Question

Joe owns a tree cutting company. His firm uses tree cutters (L) and equipment (K) in cutting trees. Suppose that the cost of hiring a tree cutter (w) is $10 an hour and the cost of using equipment (r) is $30 an hour. We will consider how much K and L Joe should use to cut 75 (i.e., Q = 75) trees. (Make sure that you specify intercepts, optimal amounts of K and L and isoquants clearly on graphs.)

a) Suppose that Joe’s production function is Q = 15K + (2.5)L. Marginal product of capital MPK = 15, and marginal product of labor MPL = 2.5. What are the values of the cost-minimization bundle of K and L? Draw his isoquant and isocost curves and identify the firm’s cost minimizing combination of K and L to represent the cost minimization solution on the graph.

b) Suppose that Joe’s production function is now Q = KL. Joe’s marginal product of capital and labor are MPK = L and MPL= K, respectively. What are the values of the cost-minimization bundle of K and L? Draw his isoquant and isocost curves and identify the firm’s cost minimizing combination of K and L to represent the cost minimization solution on the graph.

c) Suppose that the wage rate increases to $15 per hour. For each of the production functions identified in parts (a) and (b), identify what will happen generally to the optimal amounts of K and L. (Just identify whether K will increase, decrease or stay the same and whether L will increase, decrease or stay the same. You do not have to solve for the exact changes.) Justify your answers using graphs.

Answer 1