Assume that the production function for a firm is q = 10K^.5L^.5. The price of L and K are both $20 each. In the short run, the firm has 1 unit of capital.

1.What is the firm's short-run cost function, expressed as a function of q?

To solve, follow these steps:

a.Solve for Labor as a function of output (given that K is fixed at 1, this should be relatively easy).

b.TC = wL + rK (rK is already fixed at $20, and wL depends on how much labor you need to use to produce output. So when you plug in the function you found in part a, you should have TC as a function of q.

2.If the firm wanted to produce 20 units of output, how much labor would it hire? What would the ATC of producing 20 units of output be?

3.At what level of output would the firm's average total cost be minimized?

4.What is the firm's long-run cost function? (Note: MPL = and MPK = (5)

5.In the long run, when the firm can vary K and L, if the firm wants to produce 20 units of output how much L and K does it use, and what is the ATC of producing 20 units of output?