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/ 2^1/2, 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 firm's 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 firm's optimal choice of labor. What is the profit-maximizing level of legal services? How much profit does it make at the optimum? (d) When 0 sz 16, the firm can only employ inexperienced labor, which means its production function becomes f(x, z)=1/4x^z. When z> 16, the firm has the original function f(x, z)= The price of labor is $6. Calculate the firm's 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 profit-maximizing level of legal services? How much profit does it make at the optimum?