A firm's production process uses labor,L,and capital,K,to produce an output,Q according to the function Q = 25KL.Let labor be fixed at level .What is the cost minimizing level of capital that the firm must use to produce a target level of output, ?

Question

A firm's production process uses labor,L,and capital,K,to produce an output,Q according to the function Q = 25KL.Let labor be fixed at level  .What is the cost minimizing level of capital that the firm must use to produce a target level of output,  ?

Quizplus · Accepted Answer

To find the cost-minimizing level of capital, we need to use the formula for the marginal product of capital (MPL) which is the change in output resulting from a one-unit change in capital while holding labor constant. MPL = 25L.

Next, we need to use the formula for the marginal cost of capital (MC) which is the cost of using an additional unit of capital while holding output constant. MC = r, where r is the rental rate of capital.

Since the firm wants to produce a target level of output, we need to set MPL equal to the target level of output divided by the fixed level of labor (11).

So, MPL = Q/L = (11ea71e2_6319_bcbd_89cd_3da38137caf8_TB1644_11)/11 = 11ea71e2_6319_e3d0_89cd_6f8d592cb166_TB1644_11.

Equating this to MC, we get 11ea71e2_6319_e3d0_89cd_6f8d592cb166_TB1644_11 = r. Therefore, the cost-minimizing level of capital is 11ea71e2_6319_e3d0_89cd_6f8d592cb166_TB1644_11.

A Firm's Production Process Uses Labor,L,and Capital,K,to Produce an Output,Q