price of the output good is $2, how many hours of labor

should the firm hire, given the current wage rate?