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Suppose that a firm has production function F(L, K) = L1/4 K3/4 for producing widgets, the...

Suppose that a firm has production function F(L, K) = L1/4 K3/4 for producing widgets, the wage rate for labor is w = $32, and the rental rate of capital is r = $6. Suppose the firm has an order to produce 40 units of output.

a) Carefully write out the firm’s cost minimization problem, using information specific to this problem.

b) Express two equations—specific to this problem—that the optimal solution satisfies.

c) Solve these two equations for L* and K*.

d) Determine the firm’s cost of meeting the order.

e) Resolve this problem, leaving the production goal Q as a variable in order to get the firm’s cost function C(Q).

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