Production function f(x1, x2) = x1x2. The prices for the inputs are 2 and 8, respectively.
a. If x2 is fixed at x2=10 derive the short-run cost function of the firm as a function of Y - output level, and the prices for inputs given above. (Hint: with 1 input there is no cost minimization.)
b. Now suppose that x2 is also free to vary. Derive the demands for the inputs and the long-run cost function of the firm.
c. What value of Y makes the value of the short-run (in a) and long-run (in b) cost functions equal. Draw the two cost functions on the graph. Do they cross? Which one lies higher?