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microeconomics

Questions and Answers of Microeconomics

Suppose instead that y is defined as the overall spending in public schools. What is the slope of the “budget line” under the same conditions as described in exercise 28a.1?
Suppose y is defined as per pupil spending in public schools. If there are N different taxpayers and an equal number of school children, and if all taxpayers share the financing of public schools
B. Now consider the way we modeled these issues in part B of exercise 27.11. Each district gets a project, with the costs and benefits varying with the size of the project. The cost of providing y in
27.12 Policy Application: Local and National Public Goods as Pork Barrel Projects: Consider again, as in exercise 27.11, the political incentives for legislators that represent districts. In exercise
B. Consider the same set of issues modeled slightly differently. Instead of thinking about a number of different projects per district, suppose there is a single project per district but it can vary
g. In what sense do legislators have an incentive to propose inefficient projects even though all of their constituents would be better off if no inefficient projects were located in any district?Can
f. How does the set of inefficient projects that the legislator includes in bills change as N increases?
e. If there is only a single district (i.e., if N 5 1) is there a difference between your answer to(c) and (d)?
d. Now consider a legislator who represents district i and whose payoff is proportional to the surplus her district gets from the projects she brings to the district. What projects will this
c. Suppose the possible projects that can be brought to district i range in benefits from B 5 0 to B 5 B where B . C. Which projects should be built in district i if the legislature cares only about
b. How much of a benefit do the citizens in district i receive if the project is located in district i?What if it is not?
A. Suppose that there are N different legislative districts, each with an equal proportion of the population. Suppose for simplicity that all citizens are identical and that tax laws affect all
27.11 Policy Application: The Pork Barrel Commons: In representative democracies where legislators represent geographic districts in legislative bodies (such as the U.S. House of Representatives), we
27.10 Policy Application: Social Norms and Private Actions: In exercise 21.12 of Chapter 21, we investigated the role of social norms in determining the number of “green cars” on a city’s
f. Does the optimal tax rate differ from what you derived before? What fraction of tax revenues will be spent on national defense?
. Modify the optimization problem in (c) to one appropriate for this setting, with the government now choosing both t and the fraction k of tax revenues spent on national defense (versus the fraction
e. Suppose next that the government provides two pure public goods: spending on national defense y1 and spending on the alleviation of poverty y2(where the latter is a public good in the ways
B. Suppose we approximate the demand side for goods by assuming a representative consumer with utility function u1x, y2 5 x 1/2 y1/2 and income I, where x is private consumption (in dollars) and y is
e. What do you think of the following statement: “Nations that have devised more efficient tax systems are more likely to win wars than nations with inefficient tax systems.”
d. Use your answer to (c) to explain the following statement: “As the inefficiency of the tax system increases, the optimal level of national defense spending by the government falls.”
c. How does the marginal cost of providing this public good change as the tax system becomes more inefficient?
b. True or False: If the public good is defined as “spending on national defense,” then the marginal cost of providing $1 of increased funding for the public good is $1 under an efficient tax
A. Consider varying degrees of inefficiency in the nation’s tax system.a. In our development of the concept of deadweight loss from taxation, we found that the deadweight loss from taxes tends to
Policy Application: Distortionary Taxes and National Security: In the real world, government provision of public goods usually entails the use of distortionary taxes to raise the required revenues.
j. Under what condition will the balanced budget 1t, g2 government program raise the overall funding level for antipoverty programs?
i. If the government instead imposes a proportional income tax t and uses the revenues solely to fund g, what happens to overall funding of antipoverty efforts, assuming the N individuals still give
h. What happens to overall funding (both public and private) when the government increases g without changing taxes?
g. Suppose instead that the condition you derived in (b) holds. To simplify the analysis, suppose that the N people who care about antipoverty programs all have the same income level I(as well as the
f. Can this government intervention in antipoverty efforts be justified on efficiency grounds?
e. Suppose the government instead levies a proportional tax t on all income and uses the funds solely to fund g. How much private funding for antipoverty programs will this government intervention
d. If the government increases g without raising taxes, will private contributions to antipoverty efforts be affected (assuming still that the condition derived in (a) holds)? (Hint: How does the
. Will private antipoverty efforts be funded efficiently when g 5 0? What will be the equilibrium level of private funding for antipoverty programs when g 5 0 as N gets large?
c. Suppose the condition you derived in (a) applies (and maintain this assumption until you get to part (g)). Suppose further that there are N individuals who have different income levels, with n’s
b. What has to be true for antipoverty efforts to be pure public goods?
a. What has to be true for antipoverty efforts to be strictly private goods?
B. Denote individual n’s private good consumption as xn, the government contribution to antipoverty efforts as g and individual n’s contribution to antipoverty efforts as zn. Let individual n’s
h. Some argue that private anti-poverty programs are inherently more effective because civil society anti-poverty programs make use of information that government programs cannot get to. As a result,
g. How does your answer to (f) change if there is a third set of individuals that does not give to antipoverty programs or does not benefit from them but would be taxed (together with those who are
f. If government redistribution programs are funded through taxes on the individuals who are voluntarily giving to antipoverty programs, why might the government’s program have to be large in order
e. If the conditions in (d) hold, why is there an efficiency case for government redistribution programs?
d. How would individuals have to view their contributions to antipoverty programs in order for such programs to be pure public goods?
b. How would the individuals who give to antipoverty programs have to view such programs in order for there to be no externality to private giving?c. If your answer to (b) is in fact how individuals
A. Suppose there is a set A of individuals that contribute to antipoverty programs and a different set B of individuals that receive income transfers from such programs (and suppose that everyone in
27.8 Policy Application: Do Antipoverty Efforts Provide a Public Good? There are many equity- or fairness-based arguments for government engagement in antipoverty programs, and for general government
27.7 Policy Application: Demand for Charities and Tax Deductibility: In end-of-chapter exercise 9.9 of Chapter 9, we investigated the impact of various U.S. income tax changes on the level of
1.1 2. By modifying the spreadsheet that you used to create the table in part (d), can you determine the optimal number of hours the entrepreneur should put into his two fundraising activities now?
f.** Suppose all the parameters of the problem remain the same except for the following:g 5 0.0111 1 ,2 0.5 1 0.001N
e. Approximately how would you recommend that the entrepreneur split his time between recruiting more donors and working with existing donors?
d.** Next, suppose that N1,1 2 5 1,00011 1 ,1 1/2 2, and g1,2 2 5 0.0111 1 ,2 1/2 2, and suppose that the entrepreneur has a total of 1,000 hours to devote to the fundraising effort. Assume that he
c. In equation (27.54), we determined the individual equilibrium contribution in the presence of a warm glow effect. Suppose that this represents the equilibrium contribution level for the donors
B. Suppose that the two production processes introduced in part A are f1 1,1 2 and f2 1,2 2, with dfi/d,i , 0 for i 5 1,2 and with “output” in each process defined as “dollars raised.”a.
27.6 Business Application: The Marketing Challenge for Social Entrepreneurs: Social entrepreneurs are entrepreneurs who use their talents to advance social causes that are typically linked to the
h. True or False: In subscription campaigns, we should expect initial pledges to be small and the campaign to “show increasing momentum” as time passes, with pledges increasing as we near the
g. True or False: A subscription campaign will eventually succeed in raising the necessary funds so long as it is efficient for us to build the streetlight.
f. Recalling that g`t50d t 5 1/11 2 d2, what is the greatest amount that a subscription campaign can raise if it goes on sufficiently long such that we can approximate the period of the campaign as
e. What is the highest that C can be in order for 1T 1 12 pledges, pledges starting on day 0 and ending on day T, to cover the full cost of the light?
d. What is the amount pledged today; that is, in period 0?
B. Now consider the more general case where you and I both value the street light at $V, it costs $C, and$1 tomorrow is worth $d , 1 today. Assume throughout that the equilibrium is subgame
g. Why might a subscription campaign be a good way for a pastor of a church to raise money for a new building but not for the American Cancer Association to raise money for funding cancer research?
f. What is the remaining source of inefficiency in the subscription campaign?
e. How much would each of us be willing to pay the government to tax us an amount equal to what we end up contributing but to do so today and thus put up the light today?
d. How much does each of us have to pay for the streetlight (assuming you go first)?
a. Suppose it ends up taking T days for us to raise enough pledges to fund the light. Let xT ibe the last pledge that is made before we reach the goal. What does subgame perfection imply xT iis?
27.5* Everyday and Business Application: Raising Money for a Streetlight through a “Subscription Campaign”: Sometimes, a civil society institution’s goal can be clearly articulated in terms of
f.* Can you argue that, in light of your answer to A(g), the same might be true if zoning regulations are not uniformly the same within a community?
e. In the extreme, a model with exclusionary zoning might result in complete self-selection of household types into communities, with everyone within a community being identical to everyone else. How
d. Would the (unconstitutional) practice of being able to set a minimum income level for community members establish a way for an equilibrium to emerge? How does the practice of exclusionary zoning
B. Consider again the cost function c1N2 5 FC 1 aN bwith a . 0 and b $ 0 (as we did in exercise 27.3).a. In the case of competitive firms providing this excludable public good, calculate the long-run
i. True or False: The insights from this exercise suggest that local community competition might result in efficient provision of local public goods, but they also raise the “equity” concern that
h. Suppose that a court rules (as real-world courts have) that even wealthy communities must set aside some fraction of their land for “low income housing.” How would you expect the prices of
27.4 Everyday, Business, and Policy Application: Competitive Local Public and Club Good Production: In exercise 27.3, we considered some ways in which we can differentiate between goods that lie in
B. Consider in this part of the exercise only crowding on the cost side, with the cost of providing some discrete public good given by the function c1N2 5 FC 1 aN bwith a . 0 and b $ 0. Assume
27.3 Everyday Application: Sandwiches, Chess Clubs, Movie Theaters, and Fireworks: In the introduction, we mentioned that while we often treat public and private goods as distinct concepts, many
B. Consider the same set-up as in exercise 27.1, but now suppose that each individual assumes the government will balance its budget and therefore anticipates the impact his giving has on the tax
g. Finally, suppose we start with N 5 2 and raise N. What happens to the degree to which n’s giving decisions impact n’s tax obligations as N increases? What happens to the size of the free-rider
f. True or False: The efficient level of the subsidy is the same when N 5 2 as when N is very large if individuals take into account the tax implication of increasing their giving to the subsidized
e. Next suppose N is very large. Explain why it is now a good approximation to assume that individual n takes t as given when he chooses his contribution level to the public good (as he did in
27.2* In exercise 27.1, we extended our analysis of subsidized voluntary giving from 2 to N people. In the process, we simply assumed the government would set t to cover its costs, and that
i. What does this optimal policy converge to as N gets large? Interpret what this means.
h. Can you explain s* when N is 2, 3, and 4 in terms of how the externality changes as N increases? Does s* for N 5 1 make intuitive sense?
g. Derive the optimal policy 1t*, s*2 that results in efficient levels of public good provision through voluntary giving. What is the optimal policy when N 5 2? (Your answer should be equal to what
f. Substitute your expression for t from (e) into your answer to (d). Then determine what level of s is necessary in order for private giving to result in the efficient level of output you
e. For the policy 1t, s2 to result in the optimal level of public good funding, what has to be the relationship between t and s if the government is to cover the cost of the subsidy with the tax
d. What is the equilibrium quantity of the public good for policy 1t, s2?
B. In Section 27B.2.2, we considered how two individuals respond to having the government subsidize their voluntary giving to the production of a public good. Suppose again that individuals have
g. Explain how, as N becomes large, the optimal subsidy policy becomes pretty much equivalent to the government simply providing the public good.
f. What does your answer imply for the level of subsidy s that is necessary to get people to contribute to the efficient level of the public good as N increases? (Define s as the level of subsidy
e. When N 5 2, how much of the overall benefit from his contribution is individual 1 taking into account as she determines her level of giving? How does this change when N increases to 3 and 4? How
d. Given your answers to (b) and (c), what happens to person 1’s equilibrium contribution as N increases? (Hint: Where on the best response function will the equilibrium contribution lie?)
27.1 We discussed in the text the basic externality problem that we face when we rely on private giving to public projects. In this exercise, we consider how this changes as the number of people
2. Can you use our solutions for s* and t* to show that this level is achieved through the voluntary contributions of the two individuals when the policy 1s*, t*) is implemented?
We previously concluded that the optimal level of the public good is 11 2 a2 1I1 1 I2
Can you offer an intuitive explanation for why s* 5 1/2? How would you expect this to change as the number of consumers increases?
Can you tell if there is any crowd-out for the last dollar spent by the government if the government provides the optimal level of the public good in this case?
Demonstrate that these best response functions converge to those in equations (27.20) and (27.21) as g goes to zero.
Can you explain in a bit more detail why the tax in this case is efficient?
as N gets larger, what do y* and y eq converge to for the example in Table 27.2? What does the equilibrium level of public good as a fraction of the optimal level converge to?
Consider the equilibrium public good level as a fraction of the optimal public good level. In our example, what is the lowest this fraction can become, and what is the critical variable?
Why do private contributions to the public good result in the optimal level of the public good when a 50?
Draw the best response functions for the two individuals in a graph similar to Graph 27.3. Carefully label intercepts and slopes.

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