Consider a firm which has the production function f (L, K) = 3L^(1/3)K^(-1/6) , where L is the quantity of labor and K is the quantity of capital. The wage level is given as w = 1 and the rental rate of capital is r = 4

1) Find out if this firm has increasing, decreasing, or constant returns to scale.

Short Run: Now we assume that the level of capital is fixed at K = 1

2) Find the Average Cost, Average Variable Cost, and Marginal Cost functions of the firm in the short run

3) Show that the graph of the Average Cost curve has a U-shape (decreasing for small values of q and increasing for larger values)

Long Run: In the long run, the firm can change its capital level freely

4) Find the Total Cost, Average Cost, and Marginal Cost functions of the firm in the long run.

5) Find out if this firm exhibits an economy or diseconomy of scale