Question 2. (20 Marks) Lime & Associates is a law rm that uses two inputs, land and labor, to provide legal services. Its production function is given by f(:l?, z) = 23% 25%, where 3: denotes the amount of land and 2 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. (5 Marks) (b) In the long run, the rm can choose both land and labor. The longrun price of labor is $5. Calculate the rm's optimal choice of land and labor when it maximizes its prot. What is the protmaximizing level of legal services? How much prot does it make at the optimum? (5 Marks) For parts (c)(d), consider the shortrun case where the amount of land is xed at 32. (c) The short-run price of labor is $4. Calculate the rm's optimal choice of labor. What is the protmaximizing level of legal services? How much prot does it make at the optimum? (4 Marks) (d) When 0 S 2 g 16, the firm can only employ inexperienced labor, which means its production function becomes f (2:, z) = mgz. When 2 > 16, the rm has the original function x, 2) = xgzi. The price of labor is $6 Calculate the rm's optimal choice of labor in this case. Draw a diagram of the production function and the isoprot line to illustrate the optimum. What is the prot maximizing level of legal services? How much prot does it make at the optimum? (6 Marks)