Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, the wage rate for labor is w = $400, and the rental rate of capital is r = $25. a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s cost minimization problem, using the particulars associated with this problem. b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of this problem. c) Solve the two equations for the firm’s optimal choice. Show your work. d) Determine this firm’s minimum cost of producing 120 units. e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s cost function C(Q). Show your work.
Suppose that a firm has production function F(L, K) = L^2/3 K^1/3 for producing widgets, the
wage rate for labor is w = $400, and the rental rate of capital is r = $25.
a) Suppose that the firm has received an order for Q = 120 units of output. Neatly specify this firm’s cost
minimization problem, using the particulars associated with this problem.
b) Give two equations that an interior solution satisfies, tailoring your equations to the particulars of this
problem.
c) Solve the two equations for the firm’s optimal choice. Show your work.
d) Determine this firm’s minimum cost of producing 120 units.
e) Now suppose that the firm’s production goal is left as the variable Q. Come up with the firm’s cost
function C(Q). Show your work.
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