Question

Suppose the production function of a firm is given by q = L^1/4K^1/4. The prices of labor and capital are given by w = $10 and r = $20, respectively.

a) Write down the firm's cost minimization problem.

b) What returns to scale does the production function exhibit? Explain

c) What is the Marginal Rate of Technical Substitution (MRTS) between capital and labor?

d) What is the optimal capital to labor ratio? Show your work.

e) Derive the long run cost function. Show your work.

f) What happens to the firm's average cost as it increases production and why?

g) Derive the firm's long run supply function.

h) What will be the quantity of output that maximizes the firm's profit when the price of output is $2?

i) Suppose the government imposes a 30 cents unit tax on producers. Derive the new post-tax supply function.

Answer 1

eth ネunution to minimas e ch 11 4 Alinad ral-Substitution. (MRTS)2.NL ___ y 114 nle.de.二ㄧ一1k 多,づ. と l 0 2 0 2.5 2