Chocolate-R-Us produces chocolate santas using the production function: Q=2k^1/2 L^1/2 where K is the amount of capital and L is the amount of labor used in the process. Assume that the price of capital is r and the wage rate is w.

a. Find the firm's long-run cost function, C(w,r,q).

b. Suppose the capital is fixed at 10 units in the short-run. What is the firm's shortrun cost function? Calculate marginal cost, average variable cost, and average fixed cost.

c. Illustrate on an isoquant/isocost graph the difference between your answers to part a and b. Explain intuitively why long run costs should always be lower than shortrun costs.