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)

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.