1. Consider two metropolitan areas, one that has many small school districts and one that has only a few large school districts. In a paragraph, what are the efficiency and equity effects of introducing a voucher system likely to differ across these two areas?2. Suppose the town of State College has three families, each with one child, and each of which earns $20,000 per year (pre-tax). Each family is taxed $4,000 per year to finance the public school system in the town, which any family can then freely attend. Education spending is $6,000 per student in the public schools. The three families differ in their preferences for education. Though families A and B both send their children to the public school, family B places a greater value on education than family A. Family C places the greatest relative value on education and sends its child to private school.a. Graph the budget constraints facing each of the three families and draw a possible indifference curve which could correspond to the choice each family makes.The city council is considering replacing its current system with a voucher system. Under the new system, each family would receive a $6,000 voucher for education, and families would still be able to send their children to the same public school. Since this would be more costly than the current system, they would also raise taxes to $6,000 per household to pay for it.b. Draw the budget constraint the families would face under this system.Suppose that, when the new system is introduced, family A continues to send their child to public school, but family B now sends their child to private school (along with family Cs child).c. Explain how you know that family C is made better off and family A is made worse off by the voucher policy.d. Show, using a diagram, that it is ambiguous whether B would be made better or worse off under the policy.3.In business, there is a tension between the principals (shareholders/owners) and agents (managers). The managers may choose policies that increase short-term profitability (and their bonuses) at the expense of long-term profitability. In a paragraph, describe why the same types of problems may exist in government as well, where elected officials are the agents and voters are the principals.4.Voters rarely get to choose the exact level of spending on a public good. Instead, they are provided with two optionsa proposed spending level posed by the government and a default (or reversion) level that would be enacted if the proposal were rejected by voters. The Leviathan theory of bureaucracy states that governments will select intentionally large proposed spending levels and default levels that are well below the desired level of spending. In a paragraph (or two) explain why this behavior is consistent with a size-maximizing government?5.Logrolling is a phenomenon in which elected representatives trade votes with one another. For instance, Representative A may be willing to vote for Representative Bs prefered policy, even if A doesnt like it, provided that B will vote for Representative As prefered policy, even if B doesnt like it.Suppose we have the follwing three projects up for vote: A naval ship, a hospital, and a park. There are three representatives who will individually vote on the projects. The net social benefits to the constituents of each representative are given in the table below. Note these benefits may be negative, meaning that the policy actually does harm to the constituents of the representative.Project John Dennis SusanNaval Ship 200 -75 -40Hospital -40 150 -25Park -100 -80 360a) What are the total benefits from each project?b) If a vote were held for each project, what would be the result for each project? Is this socially optimal?c) If these reperesentatives were to logroll (trade votes) to get their prefered policy to pass, what would be the result? (Hint: one of these representatives will be disappointed.)d) Is the final result from c) an improvement over the outcome of b)? Is it optimal?e) As hinted, one of the representatives will be left out of the logrolling. In principal, is there anything else that representative can do to get his/her prefered policy passed?Now suppose the benefits looked like this:Project John Dennis SusanNaval Ship 200 -170 -90Hospital -100 150 -80Park -250 -130 360f) What are the total benefits from each project?g) If a vote were held for each project, what would be the result for each project? Is this socially optimal?h) If these reperesentatives were to logroll (trade votes) to get their prefered policy to pass, what would be the result?i) Is the final result from h) an improvement over the outcome of g)?j) What conclusions, if any, can we make about the practice of logrolling from these examples?