A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor is $30 and the price of capital is $10. The firm has a production goal of 100 units of output.
a) Carefully write out this firm’s cost minimization problem, using the particulars of this problem.
b) Give two equations—particular to this problem—that the solution satisfies.
c) Solve for the firm’s optimal input bundle.
d) Determine the firm’s cost of producing 100 units of output.
e) Resolve this problem, leaving the production goal Q as a variable in order to get the firm’s cost function C(Q).
A firm has the production function F(L, K) = L1/2 + K1/2. The price of labor...
5. Suppose a firm has the production function Q = K1/2 L1/4 M1/4 The wage rate w = 16 , rental rate r = 2 , and the price of the materials m = 1. 1) Suppose in the short run, K is fixed at K *. What’s the solution to the firm’s short run cost-minimization problem? 2) What is the solution to the firm’s long run cost minimization problem given that the firm wants to produce Q units of...
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2 a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function. b) What is the firm’s marginal cost? c) For this problem, you will sketch the graph of the firm’s isoquant for Q...
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Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 36. If the price of Labor, w = $12 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 48 units of output? MC = ________________________
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5. Suppose a firm has the production function Q=K1/2 [4M1/4 The wage rate w=16, rental rate r=2, and the price of the materials m=1. 1) Suppose in the short run, K is fixed at K*. What's the solution to the firm's short run cost-minimization problem? 2) What is the solution to the firm's long run cost minimization problem given that the firm wants to produce Q units of output? 3) Suppose that Q = 10,K* = 20. Compare the long...
Suppose that a firm has a production function ? = K^a ?^b , where a>0 and b>0. K is capital and L is labor. Assume the firm is a price taker and takes the prices of inputs, (r and w) as given. 1) Write down the firm’s cost minimization problem using a Lagrangean. 2) Solve for the optimal choses of L and K for given factor prices and output Q. 3) Now use these optimal choices in the objective function...