Question

A firm has the production function: Q= 10K^.5L^.5 If the firm has 36 units of capital (K), how much labor is needed to produce 240 units of output?

Answer 1

Answer: 16 units of labor.

The production function is as follows;

.......................(1)

The firm has 36 units of capital, i.e., capital is fixed at 36 units.

Let us see, how much labor is needed to produce 240 units of output(Q).

Putting Q = 240 , and K = 36 in equation(1), we get,

Or,

Or,  

Or,  

Or,

Or,  

Or,

Or,  

So, 16 units of labor are needed to produce 240 units of output.

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