1) Consider a firm with the production function, q = (K^(0.5) + L^(0.5))^2. In the short-run, the level of capital is fixed.
a) Determine the equations for MPL and APL.
b) Solve for the short-run cost function (i.e. total costs as a function of output)
c) Determine the equations for MC, ATC, AVC, and AFC.
2) Using the same production function as in question 1, suppose that the firm is now operating inthe 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 2a and 1b. 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.