1. Suppose that the Idaho State Board of Education forcibly removes the mighty C. Scott Green from the Presidency at the University of Idaho. They decide they will run UI as a true bureaucracy and use costs and benefits to determine how many new freshmen to enroll each year. Higher education will now be treated as a fully public good. A humbled Green grows a half-hearted beard and becomes a permanent fixture at the end of the bar at the Corner Club. He is often heard weeping as he slowly recites a somber rendition of the Idaho fight song. After a painstaking analysis, the State determines the benefits to Idaho from having more college education can be described by STB = 18,000Q 2Q² and the total costs of educating the students is described by STC = 10,000Q, where Q = the number of new students enrolling. This means the marginal benefit and marginal costs are given, respectively, by SMB = 18,000 4Q and SMC = 10,000.

a. Suppose the State Board of Education truly does have the states best interests in mind. They will use the information provided from the equations above to determine the efficient level of new students to enroll each year. What is the optimal quantity, and how much will the state spend in resources each year?

b. . Based on the efficient level of enrollment found in part a, what would be the social marginal benefit and social marginal cost of enrolling the next student? Explain briefly what these numbers tell us. Does the nature of the SMB function make sense in this example? Explain your reasoning.

c. Now suppose the State Board actually took over the UI to try to maximize their power and influence on the state budget. In this case, they will act as a size-maximizing bureaucrat. Determine the number of new students they will allow to enroll each year in this case, then find how much in resources the state spends now.

d. With the aid of a diagram, demonstrate the difference in the two quantities and show the amount of inefficiency caused by the agency that is interested in maximizing the size of the budget. Solve to determine the level of inefficiency. Briefly explain why the bureaucracy might act in this way, and how it might be able to make the case to the public for maximizing the size of the agency.