Manufac Inc. produces industrial equipment using mainly Labor and Capital. It is

Question

Manufac Inc. produces industrial equipment using mainly Labor and Capital. It is currently using K = 1 (one unit of capital is 1000 machine-hour per day) and L = 20 (one unit of labor is 1000 man-hour per day). You estimated that its production function is Q = 100LK. The price per unit of labor is MCL = 20 ($000) and the price per unit of capital is MCK = 100 ($000).

(a) Is Manufac Inc. using the right mix of inputs? Should Manufac Inc. invest in more machines?

(b) Keeping output constant at 2000, how much labor and capital should Manufac Inc. choose?

Thank you!

Explanation / Answer

a) Manfac Inc. is not using the right mix of inputs w/r = MCL/MCK =dQ/dL / dQ/dK = 100K/100L = K/L= 20/100=1/5

so L=5K, Here in this case L = 20 K which is not optimal so Manufac Inc. should invest in more machines

b) if L =5K and Q =2000 then 2000 = 100*K*5K = K^2 = 4 so K=2 and L= 10

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