Even if public schools are not profit maximizing, no school administrator wants to be a part of a declining school. A thriving school is one where enrollment is either rising or stable. Consider a school principle who values how well her school is thriving according to the production function f(), which is a function of a single variable e, for enrollment. Her net benefit y, can be expressed as y = B*f(e) - C(e), (1) where C(e) is the total cost function, which is strictly increasing in enrollment. B is a con- stant term. Qla. In this setting the administrator cannot choose the enrollment levels at her school per se. However, there can still exist an theoretically optimal school size. Express the first order condition for the optimization problem in general terms. Q1b. Let the total cost function is specified as C(e) = 250, 000 + 8e2. What is the average cost for a school with 1,500 students? Q1c. Given the total cost function in 1b, write down the expression for the marginal cost curve for the school. Q1d. Choose one of the below. Which of the following best characterizes the marginal cost curve you found in 1c? 1. Constant 2. Strictly increasing in X 3. Strictly decreasing in X 4. Neither strictly increasing or decreasing in X