Suppose a firm's production function is given by f (L ,K) =5 (LK)1/2 , where L denotes the use of labor and K denotes the use of capital. Letting w denote the price of labor and r the price of capital, suppose that w = $6, and r = $48. Answer the following question for this firm
a) Derive the conditional input demand functions for both labor and capital.
b) What is the equation for the firm's cost function?
c) Derive the expressions for the marginal and average cost functions , and illustrate them together graphically.
d) Write an expression for the firm's long-run supply function and depict it on your graph.