A firm's production function is qi = 4*Ki.2Li.4. The wage rate in this area is w = $15, and the cost of capital is r = .05.
a. Find the firm's short run cost function, if Ki is fixed at $100,000.
b. If the good is exported around the world at a price of $100, what is the firm's optimal output, and what is its profit or loss? (We would describe this as "perfectly elastic demand" for this good)
c. Now suppose that the price is not known. Derive the firm's short run supply function qi (P). (hint, follow the same steps as in b, but replace the $100 value with the variable, P)
d. Now imagine that time passes, such that Ki can be adjusted to reflect market conditions. What is the firm's long run cost function? What is its long run supply function? How much would it produce if P=$100? What would be its profit or loss?