A steel producer has the production function q=10K^0.75 E^0.25 where q is the quantity of steel, in metric tons, K is the firm's capital stock, and E is the number of labor hours it employs (measured in thousands).
a) Assume the firm's current capital stock is fixed at K = 4096. If the firm employs E = 81 labor units, then how much steel does it produce?
b) Suppose the firm receives an order to produce 10,000 metric tons of steel. If its capital stock is fixed at K = 4096, then how many hours of labor must it employ to satisfy the order?
c) In the long run, the firm is free to vary both its capital stock and the number of workers it employs. Given this, what would happen to the firm's output if it doubles the amount of labor and capital it uses? What happens if it quadruples the amount? What does this result suggest in general?