Public Economics by sazizaq


									                                    Public Economics

                                     Edgar O. Olsen
                                Department of Economics
                                 University of Virginia
                                Charlottesville, VA 22901

                                      June 12, 2011

Forthcoming in Gail Hoyt and KimMarie McGoldrick (eds.), The International Handbook on
Teaching and Learning Economics, Edward Elgar Press, expected publication 2011.

                                         Public Economics

                                           Edgar O. Olsen

In almost all countries, governments play a large role in determining who consumes how much

of each good, who does how much of each type of work, when they do them, and hence the

levels of well-being enjoyed by the members of the society. In the United States, governments

achieve these effects through thousands of expenditure programs and regulations and many

taxes. The tax revenue and the expenditure of all levels of government in the US exceed thirty

percent of GDP. Because government action is so important in determining economic outcomes,

a substantial number of economists spend at least a part of their time studying public policies.

        Public economics is the only broad field devoted entirely to public policy. Although

other fields deal with particular public policies that fit naturally within their scope such as

minimum wage laws (labor economics), tariffs (international economics), and anti-trust policy

(industrial organization), they focus primarily on understanding behavior in private markets. The

coverage of public policies in undergraduate public economics courses is much broader. Public

economics courses focus on the justifications for a wide range of government activities and the

effects of major expenditure programs and taxes, with some attention to the behavior of actors in

the political process.

        I have taught the general undergraduate public economics course at the University of

Virginia for more than thirty years. The broad goal of this course is to develop each student’s

ability to think clearly about public policy issues. This involves aligning their views concerning

the desirability of particular government actions with their underlying preferences by helping

them think through what it is that they care about beyond their own consumption of private

goods and providing a more accurate picture of the effects of different government actions.

Although I cover the standard topics in the leading public economics textbooks, my treatment of

these topics deviates from these textbooks in many cases. In some cases, the alternatives involve

more detailed analyses. In others, the deviations are more fundamental. This is most marked in

the treatment of the concern that individuals have for others. In my view, this is the primary

justification for many government programs, and it influences the actual and optimal design of

many others.

       The purpose of this chapter is to share some general thoughts about teaching the broad

undergraduate public economics course that might be helpful to new teachers of this course and

some ideas about dealing with particular topics that might be useful to even experienced

teachers. Like others who teach courses in the United States, my coverage of particular

programs is limited to expenditure programs and taxes in the US. However, the advice in this

chapter is not US centric. My hope is that all readers will find a least few nuggets that are

helpful in their teaching.

General advice

What material should I cover in the course?

Because the field of public economics is so vast, considerable selectivity is necessary in teaching

a one-semester course on this topic. The leading public economics textbooks such as Gruber

(2010) and Rosen and Gayer (2008) provide excellent overviews of the most important

theoretical and empirical research in the field. In the interest of appealing to a broad audience,

their technical level is modest and it might be possible to cover the entire textbook in a semester

at the most selective colleges. However, I doubt that many experienced teachers at any

university attempt to cover this much material. Some teachers will want to cover material at a

higher technical level and assign outside reading, while others will want their students to spend

some time outside of class solving problems rather than reading.

       My approach is to cover a smaller number of topics in greater detail, specifically, the

largest expenditure programs and taxes in the US – the social security retirement program,

Medicare, Medicaid and several other welfare programs, the public school system, and the

federal individual income and social security taxes. These few expenditure programs and taxes

account for most government spending and revenue. Fortunately, dealing with these programs

provides the opportunity to talk about how government programs influence choices between

different produced goods, between all produced goods and leisure, and between present and

future consumption.

       The omissions and inclusions in my list illustrate important general principles for

selection of topics, namely, playing to instructor expertise and student interest. I give more

attention to several welfare programs such as the Earned Income Tax Credit (EITC) than to

national defense on that account. Although public expenditure on these welfare programs is

substantial, it is much smaller than spending on national defense. However, my knowledge of

the welfare programs is so much greater that I can provide deeper insights in this area than in

most others in the small amount of time devoted to them. Even though environmental protection

is not one of the largest areas of government activity as measured by public expenditure, it is

certainly one of the largest in terms of its effect on the allocation of resources. Furthermore,

students are very interested in this topic. Its inclusion in many public economics courses

reflects, in part, the view of many economists that environmental protection should be pursued

primarily through taxation rather than regulation. My coverage is limited to the welfare

economics of negative external effects using pollution as the example. However, time spent

discussing the cost-effectiveness of alternative approaches to environmental protection would be

time well spent.

What readings should I assign?

In courses required for the economics major, there is considerable unanimity concerning what

material should be covered, lectures often follow textbooks closely, and the primary decision is

what textbook to choose. This is far less true for courses in broad fields such as public


       Over time, my course has deviated so much from textbooks that it became increasingly

difficult to justify asking students to buy an expensive textbook. I cover a very small fraction of

their material, and my treatment of many topics deviates significantly. Nevertheless, my advice

to new teachers of public economics is to assign a textbook in their early years. Some of the

country’s leading public economics scholars and most thoughtful teachers such as Gruber (2010)

and Rosen and Gayer (2008) have written textbooks that provide an excellent account of the state

of knowledge of the field. The textbook will be especially valuable to students while new

teachers are determining an approach to the course that suits them. Over time, instructors will

surely want to replace or supplement assigned readings from textbooks with readings from other


       How should a new instructor choose a textbook? Few are likely to find the time to read

several textbooks in their entirety for this purpose. A more realistic approach is to get

recommendations from former teachers and current senior colleagues who have tried several

alternatives and compare chapters on one justification for government action such as external

effects, one area of public expenditure, and one area of taxation in several recommended or

widely used textbooks.

What should I cover in class?

In general, class time should be devoted to aspects of topics covered that are most important and

complicated. For example, I present an indifference-curve analysis that simultaneously

considers multiple features of the individual income tax (the personal exemption, standard and

itemized deductions, and marginal tax rates that rise in steps with taxable income) in order to

show that the current federal income tax is equivalent to a simpler income tax combined with a

rather strange subsidy for the goods involved in itemized deductions. This leads to a piecewise

linear budget constraint in a diagram with two private produced goods on the axes. No

undergraduate textbook contains such a complicated diagram. In general, if a more detailed

analysis is available in print at all, it is embedded in a longer paper written for an audience with a

very substantial background in economics and hence not explained as patiently as is appropriate

for undergraduate students. By presenting more detailed analyses in lectures, instructors can

deepen student understanding of the matters discussed in textbooks. This has the substantial side

benefit of giving students practice in using the tools of intermediate microeconomics.

       What I emphasize in class has been influenced by my perceptions of the importance of

various confused arguments in popular public policy debates. I devote much more time than any

textbook to addressing problematic popular arguments for government action. For example, it is

often argued that we should provide a particular subsidy in kind such as for homeownership or

health insurance because that is the first priority of the recipients. I go to unusual lengths to

explain the defect of this argument. The short version is that an equally costly unrestricted cash

grant would enable the recipient to achieve exactly the same outcome as would result from the

subsidy in kind. If the recipient does not choose this outcome, this must not have been his or her

highest priority. In this case, the recipient prefers the cash grant. Another example is the

argument that we should provide subsidies for investment in small businesses because these

businesses account for the bulk of new employment. Such invalid arguments dominate popular

policy debates and lead to bad public policies.

What is the appropriate technical level?

The appropriate technical level for teaching any course depends on its prerequisites.

Microeconomic principles is the only prerequisite for the general public economics courses at

some schools. At many others, intermediate microeconomics is a prerequisite. At a few

colleges, all students in the course have taken calculus.

       Regardless of the stated prerequisites, students need to have a good understanding of

budget constraints and indifference curve analysis because government programs affect

outcomes by affecting what is possible for individual decision makers, and most programs lead

to non-linear budget frontiers. Indifference curves are also the best tool for analyzing the

magnitudes of gains and losses from government actions. Three lectures on this topic at the

beginning of a public economics course together with the material covered in principles provide

sufficient background.

       Calculus is not important for teaching undergraduate public economics. Diagrams can be

used to provide rigorous theoretical analyses at the level of generality appropriate for an

undergraduate course, and because the budget frontiers that result from government programs are

often piecewise linear, simple calculus cannot be used to analyze the qualitative effects of many

programs. If calculus were not a prerequisite for my course, I could easily replace its rare

appearance in lectures with diagrams, and I would reword numerical problems involving

constrained utility maximization by specifying the equation of the marginal rate of commodity

substitution rather than the utility function.

How should I incorporate empirical research into the course?
Most public economists want to integrate the results of empirical research into their course. It is

important for students to understand that what economists say about public policies is not based

exclusively on theoretical analyses. At best, the standard general assumptions of microeconomic

theory have qualitative implications for the effect of an existing government program or

proposed policy reform. Furthermore, the magnitudes of the effects are important for judging

their desirability.

        A perennial problem in teaching public economics is that few students have the

background in econometrics to read with much comprehension the best empirical research. Only

a few colleges have an introductory econometrics course as a prerequisite for their course. The

traditional solution in public economics textbooks has been to cite the results of empirical studies

with little or no attempt to explain their methods. Therefore, unlike the theoretical analyses, the

students have little basis for assessing the credibility of the results. My solution has been to give

disproportionate attention to the results of random-assignment experiments because it is easy to

explain to students with little or no background in econometrics why the estimates are unbiased

on average. In some cases, I use them to support the implications of theoretical analyses. For

example, the results of the negative income tax (NIT) experiments indicate that this type of

subsidy leads recipients to work less (Robins, 1985). In other cases where the effect is

theoretically ambiguous such as the effect of cashing out the food stamp program on food

consumption, I use it to show the direction as well as the magnitude of the effect (Fraker,

Martini, and Ohls, 1995). 1 In recent years, the leading textbooks have devoted chapters to the

tools of empirical analysis used in public economics and made a greater effort to discuss

methods underlying some of the particular empirical studies mentioned.

Deviations from standard textbook treatment

This section presents alternatives to the standard textbook treatment of several topics that some

readers might find helpful. They include a very general proof of the important result that

recipients prefer lump-sum grants to any subsidy in kind with the same cost to the donor, an

alternative treatment of distributional issues to replace the social welfare approach, a simple

diagrammatic general equilibrium approach to public goods and external effects to replace

marginal social benefit and cost curves, and thoughts about addressing defective popular

arguments for government action, expanding the analyses of government expenditure programs

to include the additional taxes needed to fund them, and the desirability of using indifference

curves to discuss the inefficiencies that result from many government actions.

Recipient prefers a lump-sum grant to any subsidy in kind with same donor cost
Many government actions are intended to help particular subsets of the population. One of the

most important insights of economics for public policy is that a recipient prefers lump-sum grant

to any subsidy in kind with same donor cost. Most intermediate microeconomics textbooks

prove this result for the special case of a per-unit subsidy for a single good. In my experience,

students who have seen this proof do not appreciate the generality of the result. They often

associate the term subsidy-in-kind with this particular type. Therefore, I prove a much more

general result that accounts for all types of subsidies in kind. In courses that have intermediate

microeconomics as a prerequisite, I do it in the first class. In courses with only microeconomic

principles as a prerequisite, I do it directly following the theory of individual choice presented at

the beginning of the course.

        To provide a simplified proof, I assume that the recipient cares about two goods and has

an income that is not subject to choice and that market prices are unaffected by government

action. The latter can be justified by the assumption of completely elastic supply curves. I

further assume that if the government directly provides a good as in the case of public housing,

its cost per unit is the same as the price per unit that private sellers would charge for it. That is,

government is neither more nor less efficient than the private sector in producing the good.

        In Figure 1, DE is the recipient’s budget line in the absence of government action, B is

the recipient’s preferred bundle on this line, and ICC is the person’s income consumption curve

associated with the initial prices. A lump-sum grant or a grant that is equivalent to a lump-sum

grant for this person would induce the person to choose a bundle on the ICC above B. Any

subsidy in kind would induce the person to choose a bundle such as A above DE that is not on

cost of this bundle is ����1 ����1 + ����2 ����2 and the cost to donors is ����1 ����1 + ����2 ����2 − ����. If an equally
ICC. Whether the goods are provided by governments or purchased from private firms, the total
                             ����        ����                                ����        ����

costly lump-sum grant replaced the subsidy in kind, the budget frontier would be the dashed line,

the chosen bundle would be C, and the recipient would be better off as he judged his own well-

being. The bundle A chosen under the subsidy in kind is a possible choice under the equally cash

grant, but the recipient prefers infinitely many other bundles that become possible when the

lump-sum grant replaces the subsidy in kind.

                                               Insert Figure 1 here

        To broaden the horizons of the students concerning the wide variety of subsidies in kind

and make this highly abstract proof concrete, I mention several alternative subsidies in kind that

person a particular quantity of one good (in this case ����1 ) that can be neither supplemented nor
would induce the recipient to choose bundle A. For example, the government might offer the

government might offer this person a grant in the amount ����1 ����1 + ����2 ����2 − ���� on the condition
sold for less than its market value. Public housing is a subsidy of this type. Alternatively, the
                                                               ����        ����

that the recipient consumes at least ����1 units of the first good. HUD operated a housing voucher

could only be used to buy the first good for a charge of ���� − ����2 ����2 . This is a simplified
program of this sort. Another example is a program that offered to sell the person a voucher that

description of the original food stamp program. Finally, I would draw the tangent line to the

indifference curve at A to show how a per-unit subsidy for consumption of the first good

combined with either a lump-sum grant or tax would induce the recipient to choose this bundle.

        To explain the defects of several arguments for the superiority of lump-sum grants,

instructors might also prove the theorem for the special case of a per-unit subsidy for one good.

One erroneous argument is that recipients prefer lump-sum grants because they offer additional

bundles. In fact, replacing a per-unit subsidy for a particular good with an equally costly lump-

sum grant both adds and subtracts bundles from the budget space. The proof shows that many of

the bundles added by the replacement are better than the best bundle available under the per-unit

subsidy. Another erroneous argument is that the subsidy in kind offers fewer choices.

Examination of the budget lines with the per-unit subsidy for one good and the lump-sum grant

makes clear that this is not the case for all subsidies in kind.

Treatment of distributional issues

The standard model that economists use to study behavior in markets assumes that actors care

only about their own consumption of private goods. This model has performed very well in

explaining most market behavior. Understanding behavior in the political sphere and the

justifications for government actions, however, requires a broader view of what individuals care

about. Economists are very clear about this matter as it pertains to public goods such as national

defense and tangible external effects such as pollution. Clarity about the implications for public

policy of a concern for others is lacking in most economic analyses.

       The standard textbook treatment of distributional issues involves the concept of a social

welfare function. In my view, this approach is so flawed that I avoid parts of textbooks that

mention it. It incorrectly imagines that we can determine which allocations are feasible and

which feasible allocations are efficient by reference to individual preferences defined over each

individual’s own consumption of goods and then we can somehow determine which efficient

allocation is best by reference to the weight that society places on the well-being of its different

members. If individuals care about each other, these preferences affect which allocations are

feasible and which feasible allocations are efficient. Furthermore, society does not have views

about which feasible allocation is best. Different members have different views.

       My dissatisfaction with the standard treatment led me to develop an alternative

diagrammatic analysis dealing with tangible external effects and altruism (Olsen, 1979; Olsen,

1981). These analyses build on Samuelson’s (1955) classic article and Dolbear’s (1967)

extension, but they avoid social welfare functions and go far beyond these papers in deriving

important results. The diagrams are similar to Edgeworth box diagrams, but they allow for all

feasible combinations of total amounts of goods. In dealing with altruism, I integrate the

concern of each member of a society for other members into that person’s utility function. With

this formulation, the set of efficient allocations incorporates such feelings.

       With or without tangible external effects and with and without altruism, there are

infinitely many efficient allocations. Each member of society will have some most preferred

feasible allocation, and this allocation is efficient. The latter result follows directly from the

fundamental definition of an efficient allocation. An allocation is efficient if and only if every

feasible change from it hurts someone. Obviously every feasible change from the most preferred

feasible allocation of a member of society hurts that person. Different people will have different

most preferred efficient allocations, and most efficient allocations will not be the preferred

feasible allocation of any member of society.

       In discussing distributional issues, economists have particular difficulty accepting

paternalistic altruism as a justification for government action. Because paternalistic altruism is a

widespread and important phenomenon, this severely handicaps their ability to contribute to the

development of public policies. Since standard welfare economics is based on the acceptance of

individual preferences, it requires respecting the preferences of paternalistic altruists who care

about others but believe that at least some of the people that they care about undervalue some

goods and overvalue others. Acceptance of paternalistic preferences does not imply support for

government policies that force people to change their consumption patterns within their current

resources. While it may be possible to achieve an efficient allocation by this means, this

efficient allocation will not be preferred by all members of society to the allocation in the

absence of government action. Achieving an efficient allocation that makes everyone better off

requires imposing taxes on paternalistic altruists to provide subsidies in kind to the objects of

their concern. This makes recipients better off as they judge their own well-being. Participation

in the subsidies in kind that dominate the welfare system is voluntary, and hence they do not

make recipients worse off as they judge their own well-being. In-kind subsidies are not limited

to governments. Private charities usually provide them based on the views of donors who

believe that recipients undervalue certain goods.

       It is true that the non-paternalistic altruists in the society who care about the same people

prefer to give them lump-sum grants or grants as close as feasible to lump-sum. Their most

preferred feasible allocations differ in this respect from the most preferred feasible allocations of

paternalistic altruists. Efficient allocations that give some weight to views of both types of

altruists involve less ‘distortions’ in recipient consumption patterns than favored by paternalistic

altruists. This is not fundamentally different from the situation with public goods such as

national defense. Some member of society has a most preferred feasible allocation that involves

the largest amount of national defense and another has a most preferred feasible allocation that

involves the smallest amount. Almost all other efficient allocations involve amounts between the

two extremes.

       It is impossible to argue against anyone else’s most preferred feasible allocation on

efficiency grounds. This does not mean that it is impossible to argue against a person’s views on

what government policies should be pursued. Views on that matter depend on the person’s

perceptions of the effects of these policies and all other policies that could be pursued,

perceptions which may be wildly inaccurate. Reducing these misperceptions is arguably the

most important role of economics in public policy. A person’s views on what government

policies should be pursued also depends on the strength of the person’s feelings for a potentially

enormous number of people that the person is willing to help and how, if at all, this person thinks

that the decisions of others deviate from what is in their best interest.

Simple general equilibrium analysis of public goods and external effects

The standard textbook analysis of public goods and external effects involves marginal social

benefit and cost curves. This analysis gives the misleading impression that only one quantity of

the public good or one level of the external effect is consistent with efficient resource allocation.

It is also severely limited in its ability to deal with distributional issues. I use the diagrams

developed in Samuelson (1955) and Olsen (1979) to show that there are normally infinitely many

quantities of the public good or levels of the external effect consistent with efficient resource

allocation and prove a wide range of other important results. For example, reducing pollution is

not necessary to achieve an efficient allocation of resources, but it is necessary to achieve an

efficient allocation that everyone prefers to the allocation in the absence of government action.

Dealing with popular arguments for government action

Textbook treatments of the rationales for government actions other than lump-sum transfers

focus on valid arguments, that is, arguments that imply that there exists a government policy that

would make everyone better off. If no such policy exists, the allocation of resources in the

absence of government action is efficient, and transfers as close as feasible to lump-sum will

dominate any other type of government action. Most arguments for government action in

popular debates over public policy are not of this type, but popular arguments have had

substantial influence on the types of government programs adopted.

        Before the discussion of each major area of government activity, I ask the students to

think about whether they favor government activity of the general type that we will consider, and

if so, to come to class prepared to explain why. I begin the first class meeting on the topic

describing the general nature of the programs under consideration. For example, the general

nature of cash assistance programs such as SSI and the EITC is that they provide subsidies to

families with incomes below a certain level and the magnitude of the subsidy to a family does

not depend on how it allocates its expenditures between produced goods. I then ask the students

who favor programs of this general type to raise their hands, making clear that they are free to

change their opinions in light of our discussion and analysis of the actual effects of programs.

This encourages them to reveal their initial views. If no one raises his or her hand, I offer a

widely-used problematic argument, ask them to react to it, and raise questions that reveal its

defects. I want to disabuse students of notions such as the government should subsidize

homeownership because this allows recipients to pursue the American Dream. In my

experience, most popular arguments for particular government actions cannot withstand critical


Using indifference curves to talk about gains and losses

All gains and losses from government action ultimately accrue to individuals in their roles as

buyers of goods and suppliers of inputs. Most textbooks use areas around market demand and

supply curves to measure these gains and losses. The usual approach assumes that all buyers of a

good pay the same price and can buy as much as they want at that price and similarly for all

sellers. Most government programs lead to nonlinear budget frontiers for individuals, and thus

market demand and supply curves are poorly suited for measuring gains and losses to

individuals. Even in a world with linear budget constraints, the usual approach to dealing with

the gains and losses due to changes in the prices of inputs facing individual providers is

problematic. The standard measure of the increase in producer surplus is often interpreted as the

increase in the profits of firms that presumably accrue to their residual income recipients.

However, this is not generally true. In the simplest general equilibrium model where all firms in

an industry are identical, an upward sloping long-run supply curve results from the increase in

the prices of inputs used most heavily by this industry when its output increases and the decrease

in the prices of the inputs used least heavily. At the higher and the lower output price, all firms

earn zero economic profit. So the usual producer surplus measure does not measure the increase

in profits. For these reasons, I use indifference curves to analyze the gains and losses from

government action.

Analyzing the combined effect of expenditure programs and taxes needed to fund them

Because one of the most pernicious aspects of popular discussions of proposed expenditure

programs is the failure to consider consequences of the method used to raise money to pay for

them, thereby giving citizens the idea that they can get something for nothing, I devote more

time in class to such analyses than textbooks. For example, when I analyze the work

disincentive effects of an NIT, I assume that it is funded by a positive income tax on earnings in

excess of the NIT’s breakeven income. Similarly, my analysis of the effect of the public school

system on consumption of education services and other goods assumes that the public school

system is funded by lump-sum taxes.

Analyzing the effect of government programs on equilibrium prices

Because government programs usually create budget frontiers for individuals that are not linear,

it is not easy to analyze their effects on market prices using only demand and supply curves. My

standard procedure for analyzing the effect of such a program is to first analyze their effect on

desired consumption of various goods in an indifference curve diagram assuming no effect on

market prices and then use the results to show how the relevant demand or supply curve shifts in

response to this change in desired consumption at the initial market prices. For example, a

negative income tax would induce all recipients to work less at the initial wage rate and market

prices of produced goods. In a demand and supply curve diagram for a type of labor service

provided entirely by NIT recipients, this leads to a leftward shift in the labor supply curve as a

function of the market wage rate and hence an increase in the market wage rate.

Closing Thoughts

I close with two suggestions for future empirical research in public economics that will increase

the significance of material that we can bring to the attention of our students, namely, more

emphasis on important effects of public policies as opposed to effects that can be estimated with

the greatest precision and more attention to the rationales for government policies in deciding

what effects to study. I appreciate the professional norms that place high value on precision, but

I am embarrassed to be unable to provide students with estimates of the effects of such large

government activities as the public school system and Medicaid. The failure to think carefully

about rationales for government programs has had a significant effect on the relevance of

empirical research on effects of government programs. Almost all empirical studies of these

effects attempt to estimate the difference between outcomes with the program and in its absence.

This provides a poor basis for judging the success of a program. Almost all programs are

intended to produce outcomes that differ from the outcomes of grants as close as feasible to

lump-sum. These programs are not successful unless they change consumption patterns in

particular directions compared with equally costly cash grants. Few studies make this



Dolbear, F. T. (1967), ‘On the theory of optimum externality’, American Economic Review, 57
(1), 90-103.

Fraker, T. M., A. P. Martini and J. C. Ohls (1995), ‘The effect of food stamp cashout on food
expenditures: An assessment of the findings from four demonstrations’, Journal of Human
Resources, 30 (4), 633-649.

Gruber, J. (2010), Public Finance and Public Policy. (Third Edition) New York: Worth

Olsen, E. O. (1981), ‘The simple analytics of the externality argument for redistribution’, in M.
B. Ballabon (ed.) Economic Perspectives: An Annual Survey of Economics, Vol. 2, New York:
Harwood Academic Publishers, pp. 155-173.

Olsen, E. O. (1979), ‘The simple analytics of external effects’, Southern Economic Journal, 45
(3), 847-854.

Robins, P. K. (1985), ‘A comparison of the labor supply findings from the four negative income
tax experiments’, Journal of Human Resources, 20 (4), 567-582.

Rosen, H. S. and T. Gayer, (2008), Public Finance, (Eighth Edition) New York: McGraw-Hill.

Samuelson, P. A. (1955), ‘Diagrammatic exposition of a theory of public expenditure’, Review of
Economics and Statistics, 37 (4), 350-356.


  The theoretical ambiguity stems from the program’s housing deduction in determining adjusted income. Over a
certain range of housing expenditure, the food stamp subsidy increases with increases in housing expenditure. The
food stamp subsidy is a housing subsidy over that range, and many food stamp recipients are in that range.


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