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Urban Political Economics

Urban Political Economics
Urban Political Economics

Urban Political Economics*

Robert W. Helsley

University of British Columbia, Vancouver

August 2003

Contents

1.Introduction

2.Objectives and local policy formation

2.1.Politics

2.2.Property values

2.3.Profits

https://www.doczj.com/doc/421962961.html,plex politics

3.Local political institutions

3.1.The institutions and their consequences

3.2.The common pool problem in city councils

3.3.Equilibrium models of distributive politics

4.Private government

4.1.Supplementary provision and the strategic response

4.2.Supplementary regulation

4.3.Potential competition

4.4.Gated communities

5.Conclusion

References

*I thank Richard Arnott, Keith Head, Vernon Henderson, Will Strange, Ralph Winter, and especially Jacques Thisse for helpful comments. Ron Cheung provided outstanding research assistance. The financial support of the UBC Center for Urban Economics and Real Estate is gratefully acknowledged.

Abstract

This chapter considers the role of economic and political institutions in the formation of local public policies. The chapter has three objectives. First, to synthesize the dominant models of local policy formation with mobile households, with particular emphasis on the objectives that are attributed to the institutions that provide collective goods. Second, to describe and model local political institutions, and consider their implications for taxes, expenditures and voting behavior. Third, to examine how institutional change, specifically the entry of new institutions in the form of private government, influences policy outcomes and the welfare of residents.

Keywords: multi-community democracy, stratification, property value maximization, developers, local political institutions, legislative decision making, the common pool problem, citizen candidates, private government, supplementary provision, supplementary regulation, potential competition, gated communities.

1.Introduction

The "new" political economics uses the tools of modern economic analysis and game theory to study how economics and politics interact to determine public policies.

In contrast to public economics, with its emphasis on the positive and normative effects of tax and spending policies, and public choice, with its emphasis on collective choice rules, political economy emphasizes the process of policy formation. Political economics is fundamentally concerned with how optimal policies are modified by political and institutional constraints. Much of modern political economics has been developed in macroeconomics, where, for example, questions about differences in public sector performance across countries are a natural concern. In this context, the political economics approach is to ask whether there are institutional differences between governments that lead to systematic variations in spending, or whether there are systematic failures in legislative decision making processes that lead to excessive levels of spending or public debt. In political economics, the emphasis is on how government policies are determined.

For better or worse, urban political economics does not exist as a well defined field of study. This is not to say that economics and politics do not combine to determine local public policies. Surely they do. However, political economics is a very new field, and the perspectives and models of political economics have not been widely applied to urban policy issues. What follows is a selective review of a particular set of topics where local politics and urban economics intersect. Specifically, this chapter considers the role of economic and political institutions in the formation of local public policies. The

chapter has three objectives. First, to synthesize the dominant models of local policy formation with mobile households, with particular emphasis on the objectives that are attributed to the institutions that provide collective goods. Second, to describe and model local political institutions, and consider their implications for taxes, expenditures and voting behavior. Third, to examine how institutional change, specifically the entry of new institutions in the form of private government, influences policy outcomes and the welfare of residents. If this chapter has a unifying theme, it is that local economic and political institutions are interesting and important.

Caplin and Nalebuff (1997) argue that institutions should be integrated more fully into economic theory. They classify economic models of institutions into three groups: (1) models that focus on how the economic environment influences institutions, (2) models that focus on the implications of a given institutional structure for economic outcomes, and (3) integrated models that allow for "the influence of institutions on economic outcomes and for the influence of the environment of the institutions." (p. 307) The models that are considered in this review fit this classification quite naturally. The models of local policy formation reviewed in Section 2 focus on how the economic environment influences the formation of communities. The models of local political institutions in Section 3 take membership as fixed, and examine the consequences of different institutions for outcomes. The models of private government in Section 4 are integrative. They consider how the institutional environment influences policy outcomes, and how the economic environment influences the formation or entry of new institutions.

2.Objectives and local policy formation

There are three basic approaches to modeling the formation of public policy at the local level. Each approach considers a system of local governments providing collective goods to mobile residents who choose between jurisdictions to maximize utility. The approaches differ fundamentally in their treatment of the problem of collective choice and in the objectives that are attributed to the institutions that provide collective goods. The first approach, pioneered by Westhoff (1977,1979) and Rose-Ackerman (1979), assumes that community tax and spending policies are made through open agenda majority voting. The second approach, initiated by Wildasin (1979) and Brueckner (1979), supposes that local policies are chosen to maximize aggregate property values in a community. The third approach, initiated by Henderson (1974) and Stiglitz (1977), assumes that local policy is formed by profit maximizing entrepreneurial governments or developers.

2.1.Politics

One of the interesting consequences of the dominance of the Tiebout (1956) tradition in local public finance is that models of local government have historically paid little attention to politics or political institutions. As noted by Rose-Ackerman (1983ab) and others, Tiebout’s original model can be seen as an explicit attempt to eliminate the need for politics at the local level. A metropolitan area in Tiebout's world is composed of an arbitrarily large number of competitive local governments, each offering a different

bundle of taxes and public expenditures. Since each voter’s ideal policy is offered by one of these local governments, an individual can always secure her most preferred policy outcome by moving. Mobility is thus a substitute for politics in the informal Tiebout tradition.

However, attempts to formalize Tiebout's insights inevitably forced authors to confront the collective choice problem, and led to the development of equilibrium models of local government in which politics play an important role. Here we briefly review the key elements of such a model, focusing on the characteristics of the political equilibrium within a community. 1

Following Epple, Filimon and Romer (1984), consider a metropolitan area composed of a fixed number of communities with fixed geographic boundaries. Each community provides a congestible local public good to its residents. There are no spillovers between communities. Public good provision in each community is financed by a local tax on housing services that balances the community government's budget. The public good and tax package, or policy vector, in each community is chosen by majority rule.

Preferences are represented by the increasing and strictly quasi-concave utility function U(g,h,x), where g is the level of the local public good in the consumer's community, h is housing services, and x is a composite numeraire commodity. Residents

1 See Ross and Yinger (1999) for an extensive review of the literature on models of "sorting and voting," with particular emphasis on the determinants and consequences of the capitalization of fiscal variables into housing prices.

differ in income y, which is continuously distributed on a closed support.2 Letting p h represent the before-tax price of housing and t represent the local property tax rate, the budget constraint of a resident with income y is x + ph £ y, where p = (1 + t)p h is the after-tax price. Residents are perfectly mobile, and move between communities in response to perceived differences in utility levels, which in turn reflect differences public goods, taxes, and housing prices.

The indirect utility function of a consumer with income y is

V(p,y,g) ≡ Max

U(g,h,y - ph) = U(g,h(p,y,g),y – ph(p,y,g)), (2.1)

h

where h(p,y,g) is the Marshallian demand function for housing. The assumptions made about the form of the direct utility function imply that the level sets of V(p,y,g) in (g,p) space slope upward and are strictly concave. Further, the slope of such an indifference curve, dp/dg = -(?V/?g)/(?V/?p), is assumed to be strictly increasing in income. This is an instance of the Spence-Mirrlees "single-crossing property" (Gans and Smart (1996), Edlin and Shannon (1998)). The single-crossing property serves two important functions in this setting. First, it ensures that consumers are sorted by income in equilibrium. In particular, it ensures that each community is occupied by consumers with incomes in a connected interval, and that higher income consumers reside in communities that provide higher levels of the public good. Second, as discussed below, it ensures that there is a policy vector for each community that a majority of community residents prefers to any other.

2 More recent work in this literature assumes that individuals are differentiated by income and a taste parameter. See, for example, Epple and Platt (1998), Epple and Romano (1998) and Epple, Romer and Sieg (2001).

The budget constraint of a community government is tp h H - c(g,N) = 0, where H is aggregate housing consumption in the community, N is community population, and c(g,N) is the increasing and convex cost of public good provision.3 Solving the

government budget for p = p h + c(g,N)/H (thus eliminating the tax rate), and substituting this into the indirect utility function yields a consumer's "policy preference" function W(g,y) ≡ V(p h + c(g,N)/H,y,g). As noted by Persson and Tabellini (2000, p. 20), the salient assumption about individual behavior in political economics is that the consumer,as a political agent, engages in "voting, lobbying or some other form of political activity"to maximize her policy preferences. The most preferred policy or "bliss point" of a resident with income y is

g(y) = Argmax g W(g,y) = Argmax g V(p h + c(g,N)/H,y,g),(2.2)where g ¢(y) > 0 by the single-crossing condition.

The characteristics of a consumer's most preferred policy, and the political actions that follow from the pursuit of that outcome, depend in part on how the consumer expects the endogenous variables N, H and p h to respond to changes in the community's tax and expenditure policy. Two different assumptions about voter expectations have been made in this literature. Prior to Epple and Romer (1991), most authors assumed voter myopia.Myopic voters treat N, H and p h as fixed. In this case, the locus that describes the set of feasible (g,p) pairs from the voter's perspective (the "government services frontier," p =p h + c(g,N)/H) is increasing and convex, and the consumer's most preferred policy lies at the tangency of this locus and the highest indifference curve that the voter can reach, as 3 If the distribution of income is F(y), and this community contains all consumers with incomes in the interval [y -,y +], then N = F(y +) – F(y -), and, in equilibrium, housing consumption is

H =h(p,y,g)dF(y)y -y +

ú.

shown in Figure 2.1. Further, the policy preferences of each consumer are "single-peaked" (Black (1948)) under these conditions: a consumer's ordering of policy alternatives is determined by their relative distances from her bliss point g(y). More formally, if policy preferences are single-peaked, then for any alternative policies g'' and g', g'' ≥ g' ≥ g(y) or g'' £ g' £ g(y) implies W(g'',y) £ W(g',y).

In subsequent work, some authors have endowed voters with a limited amount of foresight regarding the impacts of policy choices on community populations and housing market outcomes. More specifically, Epple and Romer (1991) and Epple and Platt (1998) assume that voters take only the policy vectors of other communities as fixed when making political choices. This implies that each voter takes the level of utility available in other communities as fixed, but is cognizant of how policy changes in their home community will influence population and housing market outcomes through intra-metropolitan migration. Epple, Romer and Sieg (2001) find that local policy choices in a sample of Boston communities are more consistent with this utility taking assumption than the with simpler assumption of voter myopia.

An equilibrium in this model requires that every consumer maximize utility, over goods and communities, that community budgets balance, and that community housing markets clear.45 In addition, and most important for our purposes, the policy vector in each community must be a political equilibrium. In this literature, the political process is

4 The tradition is to close the model by assuming an exogenous housing supply function for each community. See Epple, Filimon and Romer (1984) for this convention, and Henderson (1985) for an alternative.

5 The existence of an equilibrium in the model outlined in this section has been demonstrated by Epple, Filimon and Romer (1993). However, the existence of equilibria in models of multicommunity democracy is, in general, problematic. See Caplin and Nalebuff (1997) for a general discussion. Hansen and Kessler (2001) present conditions under which an equilibrium fails to exist the original Westhoff (1977, 1979) model. The Westhoff model differs from the model described above in two ways: housing is not considered, and local public goods are financed through a proportional income tax. Nechyba (1997) provides an existence proof for a related model in which housing consumption is exogenous.

an idealized form of majority voting, sometimes called open agenda or institutionless majority rule, in which each element of the government services frontier is put against every other element in a sequence of pairwise elections until a Condorcet winner emerges. The essence of the celebrated median voter theorem (Black (1948)) is that with single-peaked policy preferences, such an equilibrium policy exists and corresponds to the median of the most preferred policies of the voters in a community. 6 Since the most preferred policy function g(y) is monotonic, the median of the most preferred policies in turn corresponds to the most preferred policy of the consumer with the median income, that is, to the bliss point of the median voter.7

The resulting equilibrium has three properties. The first is "stratification": each community is composed of individuals with incomes in a single, connected interval.8 The second property is "boundary indifference": the border consumer between two adjacent communities must be indifferent between them. The final property is "ascending bundles": public good levels (and housing prices) increase with the highest income in a community.

Stratification, or the sorting of consumers into imperfectly homogeneous communities, plays a role in many important policy issues. Epple and Romer (1991) show, in contrast to the traditional view, that local redistribution may occur in equilibrium in a system of stratified communities.9 In the case of education, stratification

6 See Gans and Smart (1996) for a general examination of the implications of single-crossing conditions for the existence and stability of majority voting equilibria.

7 If the distribution of income is F(y), and this particular community contains all consumers with incomes in the interval [y-,y+], then the equilibrium policy of the community is g(y M), where the median income y M satisfies F(y+) – F(y M) = N/2. Median voter models of local politics have a very long history. See, for example, Bowen (1943) and Bergstrom and Goodman (1973).

8 In models with two-dimensional heterogeneity (e.g., Epple and Platt (1998)), stratification is imperfect in the sense that two residents with identical incomes (but different taste parameters) may reside in different communities in equilibrium.

9 The traditional view is that local redistribution with mobile households is infeasible since generous redistributive policies will repel high-income households, and thus

and local property tax finance lead to differences in educational spending and presumably outcomes across communities. Fernandez and Rogerson (1996,1997,1998,1999) examine the implications of stratification for local spending on education and education finance reform, while de Bartolome (1990) considers the implications of stratification for the production of educational peer group effects. Epple and Romano (1998) use a multicommunity model to study the implications of stratification for competition between public and private schools. The broader implications of stratification for knowledge spillovers, economic growth and the distribution of income are considered by Benabou (1993, 1996), Durlauf (1994,1996ab) and Fernandez and Rogerson (2001).

There are at least three potential sources of inefficiency in this context. First, there is in general no reason to expect the preferred policy of the median voter to coincide with the policy that maximizes welfare in the community. For example, if we take utilitarianism as our normative benchmark, the optimal policy will maximize the policy preferences of the resident with the mean rather than the median income (see, for example, Persson and Tabellini (2000), Section 3.1). Second, the method of finance may distort consumption and production decisions. This is certainly the case with property tax finance and housing, as discussed in this context by Yinger (1982) and others. Finally, the location choices of consumers may be inefficient due to externalities associated with migration, as in de Bartolome (1990). This issue arises, in general, whenever consumers choose between a finite number of jurisdictions, and changes in the population of one community cause changes in the utility levels in others (Scotchmer (1986)).

2.2.Property values

undermine the tax base. See Wildasin (1991) for a review of the literature on local redistribution, and an analysis of equilibrium and optimum redistribution policies in a federal system.

Models of multicommunity democracy assume that collective choices are made through direct majority voting. Of course, there are many other political institutions that might aggregate the policy preferences of individuals in a city, including a representative institution like a city council. We will consider the role of representative local political institutions in the next section. This subsection considers another popular, if somewhat ad hoc, rule for aggregating preferences. This is the assumption that policies are chosen to maximize property values in a community.

Following Edelson (1976), Wildasin (1979), and especially Brueckner (1979,

1982, 1983), consider a large system of small communities in which each community has an exogenous stock of houses.10 Index the houses in a particular community by i =1,2,…,N. Residents derive utility from a public good g, housing h i and a composite numeraire commodity x according to the utility function U(g,h i ,x). Public good provision is financed by a uniform tax on house value that balances the community's budget.Although residents have identical preferences, they may differ in income y. Each

community is "open" in the sense that the utility level that it must offer an individual with a particular income is exogenously determined. Heuristically, this can be justified by assuming that the number of communities is arbitrarily large, and that moving between communities is costless. Denote the equilibrium utility level that a community must offer a resident with income y by U*(y).

The maximum amount that a resident with income y is willing to pay for the

services offered by house i, the bid rent for house i, denoted R i (g,h i ,y), is implicitly defined by

U(g,h i ,y – R i ) = U*(y).(2.3) 10 Brueckner (1983) introduces housing production into the framework outlined here and shows that the welfare implications of property value maximization then depend on the method of finance. In particular, a head tax per house is required in order for property value maximization to lead to a first-best allocation.

Then the implicit function theorem implies

?R i /?g = (?U i /?g)/(?U i /?x).(2.4)In this open community model, the slope of the bid rent function with respect to the level of the public good is equal to the consumer's marginal rate of substitution between the public good and the numeraire. This means that the benefits of public spending are

perfectly capitalized into house rents. This result plays an important role in the analysis.

The value of house i is defined as the present value of the stream of net rents that the house provides. Assuming that the house earns rent R i in perpetuity, house value V i is given by the asset equilibrium condition

V i = (R i (g,h i ,y) - t V i )/q ,(2.5)where t is the property tax rate, t V i is the property tax liability per period, and q is the constant discount rate. Community budget balance requires tS i V i = C(g,N), where

C(g,N) is the provision cost function. Then (2.5) implies that aggregate property value in the community is

S i V i = (S i R i (g,h i ,y) – C(g,N))/q .(2.6)

The critical assumption in this branch of the literature is that the community

chooses the level of the public good to maximize (2.6). Of course, since resident utilities are fixed by assumption, there is nothing else to maximize in this setting. Interestingly,since all houses are owned by absentee landlords, at least in this basic version of the model, this objective implies that local policies are chosen to maximize the wealth of a

group of non-residents. Using (2.4), the first-order condition for a maximum of S i V i with respect to g implies

S i (?U i /?g)/(?U i /?x) - ?C/?g = 0. (2.7)Thus, the level of the public good that maximizes aggregate property value satisfies the Samuelson condition for efficient provision. In this system of open communities,aggregate property value maximization and welfare maximization are synonymous.11This result has been the basis of a number of tests for allocative efficiency in the local public sector.12

Several authors have argued that property value maximization may be the reduced form outcome of some unspecified political process. Wildasin and Wilson (1996) note that

"in communities where significant numbers of households are owners of their own property, voting behavior may be motivated by land-value maximization considerations; to the extent that this is so, there is no real difference between a voting model and a model based on land value maximization. Even if voters are not landowners, it is not implausible to assume that the interest of landowners is reflected in the local political process, if that process can respond to pressures brought to bear by mechanisms other than voting." (p. 179)

11 Welfare maximization can serve as an institutional objective in its own right. For example, it is reasonable to suppose that exclusive institutions like private governments (Helsley and Strange (1998)) or political parties (Caplin and Nalebuff (1997)) choose policies to maximize the welfare of their members.12 See Brueckner (1979, 1982) and, more recently, Deller (1990), Taylor (1995), and Hughes and Edwards (2000).

Many local policies seem at least consistent with the objective of property value maximization. For example, local growth controls seem to be popular with voters in part because they increase the property values of current residents.13

Others have tried to articulate the individual incentives and political institutions that might support property value maximization as political equilibrium, or to provide what Persson, Roland and Tabellini (1998) call "micro-political" foundations for this objective. Sonstelie and Portney (1980) argue that with perfect mobility and no limit on the number of communities, it is optimal for a resident property owner to separate consumption and investment decisions by voting for the policy vector that maximizes property value and then moving (if necessary) to the community that offers the highest level of utility.

Brueckner and Joo (1991) develop a dynamic model with imperfect mobility that examines how capitalization influences the policy preferences of current residents in a community. In particular, they show that expectations about future housing prices cause voters to consider the preferences of future residents when choosing the level of a durable public good. The key result is that the level of public spending that maximizes the utility of a current resident is determined by a weighted average of the net marginal benefit to the resident and the net marginal benefit to a prospective buyer of the resident’s house. This implies that "the preferences of an individual who does not yet reside in the community are reflected in the voter's ideal g and thus in the choice he makes in the voting booth." (p. 457) This also implies that property value maximization only leads to the first-best outcome if the marginal valuation of the owner and the prospective buyer are equal. If current owners and future owners have difference preferences, then utility maximization and property value maximization are not equivalent. In related work,

13 See Brueckner (1995) and Helsley and Strange (1995) for complementary models of the impacts of growth controls on housing prices, and Katz and Rosen (1987) for evidence.

Wildasin and Wilson (1996) show that imperfect mobility can severe the tie between property value maximization and welfare maximization by giving communities an incentive to overtax less mobile workers. Sprunger and Wilson (1998) present a model with resident property owners in which imperfect mobility and uncertainty about the productivity and objectives of local governments cause the benefits of durable local public goods to be imperfectly capitalized into property values. They show that this can lead to either over- or under-provision.14

2.3.Profits

Entrepreneurial incentives play several interesting roles in the process of local policy formation. First, at a normative level, Stiglitz (1977) and Bewley (1981) argue that efficiency in a system of local governments may require the active participation of "entrepreneurial" governments or land developers. Bewley (1981) shows, through a series of examples, that mobile but myopic voters, who by assumption do not consider how their migration choices impact economic conditions elsewhere in the economy, may have no incentive to leave inefficient communities. Under these conditions, efficiency may require that governments take actions to attract or repel residents. Bewley considers several objectives that such entrepreneurial governments might pursue, including maximizing population, maximizing land values, and maximizing the government budget surplus. Following Henderson (1974), Stiglitz (1977, p. 295) notes that land developers

14 Epple and Romer (1991) also consider the implications of capitalization for voting behavior in their model of multicommunity democracy and redistribution. In particular, they show that if non-myopic voters are homeowners rather than renters, then housing demand will depend on the possibility of capital gains associated with changes in local policy. This will change the slope of a voter's indifference curves in (g,p) space (generally causing them to become flatter), which implies that "an owner with a given endowed income will prefer a lower level of redistributive taxation than a renter with the same income." (p. 844)

are natural candidates to perform this active role: "The 'developer' plays a central role in this formulation [achieving efficient equilibria]. Essentially, the private developer can do anything that a centralized government can do, and, hence, if there are 'inefficiencies' he can eliminate them."

Second, at a positive level, the provision of infrastructure, public services and amenities by land or housing developers is an important part of the process of community formation. This is especially true in the case of so-called "private governments," as discussed in Section 4. Consequently, and following Henderson (1980), many models of community formation are based on the private provision and finance of a public good by a profit maximizing developer.15 In these models, the policy preferences of residents are expressed through the land market, and the developer translates these expressions into a collective choice via profit maximization. As discussed below, the analysis tends to focus on how competition between developers, or more generally market structure, impacts the efficiency of the resulting equilibrium.16 Third, and closely related, models of "profit maximizing government" (Sonstelie and Portney (1978), Epple and Zelenitz (1981)) assume that local policies are chosen by a city manager or bureaucrat to maximize the excess of tax revenue over the costs of public good provision.

To develop the basic ideas, following Helsley and Strange (1994), consider a system of monocentric community sites, where each site is owned by separate developer.

15 There are a number of formal similarities between models of local policy formation based on profit maximization and models based on property value maximization. For example, if one interprets the absentee landowners in the basic Brueckner (1979) model of property value maximization as a single land developer, then the developer's profit is proportional to aggregate land value in (2.6).

16 Many of the results in this literature originated in the literature on profit maximizing clubs (Scotchmer (1985ab)). Club models typically admit more general pricing policies. For example, a club might charge both a membership fee and a per use price for the

club's common facilities. Henderson and Thisse (1999, 2001), in a series of papers on the nature of small numbers competition in multi-community models, bridge the gap between developer and club models by considering optimal non-linear pricing strategies for a land developer.

The number of active developers, or the number of occupied sites, is denoted by M. For simplicity, suppose that each site is a long, narrow strip of land of width j, and that land in each community is differentiated only by its distance from employment, concentrated at the eastern edge of the strip. 17 Assume that the opportunity cost of urban land is zero.

There are N residents in the region, and the population of a community is denoted by N. Residents are identical and perfectly mobile, and move between communities to maximize utility. There are three goods in the model: a local public good g, land consumption l, and a numeraire x. Assuming that land consumption is exogenously fixed at one unit, and that the utility function is quasi-linear, the utility of a resident may be written as U(g) + x, where U(?) is increasing and strictly concave, and land consumption has been suppressed. The budget constraint of a resident living at distance z from the employment center is x + r(z) + tz £ y, where r(z) is land rent, t is commuting cost, and y is income, which consists of exogenous labor income w and an equal share of the profits of all developers.

If U* is the equilibrium utility level in the system, then the bid rent function for land in the community is r(z) = y + U(g) – tz – U*. The market clearing condition for land implies that the boundary of a community z* satisfies z* = N/j. Then the boundary rent condition r(z*) = 0 implies r(z) = t(z* - z) = t((N/j) – z). Using the budget to substitute for x in the utility function and in turn substituting for r(z) implies that the utility of a resident can be written as

V(g,N) = y + U(g) – tN/j.(2.8)

The profit of a developer equals aggregate differential land rent less the costs of 17 This specification of the geography is not essential, but does simplify the strategic interactions in the model. Somewhat surprisingly, the "shape" of a community matters in this context because it influences the curvature of a developer's best response function. See Helsley and Strange (1994) for details.

public good provision,

p (g,N) = (t/2)(N 2/j ) – C(g),(2.9)where the cost function C(g) is increasing and convex. Incorporating the income from land development into (2.8) yields

V(g,N) = w + U(g) – C(g)/N – (tN)/(2j ),(2.10)where each resident is assumed to receive an equal share of the profits of all developers.

The efficient allocation maximizes (2.10) with respect to g and N. The first-order conditions for this problem imply NU'(g) = C'(g), the Samuelson condition for efficient provision of the public good, and p (g,N) = 0. The latter condition, which implies that aggregate land rent equals the cost of public good provision, is an instance of the Henry George theorem (Stiglitz (1977), Arnott (1979)). Whether such an efficient allocation exists depends in part on whether the aggregate population is an integer multiple of the efficient city size. If it is not, then there is a remainder of consumers who cannot be

accommodated in a community of efficient size, and a first-best allocation does not exist.

The equilibrium is a Nash equilibrium in public good levels, where each

developer chooses g to maximize his profit, subject to the equilibrium location decisions of residents, and taking the choices of other developers as fixed. In what follows, we focus on the symmetric equilibrium. Letting g i represent the public good level chosen by developer i, and g 0 represent the conjectured public good level chosen by the other (M –

1) developers, the migration or equal utility condition is V(g i ,N i ) = V(g 0,(N - N i )/(M –

1)). This implicitly defines the population of community i as a function of g i and g 0:

N i (g i ,g 0)=N M +j t M -1M (U(g i )-U(g 0)).(2.11)Thus, the population of community i is increasing in g i , and decreasing in the level of the public good provided by developer i's rivals.

Developer i's problem is to choose g i to maximize p (g i ,N i (g i ,g 0)). The first-order condition for this problem implies

M -1M N i ¢ U (g i )-¢ C (g i )=0.(2.12)Thus, with a finite number of active developers, each provides too little of the local

public good, relative to the first-best allocation. Underprovision arises from the strategic interactions between the communities, and in particular, from the pecuniary externality identified by Scotchmer (1985a, 1986). An increase in g i attracts residents from other communities, increasing utility there. However, this contribution to welfare is ignored by an individual developer. The symmetric equilibrium population of each community equals N /M from (2.11).

As the population of the region and the number of active developers increases,maintaining the symmetric equilibrium size of each community at N /M, (2.12) implies that the level of public good provision in each community rises. In the limit, where the population and the number of active developers are arbitrarily large, equilibrium public good provision satisfies the Samuelson rule, and is therefore efficient. Intuitively, in a

西方经济学教案

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资源如何才能在全社会范围内得以充分利用这一问题的。其中心理论是国民收入决定理论,以及分析和研究在现有既定的资源未能得以充分利用的原因,以及如何充分利用的途径和实现经济稳定增长等问题,以弥补市场机制的不足,寻求政府干预经济的理论依据和干预手段,并且为政府宏观经济政策的灵活运作用,提供一套的理论规范和行为规范。本部分的教学内容主要由国民收入核算理论、决定理论、波动理论和增长理论,以及宏观经济政策等构成。 二、教学内容 宏观经济学是西方经济学的重要组成部分,主要介绍宏观经济学的基本知识、基本理论和基本政策。课程主要讲授国民生产总值的核算及决定、总供给和总需求理论、凯恩斯的国民收入决定理论、失业和通货膨胀理论、经济周期与经济增长以及宏观经济政策、和国际贸易和国际收支等内容。 三、本课程的教案主要包括下列教学活动形式 1、教学目标及基本要求 2、学时分配 3、教学重点与难点

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2018电大西方经济学小抄(完整版) (5)

四、计算题 1.当人们的平均收入增加20%时,某种商品的需求量增加了30%,计算需求收入弹性,并说明这种商品是正常物品还是低档物品,是奢侈品还是生活必需品。1.(1)根据计算收入弹性系数的公式:(2)从其收入弹性为正值来看,该商品是正常商品;由于其收入弹性大于一,故该商品为奢侈品。 2.社会原收入水平为1000亿元,消费为800亿元,当收入增加到1200亿元时,消费增加至900亿元,请计算边际消费倾向和边际储蓄倾向。(1)边际消费倾向MPC=△C/△Y=(900-800)/(1200-1000)=0.5;(2)边际储蓄倾向MPS=△S/△Y=(1200-900)-(1000-800)/(1200-1000)=0.5。(也可以用1-MPC得出)1.已知M=120,P X=20元,P Y=10元,消费者在购买X与Y商品时的组合方式,以及从X、Y中所得到的总效用如下: 组合方式MU X/P X与MU Y/P Y总效用 Q X=6 Q Y=0 1/20≠0/10 1 Q X=5 Q Y=2 2/20≠8/10 67 Q X=4 Q Y=4 5/20≠7/10 69.5 Q X=3 Q Y=6 12/20=6/10 87 Q X=2 Q Y=8 14/20≠5/10 85.5 Q X=1 Q Y=10 16/20≠4/10 80 Q X=0 Q Y=12 0/20≠3/10 70.5 从上表可看出,购买3单位X商品与6单位Y商品可以实现效用最大化 2.某国的边际消费倾向为0.6,边际进口倾向为0.2,请计算该国的对外贸易乘数。2.对外贸易乘数=1/(1-边际消费倾向+边际进口倾向)=1/(1-0.6+0.2)=1.67 1.下面是某企业的产量、边际成本、边际收益情况: 边际成本(元) 产 量 边际收益(元) 2 2 10 4 4 8 6 6 6 8 8 4 1 10 2 这个企业利润最大化的产量是多少?为什么?2.中央银行想使流 通中的货币量增加1200万元,如果现金一存款率是0.2,法定准备率是0.1,中央银行需要在金融市场上购买多少政府债券?(1)利润最大化的原则是边际收益与边际成本相等,根据题意,当产量为6单位时,实现了利润最大化。(2)在产量小于6时,边际收益大于边际成本,这表明还有潜在的利润没有得到,企业增加生产是有利的;在产量大于6时,边际收益小于边际成本,这对该企业来说就会造成亏损,因此企业必然要减少产量;只有生产6单位产量时,边际收益与边际成本相等,企业就不再调整产量,表明已把该赚的利润都赚到了,即实现了利润最大化。2.根据货币乘数的计算公式:,已知cu=0.2,r=0.1,则。已知M=1200,mm=4,根据公式,H=300万,即中央银行需要在金融市场上购买300 万元的政府债券 1.某商品的需求价格弹性系数为0.15,现价格为1.2元,试问该商品的价格上涨多少元才能使其消费量减少10%?1.已知E d=0.15,P=1.2,,根据计算弹性系数的一般公式:将已知数据代入上式:。(元),该商品的价格上涨0.8元才能使其消费量减少10%。 2.如果要使一国的经济增长率从6%提高到8%,在资本-产量比率为3 的前提下,根据哈罗德经济增长模型,储蓄率应有何变化?2.根据哈罗德经济增长模型的公式:。已知C=3,G1=6%,G2=8%,将已知数据代入,则有: S1=3×6%=18%S2=3×8%=24%因此,储蓄率应从18%提高到24%。 1.某种商品在价格由10元下降为6元时,需求量由20单位增加为40单位,用中点法计算这种商品的需求弹性。 1. 。 34 .1 5.0 67 .0 8 4 30 20 2 ) ( 2 ) ( 2 1 2 1- = - = - = + ? + ? = P P P Q Q Q E d 1.某企业产品价格弹性系数在0.5- 2.0之间,如果明年把价格降低10%,销售量预期会增加多少? 解:根据公式: P P Q Q E d? ? = P P E Q Q d ? ? = ? 当 d E=-0.5时,% 5 % 10 5.0= - ? - = ? Q Q 当 d E=-2.0时,% 20 % 10 0.2= - ? - = ? Q Q 因此,销售量预期会增加5%-20%之间。 2.某个国家共有1亿人,16岁以下儿童2000万人,65岁以上老年人1000万人。在全日制学校学生1400万人,家庭妇女500万人,残疾人和其他没有劳动能力者100万人,失业者500万人,其余为就业者。这个经济中劳动力参工率与失业率分别是多少?2.(1)该国的劳动力人数为:7000-2000=5000万人,劳动力参工率为:5000/7000=0。714。(2)该国的失业率为:500/5000=0。1,即该国的失业率为10% 2.根据如下资料,按支出法计算国内生产总值。 项目金额 (亿 元) 项目项目金额 (亿元) 耐用品 支出 318.4 劳务1165.7 厂房与 设备支 出 426 进口429.9 政府购 买支出 748 公司利 润 284.5 工资和 其它补 助 2172.7 出口363.7 所得税435.1 居民住 房支出 154.4 非耐用 品支出 858.3 企业存 货净变 动额 56.8 解:GDP=C+I+G+(X-M)=(318.4+858.3+1165.7)+(426+154.4+56.8)+748+(363.7-429.9)=3661.4 1.20世纪70年代汽油价格上升了200%,豪华汽车(耗油大)的需求量减少了50%,这两者之间的需求交叉弹性是多少?它们之间是什么关系?1.(1)根据交叉弹性的弹性系数计算公式,将已知数据代入:(2)由于交叉弹性为负值,故这两种商品为互补关系。2.一个经济中的消费需求为8000亿元,投资需求为1800亿元,出口为1000亿元,进口为800亿元,计算该经济的总需求,并计算各部分在总需求中所占的比例。2.(1)根据题意,C=8000亿元,I=1800亿元,NX=1000-800=200亿元,因此:YD=C+I +NX=8000+1800+200=10000亿元。(2)消费需求在总需求中所占的比例为:8000/10000=0。8,即80%。(3)投资需求在总需求中所占的比例为:1800/10000=0。18,即18%。(4)国外需求在总需求中所占的比例为:200/10000=0。02,即2%1.某种商品的需求弹性系数为1。5,当它降价10%时,需求量会增加多少?1.已知Ed=1。5,,根据计算弹性系数的一般公式:需求量会增加: 2.1950年,教授的平均工资为300元,2000年,教授的平均工资为4000元。以1950年的物价指数为100,2000年的物价指数为2100,教授的实际平均工资增加了,还是减少了?2.2000年教授的实际平均工资=1950年的名义工资× 从计算结果来看,教授的实际平均工资减少了。 五、问答题(每小题 15 分,共 30 分) 1.如何理解边际产量递减规律?(1)边际产量递减规律的基本内容是:在技术水平不变的情况下,当把一种可变的生产要素投入到一种或几种不变的生产要素中时,最初这种生产要素的增加会使产量增加,但当它的增加超过一定限度时,增加的产量将要递减,最终还会使产量绝对减少。2)这一规律发生作用的前提是技术水平不变。技术水平不变是指生产中所使用的技术没有发生重大变革。 1

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