Using the same production function as in question 4 {ie: q = (K^1/2 + L^1/2)^2} suppose that the firm is now operating in the long-run.
a) Solve for the long-run cost function (i.e. total costs as a function of input prices and output).
b) Consider your answer from questions 5a and 4b. How does short-run total cost compare to long-run total cost when the fixed level of capital in the short-run equals the optimal level from the long-run cost minimization problem? Prove your statement mathematically.