Suppose that a steel mill has the production function q = 10LαKβ, where Q is tons of steel producedper week, L is the number of workers employed, K is the number of smelters used, and α=.5, andβ=.5. For this production function, the Technical Rate of Substitution is TRS = αK/βL. Suppose theweekly wage of a steel mill worker is $1,000 and the weekly rental price of a smelter is $1,000.Answer the next 4 questions based on this information.
Suppose the mill is currently producing 100 tons of steel per week using the least-cost combination of K and L. The firm's short run cost function, assuming that the amount of capital is fixed in the short run, is
a. C = Q1/2 + 10,000
b. C = 100Q + 10000
c. C = Q2 + 10,000
d. C = 10Q2 + 20,000
e. C = 20Q + 10,000
A monopolist faces a constant marginal cost of $1 per unit. If at the price he is charging, theprice elasticity of demand for the monopolist=s output is !0.5, then
a. the price he is charging must be $2.
b. the price he is charging must exceed $2.
c. the price he is charging must be less than $2.
d. the monopolist cannot be maximizing profits.
e. the monopolist must use price discrimination.