lecture notes4

1

ECO 4554 Economics of State and Local Government

Lecture Notes

ORGANIZATION OF SUBNATIONAL GOVERNMENT: OPTIMAL JURISDICTIONS

Key Points 1. There are multiple criteria for determining whether larger or smaller communities are more

efficient: homogeneity of preferences (the Tiebout hypothesis), returns to scale, and spatial externalities.

2. There is an optimal size for a community, neither too small nor too large, based on each

criterion. Larger communities are not always more efficient than smaller communities. The optimal size community according to one criterion may be different from the optimal size community according to another criterion. There is a trade-off among the criteria. The benefits of achieving efficient size according to one criterion must be balanced against the costs of an inefficient size according to other criteria.

Synopsis

We first look at three criteria for determining the optimal size for a community or any government jurisdiction: homogeneity of preferences (the Tiebout hypothesis), returns to scale, and spatial externalities. We show what each criterion implies about the optimal size of a community. What happens when the criteria conflict, when a community that is optimal according to one of the criteria is not optimal according to another? We show how homogeneity of preferences as a criterion for optimality may conflict with returns to scale and look at possible approaches to addressing or resolving the conflict. When a homogeneous community encounters diseconomies of scale in the supply of public services, production of the public service can be subdivided within the community or the community can be divided into smaller communities. When a homogeneous community encounters economies of scale, the supply of public services may be contracted out to a private supplier or to another government or the community may enter into a joint service agreement with other communities. Then, we show that homogeneity of preferences may conflict with internalizing spatial externalities. We look at intergovernmental grants as a possible solution to this conflict. We also show how the inefficiency costs of non-homogeneous preferences can be balanced against the inefficiency costs of uninternalized spatial externalities so that a community that is not optimal according to either criterion alone may nevertheless minimize the sum of the inefficiency costs. Consolidation of communities within a metropolitan area or consolidation of municipal governments with a county government to form a single large metropolis is often proposed as an efficient “good government” reform. We apply the analysis of optimal size jurisdictions to show that fewer larger communities are not always more efficient than many smaller communities and may in fact be less efficient. Finally, whichever criterion of optimal size is used, there are many public services and the optimal size of government for each public service may be different. To address this conflict, we introduce the correspondence principle, which proposes a set of multiple overlapping jurisdictions, each responsible for supplying a single public service. Following the correspondence principle, however, has high

ECO 4554: Economics of State and Local Government Organization of Subnational Government: Optimal Jurisdictions

2

administrative costs so we introduce the concept of clustering, a non-scientific but useful way of thinking about how to balance all the criteria for optimal jurisdictions while keeping administrative costs relatively low.

Lecture Notes I. Three measures of optimal community size

A. There are three efficiency criteria for determining the optimal size of a community or government: homogeneity of preferences (the Tiebout hypothesis), returns to scale, and spatial externalities.

B. Tiebout hypothesis

1. According to the Tiebout hypothesis, if there are enough communities so that

all individuals can find a community that provides their preferred quantity of public services at a tax-price equal to their marginal benefit, individuals choose among communities so that in equilibrium each community is homogeneous (all residents have the same preferences) and the quantity of public services in each community is efficient given the residents’ preferences.

2. The Tiebout hypothesis implies that the optimal size of a community or

jurisdiction is no larger than the number of individuals with the same preferences for public services and that the optimal number of communities equals the number of different preference types.

3. Even if real world communities are not perfectly homogeneous, the Tiebout

hypothesis implies that the quantity of public services in communities with greater homogeneity is likely to be closer to the efficient quantity than in communities with less homogeneity.

C. Returns to scale (or economies and diseconomies of scale)

1. Increasing returns to scale (or economies of scale)

a. If all inputs are increased in the same proportion so that the scale of operation expands, output increases by a greater proportion. For example, if a 100% increase in inputs increases output by 150%, production is subject to increasing returns to scale. Increasing returns to scale imply decreasing average total cost.

b. Applied to community size, increasing returns to scale means the

average cost of supplying public services in a larger community is lower than the average cost of supplying the same quantity of public services in a smaller community.

2. Decreasing returns to scale (or diseconomies of scale)

a. If all inputs are increased in the same proportion so that the scale of operation expands, output increases by a smaller proportion. For


3

example, if a 100% increase in inputs increases output by 50%, production is subject to decreasing returns to scale. Decreasing returns to scale imply increasing average total cost.

b. Applied to community size, decreasing returns to scale means the

average cost of supplying public services in a larger community is higher than the average cost of supplying the same quantity of public services in a smaller community.

3. The optimal size community or government is just large enough to take

advantage of all economies of scale but not so large as to encounter diseconomies of scale. It includes just the number of individuals necessary to achieve minimum average cost in the supply of public services. See PowerPoint Slides Figure 4-1.

4. Illustration

a. In the diagram, the average cost of supplying public services

decreases up to a population of 20,000. For communities of fewer than 20,000 population, there are economies of scale to increasing the population.

ATC

Population

20,000

Cost per unit ofpublic services

b. The average cost of supplying public services increases as population

grows beyond 20,000. For communities of more than 20,000 population, there are diseconomies of scale to increasing the population.

c. The optimal size community in this example is 20,000 people.

5. The empirical evidence suggests that the optimal size community based on achieving maximum economies of scale is between 10,000 and 100,000 population. Economies of scale can be exploited up to about 10,000 population, but by about 100,000 population, diseconomies of scale set in.

D. Spatial externalities


4

1. If there are interjurisdictional benefit or tax spillovers, also known as spatial

externalities, the quantity of public services supplied in each community is inefficient even if there are no inefficiencies from either voting or the tax system.

2. Benefit spillovers (positive externalities) See PowerPoint Slides Figure 4-2.

a. Assume

• two adjoining communities, A and B • all residents in each community are identical in their

preferences for public services • there are no interjurisdictional tax spillovers (only residents

of A pay taxes for public services in A, and similarly for B) • there are interjurisdictional benefit spillovers (residents of B

benefit from public services supplied by A) • the marginal cost of public services is constant and all

residents of A pay an equal share of the costs.

$5

$10

$20

$25

100 125

MSC

MSB=MBA +MBB

MBB

MBA

Quantity ofPublic Services

Cost of publicservices

b. Residents in A compare their private MB, MBA, with the MSC and

vote for 100 units of the public service. But marginal social benefit includes not only the marginal benefit to residents of A but also the marginal benefit to residents of B, MBB. The efficient quantity of the public service is 125 where MSB=MSC.

c. Problem: Residents of B benefit but they do not share in the costs.

They do not vote in A, and therefore they have no voice in deciding how much of the public service to provide. Residents in A ignore, or more likely are unaware, of the external benefits received by residents of B. They vote for a quantity that is privately efficient but socially inefficient.


5

3. Tax spillovers (negative externalities) See PowerPoint Slides Figure 4-3.

a. Assume

• two adjoining communities, A and B • all residents in each community are identical in their

preferences for public services • there are interjurisdictional tax spillovers (both residents of

A and residents of B pay taxes imposed in A to pay for public services in A)

• there are no interjurisdictional benefit spillovers (residents of B obtain no benefit from public services provided in A)

• the marginal cost of public services is constant and all residents of A pay an equal share of the costs.

$2

$10

$20

100 125

MSC= MCA+MCB

MSB=MBA

Quantity ofPublic Services


MCB

MCA$8

b. Residents in A compare their private MC, MCA, with the MSB, and

vote for 125 units of the public service. But the marginal private cost to residents of A is less than the marginal social cost because part of the cost, MBB, is externalized to residents of B. The efficient quantity of the public service is 100 where MSB=MSC.

c. Problem: Residents of B contribute to the MSC of public services in

A but they do not share in the benefits. They do not vote in A, and therefore they do not have a voice in deciding how much of the public service to provide. Residents in A ignore, or most likely are unaware of, the external costs imposed on residents of B. They vote for a quantity that is privately efficient but socially inefficient.

4. The optimal size community is large enough to internalize all spatial externalities. a. Internalizing an externality: Taking action to correct an externality

by changing the incentives of the individuals who choose the


6

quantity of the good or service. If the incentives are changed appropriately, those individuals will choose the socially efficient quantity rather than the privately efficient but socially inefficient quantity.

b. The optimal size community is just large enough to internalize all

benefit and tax spillovers. It includes all individuals who benefit from the public services supplied in the community and all individuals who pay taxes to fund the public services supplied in the community.

c. In the optimal size community, all spatial externalities are

internalized because everyone who either benefits or pays for the public services is a resident of the community and participates in decisions about the quantity of public services.

E. Problem: The three criteria are not always consistent with one another. An optimal

size community according to one criterion may be less than or greater than optimal according to one or both of the other criteria. We look at several cases where the criteria conflict.

II. Conflicts between homogeneity of preferences (the Tiebout hypothesis) and returns to scale

A. A homogeneous community satisfying the Tiebout criterion of optimality may be either larger or smaller than the size necessary to achieve minimum average cost in the supply of public services.

B. Case 1: Homogeneous communities that are larger than the size necessary to achieve maximum economies of scale and minimum average cost 1. Suppose that the number of individuals with similar preferences for public

services is 40,000. That is the maximum size community that is optimal according to the Tiebout hypothesis. But suppose the average total cost of supplying public services is lowest in a community of 20,000. That is the optimal size community according to the returns to scale criterion.

ATC

Population20,000 40,000



7

2. In this case, the solution is simple. Deconsolidation of the single large homogeneous community into two smaller homogeneous communities simultaneously allows satisfaction of the Tiebout criterion of homogeneity and takes advantage of maximum economies of scale without encountering diseconomies of scale.

3. But, suppose the number of individuals with homogeneous preferences is

larger than the number needed to minimize average cost, but is not a multiple of the number needed to achieve minimum average cost.

a. For example, suppose the number of individuals with homogeneous

preferences is 30,000 rather than 40,000. b. Then, the community can still be divided into two communities. One

community with a homogeneous population of 20,000 is optimal according to both Tiebout and returns of scale. The other community with a homogeneous population of 10,000 is optimal according to Tiebout but is smaller than optimal according to returns to scale. We consider homogeneous communities that are too small to achieve maximum economies of scale next.

C. Case 2: Homogeneous communities that are smaller than the size necessary to

achieve maximum economies of scale and minimum average cost

1. Suppose the number of individuals with similar preferences for a particular public service is 10,000. That is the optimal size Tiebout community. But, the average total cost of supplying public services is lowest in a community of 20,000 population. The optimal size community for achieving maximum economies of scale is 20,000.

ATC

Population20,00010,000

Cost per unit ofpublic services

2. Now, there is a trade-off between the inefficiencies that arise in a smaller

community from increasing returns to scale and the inefficiencies that arise in a larger community from less homogeneity. Smaller communities supply a more efficient quantity of public services because of greater homogeneity of


8

preferences, but they supply that quantity at higher average cost because they are too small to achieve maximum economies of scale.

3. Resolving the conflict: Contracting out and joint service agreements

a. Contracting out for the supply of public services and joint service agreements among communities offer possible solutions to the conflict between homogeneity and returns to scale.

b. Definitions

(1). Contracting out: Each community contracts with a private

supplier or with another community to supply it with public services. The producer of the public services supplies a number of different communities, each of which is homogeneous, but by serving multiple communities, the producer is able to achieve maximum economies of scale.

(2). Joint service agreements: Several small jurisdictions join

together to supply public services so as to achieve maximum economies of scale while maintaining their population at a size consistent with homogeneity of preferences.

c. Contracting out and joint service agreements allow each community

to benefit from lower costs by achieving maximum economies of scale in production while each community retains the ability to provide a different quantity of the public service that is efficient for its residents.

(1). The residents of each community are homogeneous in their

preferences for public services, but the residents in different communities have different preferences for public services.

(2). Each community attains a Lindahl equilibrium that satisfies

the Tiebout hypothesis. (3). Because the public service is supplied to multiple

communities, it is still possible to achieve maximum economies of scale in production.

III. Conflicts between homogeneity of preferences (the Tiebout hypothesis) and internalization of

spatial externalities A. The Tiebout hypothesis places an upper limit on the optimal size of a community but

no lower limit. Spatial externalities place a lower limit on the optimal size of a community but no upper limit.

1. If a homogeneous community satisfying the Tiebout criterion of optimality is

larger than the minimum size necessary to internalize all interjurisdictional benefit and tax spillovers, there is no conflict between the two criteria.


9

2. However, if a homogeneous community satisfying the Tiebout criterion of optimality is smaller than the minimum size necessary to internalize all interjurisdictional externalities, the two criteria of optimality are in conflict.

B. Suppose there are two groups of 10,000 individuals each. The individuals in one

group all have a higher demand for public services than the individuals in the other group.

1. The Tiebout hypothesis requires that each group reside in a separate

community. All the high-demand individuals reside in community A, consume the same quantity of public services, and pay the same tax-price. All low-demand individuals reside in community B, consume a smaller quantity of public services, and pay a lower tax-price.

2. Now, suppose the residents of community B also receive some benefit from public services supplied to the residents in community A.

a. The residents of A choose the quantity of public services that is

privately efficient for them. But, because there are external benefits to residents of B, the privately efficient quantity is smaller than the socially efficient quantity.

b. Each of the two communities is homogeneous. They are the optimal

size based on the Tiebout criterion. However, the quantity of public services supplied in A is less than the socially efficient quantity because of the uninternalized spatial externalities.

c. The analysis is essentially the same when costs are externalized

except that, with uninternalized cost spillovers, the privately efficient quantity of public services is larger than the socially efficient quantity.

C. Resolving the conflict: Intergovernmental grants

1. Intergovernmental grants from a higher level of government to a lower level

of government can compensate for interjurisdictional benefit spillovers while allowing each community to maintain the size that satisfies the Tiebout criterion.

2. Suppose A is an optimal size community according to the Tiebout criterion, but suppose residents of B also benefit from the education provided to students in A. Because residents of A pay the full costs of educating their students, they choose to spend less than the socially efficient amount on education. a. If a higher level of government such as the state government

provides community A with a grant for education expenditure, residents of A have an incentive to vote for more education expenditure. If the grant is just enough to compensate for the external benefits received by the residents of B, A’s voters have an


10

incentive to increase education expenditure up to the socially efficient amount

b. Each community is still homogeneous, but the spatial externalities

are internalized by the grant. It is not necessary to consolidate the two communities in order to internalize the spatial externalities. The grant encourages residents of A to increase their education expenditure to the socially efficient level.

3. Theoretically, intergovernmental grants can internalize either benefit

spillovers (a positive grant or subsidy) or cost spillovers (a negative grant or charge imposed by a higher level of government on a lower level of government). However, in the real world, we do not observe negative grants, so the device of intergovernmental grants is mainly useful for internalizing interjurisdictional benefit spillovers.

D. Resolving the conflict: Balancing the costs of inefficiency

1. Suppose that grants are not feasible for internalizing spatial externalities.

Then, it may be necessary to compromise between a smaller size community with homogeneous preferences and a larger, non-homogeneous community that internalizes all the spatial externalities.

2. There is a trade-off between the inefficiency costs of less homogeneity in a

larger community and the inefficiency costs of uninternalized externalities in a smaller community. See PowerPoint Slides Figure 4-4.

Population

Cost

15,000

Spillover costs

Non-homogeneity costs

Total costs=Spillover+nonhomogeneity

30,0005,000

a. Suppose the optimal size community according to the Tiebout

hypothesis is 5,000. This is the largest number of individuals with the same preferences for public services. As the size of the community increases above 5,000, preferences become more and more heterogeneous, fewer and fewer residents are on their demand curves, and the quantity of public services deviates more from the


11

efficient quantity. Therefore, the inefficiency costs of non-homogeneity increase as community size increases beyond 5,000.

b. However, suppose the smallest size community that internalizes all

spatial externalities is 30,000. This is the minimum community size that is optimal according to the criterion of internalizing interjurisdictional spillovers. With multiple communities smaller than 30,000, some spillovers remain uninternalized. The more smaller communities there are, the more uninternalized externalities there are. The inefficiency costs from interjurisdictional spillovers increase as community size decreases below 30,000.

c. If it is not possible to satisfy both criteria simultaneously, an

alternative approach is to satisfy neither one, but instead to compromise between them. We find a community size that minimized the combined inefficiency costs of heterogeneity and uninternalized spatial externalities. The community will be larger than the optimal Tiebout size but smaller than the size that internalizes all interjurisdictional spillovers. In the diagram, the sum of the inefficiency costs is lowest with a population of 15,000. [Note the similarity to balancing the administrative costs of voting against the external costs of an adverse decision in choosing an optimal voting rule.]

IV. Policy implications: Metropolitan consolidation and city-county government consolidation

A. Consolidation of several smaller communities in a metropolitan area into a single larger community and consolidation of one or more city governments with a county government to form a single metropolitan government are often proposed as “good government” measures to enhance efficiency.

1. Examples of metropolitan consolidation: Modern New York City is the result

of metropolitan consolidation. In 1898 the cities of New York and Brooklyn combined with the Bronx, Queens, and Staten Island to form the single city of New York. The present city of Newport News, Virginia, is the result of a consolidation of the separate cities of Newport News and Warwick.

2. Examples of city-county consolidation: The present city of Jacksonville is

the result of a consolidation of the original city of Jacksonville and Duval County. For many government functions, the city of Miami and Dade County function as the single consolidated Metro-Dade government. The cities of Virginia Beach and Chesapeake, Virginia, are the result of consolidation of a city and a county into a single city.

B. Government consolidation and economic efficiency

1. Consolidation of communities in a metropolitan area or consolidation of city and county governments may enhance efficiency by internalizing spatial externalities or by achieving greater economies of scale or by reducing administrative costs.


12

2. If consolidation of communities reduces the homogeneity of preferences among the residents, however, the greater efficiencies from internalizing externalities or from greater economies of scale are reduced or offset by the inefficiencies from less homogeneity of preferences among the residents of the consolidated community.

3. Consolidation of governments may also result in jurisdictions that are too

large. In other words, the consolidated jurisdictions may be larger than the optimal size to achieve minimum average cost. The result of consolidation may be a change from multiple communities that are inefficiently small to a single consolidated community that is inefficiently large. Consolidation may even result in a change from multiple smaller communities that are optimal with respect to returns to scale to a consolidated community that is inefficiently large.

lecture notes4

Documents