1. A firm has a production function given by q = K^.5L^.5. The price of labor is 1 and the price of capital is 4.

a) What types of returns to scale does this production function exhibit?

b) The firm must produce 200 units of output. How much labor and capital should the firm hire in order to do this, but at the lowest possible cost? Illustrate the solution to this problem graphically.

c) Derive the firm's long-run cost function when the price of labor is 1 and the price of

capital is 4. How does your answer relate to your answer in part a)?

d) Graph the firm's long-run average cost curve. Graph two short-run average cost curves for two different levels of capital (K1

e) Suppose a firm had a production function given by q = 2K^.5^L.5. Without deriving the long-run cost function associated with this production function explain how this firm's long-run cost function compares to the function you found in part c).