Suppose q 2 middot k13 middot l12 a what are the returns

Question

Question: Suppose q = 2 middot K^1/3 middot L^1/2.

a. What are the returns to scale of this production function?

b. Find the short run cost function.

c. Find the short run supply function.

d. Suppose that in the short run k = 100, r = 1, and w = 4. Where does the short run marginal cost curve intersect with the short run average cost curve?

e. Find the long run cost function. [Use the lagrangian method]

f. Find the long run supply function.

g. How many units will this firm produce if p = 6, w = 1, and r = 5?