Lime & Associates is a law firm that uses two inputs, land and labor, to provide legal services. Its production function is given by f(x, z) = x 2 5 z 1 2 , where x denotes the amount of land and z denotes the amount of labor. The price of land is $2. The price of legal services is $10.

(a) Are returns to scale increasing, decreasing, or constant for Lime & Associates? Show your steps.

(b) In the long run, the firm can choose both land and labor. The long-run price of labor is $5. Calculate the firms optimal choice of land and labor when it maximizes its profit. What is the profit-maximizing level of legal services? How much profit does it make at the optimum?

For parts (c)-(d), consider the short-run case where the amount of land is fixed at 32.

(c) The short-run price of labor is $4. Calculate the firms optimal choice of labor. What is the profit-maximizing level of legal services? How much profit does it make at the optimum? (4 Marks)

(d) When 0 z 16, the firm can only employ inexperienced labor, which means its production function becomes f(x, z) = 1 4 x 2 5 z. When z > 16, the firm has the original function f(x, z) = x 2 5 z 1 2 . The price of labor is $6. Calculate the firms optimal choice of labor in this case. Draw a diagram of the production function and the isoprofit line to illustrate the optimum. What is the profitmaximizing level of legal services? How much profit does it make at the optimum? (6 Marks)

ONLY DO C and D please.