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microeconomics

Questions and Answers of Microeconomics

c. Suppose that the property tax is zero in all communities. Consider community i’s Leviathan mayor. If he raises ti above zero and uses the revenues only for political rents, what will have to be
b. Now consider the case where households are fully mobile across jurisdictional boundaries and thus choose to live where their utility is highest. In equilibrium, how must utility in any
A. Consider a collection N of local governments that can employ local property taxes to fund public goods and local political rents. Suppose that local governments are pure Leviathans; that is, they
28.10 Policy Application: Government Competition, Leviathan, and Benevolence: Suppose governments can spend taxpayer resources on both public goods that have social benefits and political “rents”
i. In (e), you should have concluded that, under the proportional wage tax, everyone unanimously agrees on what the tax rate should be (when there are no private schools). Would the same be true if
h. Can you think of necessary and sufficient conditions for the introduction of a private school market to result in a Pareto improvement in this model?
g. Now suppose there exists a private school market that offers spending levels demanded by those interested in opting out of public education (and assume that spending is all that matters in
f. Suppose that y is per pupil spending on public education. What does this imply that d is (in terms of average population income I, number of taxpayers K, and number of kids N in school)?
e. Now suppose that a vote is held to determine the wage tax t. What tax rate will be implemented under majority rule? (Hint: Use your result from (d) to determine the ideal point for a voter.)
d. Calculate the indirect utility function for part (a) (as a function of L, w, and t).
c. True or False: Since the wage tax does not result in a distortion of the labor supply decision while the per-capita tax does, the former has no deadweight loss while the latter does.
b. Suppose instead that a per-capita tax T is used to fund the public good; that is, everyone has to pay an equal amount T. Suppose that a per-capita tax T results in public good level y 5
a. Suppose a proportional wage tax t is used to fund the public good y and a tax rate t results in public good level y 5 dt. Calculate the demand function for x and the labor supply function.(Note:
B.* Suppose preferences over private consumption x, a public good y, and leisure , can be described by the utility function u1x,y,,2 5 x ay b, g. Individuals are endowed with the same leisure amount
g.* In the 1970s, California switched from local financing of public schools to statewide (and equalized) financing of its public schools. Statewide school spending appears to have declined as a
f. So far, we have treated public school financing without reference to the local nature of public schools. In the United States, public schools have traditionally been funded locally, with
e. Consider two factors: First, the introduction of private schools causes a change in the income level of the median voter, and second, we now have private school attending households that pay taxes
d. Assume that the set of private school students comes from high-income households. What would this model predict about the income level of the new median voter?
c. Some have argued that political debates on public school funding are driven by “the ends against the middle.” In terms of our model, this means that the households on the ends of the income
b. Next, suppose private schools compete with public schools, with private schools charging tuition and public schools funded by taxes paid by everyone. How does this change the politics of public
a. Consider first the case of public school funding in the absence of the existence of private school alternatives. Do you think the usual median voter theorem might hold in this case, with the
28.9 Policy Application: Political Coalitions and Public School Finance Policy: In this exercise, we consider some policy issues related to public support for schools, and the coalitions between
e. Finally, suppose that there is only a single beneficiary of B. How much will he contribute when b 5 0.8? What if b 5 0.6? Within this example, can even one concentrated beneficiary stop a project
d. Suppose that b is also 0.8 (and thus equal to a). If the vote-buying process is as described in part A, will legislation B pass even though there are 1,000,000 members of interest group 1 and only
b. Suppose again that B is a renewal of an inefficient government program with concentrated benefits and diffuse costs and A is the elimination of the program. What does this imply about the
a. What is the equilibrium level of contributions to the two interest groups?
B is implemented. Suppose that interest groups have successfully persuaded members to believe y is equal to the sum of their contributions to the interest group. Everyone has income I, and there are
f. How might the free-rider problem be part of the transactions costs that affect interest group 1 disproportionately?B. Consider the problem faced by the interest groups in light of results derived
. It costs interest group 2 exactly $1 for every dollar in contributions to a legislator, but, because of the transactions costs of organizing its members, it costs interest group 1 an amount $c per
because milk price support programs are inefficient. Interest group 1 represents milk consumers and interest group 2 represents milk producers. Which interest group do you think will find it easier
. What is the subgame-perfect equilibrium now?d. Suppose that project B is extending milk price support programs while project A is eliminating such programs, and suppose that y A . 1.5y B
. Does your answer to (a) change?c. Suppose y A . 1.5y B
A. To simplify the analysis, suppose that there are only three legislators. Suppose further that interest group 1 makes its contribution first, followed by interest group 2.a. If y A 5 y B, will any
28.8 Policy Application: Interest Groups, Transactions Costs, and Vote Buying: Suppose that a legislature has to vote for one of two mutually exclusive proposals: proposal A or B. Two interest groups
e. How does the social ordering of the projects change under the Borda Count? Does the Borda Count violate IIA?
d. Suppose voter 4 changed his mind and now ranks B second and D fourth (rather than the other way around). Suppose further that voter 5 similarly switches the position of B and D in her preference
c. Derive again the Borda Count ranking of the five projects in part A given the voter preferences as described.
b. In what way do your results from part A of the exercise tell us something about whether the Borda Count violates the Independence of Irrelevant Alternatives (IIA) axiom?
B. Arrow’s Theorem tells us that any nondictatorial social choice function must violate at least one of his remaining four axioms.a. Do you think the Borda Count violates Pareto Unanimity? What
d. Suppose I get to decide which projects will be considered by the group and the group allows me to use my discretion to eliminate projects that clearly do not have widespread support. Will I be
b. Suppose option D was withdrawn from consideration before the vote in which voters rank the options. How does the Borda Count now rank the remaining projects? If only one can be implemented, which
A. Suppose there are five voters denoted 1 through 5, and there are five possible projects 5A, B, C, D, E6 to be ranked. Voters 1 through 3 rank the projects in alphabetical sequence (with A ranked
28.7 Business and Policy Application: Voting with Points: Jean-Charles de Borda (1733–99), a contemporary of Condorcet in France, argued for a democratic system that deviates from our usual
d. How does the range you calculated in (c) compare to the range of c that makes it possible for two candidates with position 0.5 to run against one another in equilibrium (as derived in A(c))?
c. Let P be arbitrarily close to zero. For what range of c will two candidates with positions 10.5 2 P2 and 10.5 1 P2 be able to run against one another in equilibrium? What does this range converge
b. For what range of c is it an equilibrium for two candidates to compete, one taking position x and the other taking the position 11 2 x2? Is your answer consistent with your answers to A(d)and A(e)?
e. For what range of c is it an equilibrium for two candidates with positions 0 and 1 to compete?B. Consider the same set-up as in part A.a. Let x [ 30,0.52. For what range of c is it an equilibrium
d. For what range of c is it an equilibrium for two candidates with positions 0.25 and 0.75 to compete?
c. For what range of c will it be an equilibrium for two candidates with position 0.5 to compete in the election?
b. How high does c have to be for the following to be a possible equilibrium: A citizen with position 0.25 enters the race as the only candidate and therefore wins. How high must c be for an
a. For what range of c is the following an equilibrium: A citizen with the median position 0.5 is the only candidate to enter the race and thus wins.
A. Assume candidates cannot change their position from their ideal point, and citizens who do not become candidates get payoff equal to minus the distance of the winning candidate position x* to
28.6* Everyday Application: Citizen Candidates: Whenever we have modeled political candidates who stand for election, we have assumed that they care only about winning and are perfectly content to
c. Suppose that, instead of voter ideal points being uniformly distributed on the Hotelling line, one third of all voters hold the median voter position (with the remaining two thirds uniformly
b. Can either of these be an equilibrium under the conditions specified in part A?
B. Consider the existence of a Nash equilibrium in stage 2.a. What are two possible ways in which three candidates might take positions in the second stage of our game such that your conclusion in
f. With the marginal cost of raising additional funds to build up a campaign war chest increasing, might the incumbent still allow entry of another candidate?
e. Suppose the incumbent is one of the potential candidates, and he decides whether to enter the race and how much to spend first. Can you in this case see a role for strategic entry deterrence
d. Suppose that the probability of winning in stage 2 is a function of the number of candidates who are running as well as the amount spent in the campaign, with candidates able to choose different
c. Suppose there is a Nash equilibrium in stage 2 regardless of how many of the three candidates entered in stage 1. What determines whether there will be one, two, or three candidates running in
b. Consider the following model: In stage 1, three potential candidates decide simultaneously whether or not to get into the race and pay the costc. Then, in stage 2, they take positions on the
a. How high must the probability of getting elected be for a candidate to get into the race?
28.5 Everyday Application: To Enter or Not to Enter the Race: Suppose there are three possible candidates who might run for office, and each has to decide whether or not to enter the race. Assume the
B. In exercise 28.3, we used the 2000 election and the controversy regarding Ralph Nader’s participation to suggest that the way we elect U.S. presidents violates the spirit of Arrow’s IIA axiom.
g. Prior to running in the general election as either the Democratic or the Republican candidate, a politician first needs to win a party’s presidential nomination. This is done mainly in
f. Some states have considered switching from a statewide winner-take-all system for electing“electors” in presidential races to a system in which electors from the state represent each candidate
e. The electoral college system gives each state two electors outright plus one elector for each representative that the state has in the House of Representatives (where representation in the House
d. In exercise 28.3, we suggested that one way to view the decision of whether or not to vote is by comparing the marginal benefit of voting to the marginal cost. The marginal benefit of voting
b. Suppose instead that there are four states, states 2 and 3 that are small (with 10% of the
28.4 Everyday Application: “Winner-Take-All” Elections and the U.S. Electoral College: In the United States, presidential elections are not won by the candidate who wins the popular vote
d.* Nader is often referred to as a “spoiler” because of many people’s belief that he “spoiled” the election outcome for Gore. True or False: It is much less likely that a third candidate
c. Some election systems require the winning candidate to win with at least 50% plus 1 votes, and, if no candidate achieves this, require a run-off election between the top two candidates.Since this
B. In the 2000 U.S. presidential election, George W. Bush defeated Al Gore by 537 votes in Florida, and with those 537 votes won the election.a. The close margin in the 2000 election is often cited
g. In Chapter 27, we suggested that one way charitable organizations overcome free-rider problems among potential donors is to find ways of eliciting within donors a “warm glow”from giving. Can
e. In the 2008 U.S. presidential election, Barack Obama won by close to 10 million votes. In what sense is the puzzle not so much why more people didn’t vote but rather why so many—about 60% of
d. In light of your answer to (c), might it be rational for many people not to vote?
c. Next, consider a different way in which the “it does not matter” statement might be meant:Perhaps a voter recognizes that it matters which candidate wins (in the sense that the world will
a. First, suppose we take the median voter model really seriously and believe it accurately predicts the position of the two candidates from which we choose. How might this justify the excuse given
28.3 Everyday Application: Why Vote? Voting is costly. If you vote in person, you have to find your polling place and often stand in line until you get to the voting booth to vote. If you vote by
e. What does this imply for the real shape of the individual’s preferences over the policy variable t, assuming d . I/4?
d. Suppose that an individual with income I can purchase a perfect substitute to y on the private market at a price of 1 per unit. Determine, as a function of I, at what level of t an individual will
c. At what t does this function reach its maximum?
b. What shape does this function have with respect to the policy variable t?
B. Consider a simple example of how single-peaked and non-single-peaked tastes over policy might naturally emerge in a case where there is only a single dimensional issue. A voter has preferences
f. In the more general case where we allow ideal points to lie anywhere, the agenda setter still has some control over what policy alternative gets constructed in a structure induced equilibrium in
e. In our discussion of the “Anything-Can-Happen” theorem, we raised the possibility of singleissue committees as a mechanism for disciplining the political process (and limiting the set of
d. Revisit the “Anything-Can-Happen” theorem in the text. Suppose that the current policy A in our two-dimensional policy space is equal to the ideal point of the “median voter” along the
c. Suppose that the issue space is two-dimensional, as in the case where we have to choose spending levels on military and domestic priorities. Consider the following special case: All voters have
b. Implicitly, we have assumed an odd number of voters (such that there exists a single median voter). Can you predict a range of possible policies that cannot be beaten in pairwise elections when
a. What are the two conditions under which we can predict that the median voter’s position is such a Condorcet winner?
28.2 In the text, we discussed two main conditions under which the median voter’s favored policy is also the Condorcet winner.A. Review the definition of a Condorcet winner.
28.1* In Chapter 4, we considered different ways of thinking about single-peaked preferences over twodimensional issue spaces. We did so in particular in end-of-chapter exercise 4.11, which you can
How would you assign the members to committees if you wanted to get less spending on y and z than we did in panel (a) of Graph 28.9? What if you wanted more of y but less of z?
Can you explain how panels (d) through (f) complete the argument that G can be implemented through a sequence of pairwise votes?
Legislators (like senators) who run for executive office (like governor or president) are often confronted by the media with votes they have taken in the legislature that seem to contradict their
Which of these voters have single-peaked preferences over public school spending?
In the United States, prior to running as a party nominee in a presidential election, a potential candidate first has to win primary elections that are restricted to members of the potential
Can you see how this equilibrium prediction conforms to the equilibrium in the Hotelling model when firms are restricted to charging the same output price (and where the ideological spectrum is
In the graph, we have depicted all the single-peaked preferences as having the same shape and differing only in the placement of the ideal point. Would the same Condorcet winner arise under
Suppose that tax rates were progressive, implying that the tax rate increases as more tax revenue is being raised. Would preferences over y still be single-peaked?

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