Consider the following production function: f (l, k) = l 3 k 3 .

(a) Calculate the marginal product of labor and capital.

(b) Does the production function exhibit diminishing marginal product of labor or capital?

(c) Does the marginal product of labor go up or down when firm employs more capital?

(d) Does the production function have a constant returns of scale? (e) Calculate the MRTS. (f) Does the production function exhibit diminishing MRTS? (g) Solve the cost minimization problem to get the input demands. Produc-

tion is q0 > 0, wage (labor cost per unit) is w > 0, and capital cost per unit is r > 0.