Tiebout Model: Concept, Assumptions, Equilibrium & Simple Tiebout Model

1 year ago

Atiqur Rahman

10 minutes

According to Tiebout, the communities have two ways to acquire more persons in their community. First, by forming a cartel and enforcing a singular tax rate among various communities. Second, is health tax competition amongst the communities to acquire the individuals to their communities. This tax competition is what Tiebout stressed in his model as an integral part of the allocation of local resources without any government provisions.

As a formal definition of local public good, it is one that, instead of benefiting the total population of consumers, it benefits only consumers in the local community. The fundamental notion here is that individuals must consume all goods- both public and private – at the same location.

Although, in many public good theories, bundling is rather implied. The Tiebout elucidated that if the public goods are local, that is, the consumption of the public goods and locational choice are bundled, then a market-type solution may exist, at least “approximately and hence no government intervention will be required.

The basic Tiebout model takes many communities offering different levels of public goods. It takes into account a unique way to come down to the optimal tax rate in a community, which is called as “voted with their feet”.

According to this, the individuals will prefer their most preferred community and reveal their demand for the public good and overcoming the greatest problem with the public goods theory, which is the difficulty of revelation of true individual preferences. The concept of foot voting can be utilised to maintain discipline in the communities.

Assumptions of Tiebout’s Model:

Consumers are perfectly mobile where their preference patterns, which are set, are best satisfied.
Full information knowledge of differences among revenue and expenditure patterns and how to react to these differences
A huge number of communities in which the consumer-voters may choose to live
All income from dividends (exogenous)
There are no spillovers among communities; that is, the public services supplied exhibit no external economies or diseconomies between communities.
The average cost of providing public goods as a function of population is U-shaped, i.e. there exists a cost-minimizing population size.
Communities with population sizes below (above) the cost-minimizing size seek to expand (contract).

An allocation in the Tiebout model includes two standards- a consumption bundle for each consumer and a production plan for each firm. The case of a city that is too big and tries to get rid of residents is more complicated to imagine.

Nevertheless, economic forces are at work to push people out of it by making their cost of living go up. Every resident who moves to the suburbs to find better schools, more parks, and so forth is reacting, in part, against the pattern the city has to offer. The case of the community, which is at the optimum size and tries to remain so, is not hard to visualize.

Again, proper zoning laws, implicit agreements among realtors, and the like are sufficient to keep the population stable, for the community is small and easy to manage compared with the city.

Tiebout asserted that under these assumptions, efficient provision of public goods would be obtained. That is, communities would be of the optimal (cost-minimizing) size, and citizen voters would live in communities where the public good-tax bundles were optimal for them.

According to Musgrave and Samuelson, the expenditures are made by the central government. Services such as police, education, fire protection, etc., are mainly provided by the local governments. Hence, it is important to look into the activities of the local government. The expenditures made by the local government are generally more than that of the central government towards such activities.

The elements affecting the choice of a municipality by a person relies on the availability of schools and recreational activities such as golf course, parks, police protection, roads, parking facilities, etc., which will all enter into the decision-making process. Some non-economic variables will also be considered, but we are deliberately not putting much stress on such factors.

Equilibrium of Tiebout’s Model

The basic framework of the model is based on the general equilibrium model framework. So, according to the Tiebout model, there is an allocation plan and a production plan, respectively, for the consumer and firm.

Along with it, a public good bundle for the regional government and one region for each consumer. A Tiebout equilibrium is composed of an allocation, a price for each commodity, and a tax system for each region such that the following conditions are fulfilled:

Consumers select their consumption bundles optimally.
Consumers select their regions of residence/consumption optimally (no household wishes to move, treating as given public good levels and taxes across regions)
Firms maximize profits
Markets clear
Each regional government balances its budget.
Each regional government’s public goods and tax plan maximizes its objective

The question about the efficiency of the Tiebout model is still debated. The new efficiency margins that emerge in Tiebout models (relative to standard Arrow-Debreu type models of private good economies) are:

whether the number of regions/communities is correct
whether the allocation of individuals among communities is correct
whether the level of provision of public goods within each community is correct

The general message from most of the Tiebout literature is that efficiency is not likely to be obtained in Tiebout equilibrium except under very restrictive assumptions. Some of the characteristics of the models that are critical to equilibrium properties consist of:

the objectives of local governments
the tax instruments assumed to be feasible
the pattern of factor ownership
the nature of local government competition

Simple Tiebout Model

An economy is composed of identical individuals, each of whom is endowed with a unit of labour that is inelastically supplied independent of residence. Labour is used to produce output, good Y. A unit of Y can be transformed into one unit of private good x or one unit of (pure) public good g. The assumptions about the Y technology are:

f(0) = 0, f’ > 0, f” < 0

Preference for each public good g and private good x for each individual i is given by u(g, xi)

If there are N people in the community, then the total the resource is

Nxi + g = f(N)

If the resources are equally divided amongst all the people in the community, the allocation is given by

x_i + 𝑔/𝑁 = 𝑓(𝑁)/𝑁

Now, consider the optimal community size question. There is a tradeoff involved in increasing N in this model. The per-capita quantity of the productive good Y is decreasing in N, while the per-capita resource cost of providing a unit of the non-congestible local public good is also decreasing in N.

Pareto efficient allocation is given by the following optimization:

The planner problem is given by the following optimization,

Max u(g, xi)

s.t. Nxi + g = f(N)

First-order conditions,

U_x – λN = 0

U_g – λ = 0

λ [f’(N) x_i ] = 0

Then, the first two equation implies

𝑁(𝑈_𝑔/𝑈_𝑥) = 1 : Samuelson Condition

From the third equation,

F’(N) = xi : Individual added until marginal product equal their allocation

Thus combining the resource constraint and the three conditions gives the following result,

g = f(N) – Nf’(N)

If workers or consumers are rewarded the marginal product of labour, then at the optimal population, the return to fixed factors (for example, land) precisely cover-ups the cost of the local public good.

Two related points need to be mentioned to show the allocative results of this model:

changes in the costs of one of the public services will cause changes in the quantity produced
the costs of moving from community to community should be recognized.

Both points can be illustrated in one example. Suppose lifeguards all over the country organize and accomplish upgrading their wages. Total taxes in communities with beaches will go up.

Now, residents who are mostly indifferent to beaches will be forced to make a decision. Is the saving of this added tax worth the cost of moving to a community with little or no beach?

Obviously, this decision depends on many factors, among which the availability of and proximity to a suitable substitute community is important. If enough people leave communities with beaches and move to communities without beaches, the total amount of lifeguard services used will fall.

These models, then, unlike their private-market counterparts, have mobility as a cost of registering demand. The higher this cost, ceteris paribus, the less optimal the allocation of resources.

Tiebout Model: Concept, Assumptions, Equilibrium & Simple Tiebout Model

Assumptions of Tiebout’s Model:

Equilibrium of Tiebout’s Model

Simple Tiebout Model

Pareto efficient allocation is given by the following optimization:

Read More in: Theory of Public Finance

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Assumptions of Tiebout’s Model:

Equilibrium of Tiebout’s Model

Simple Tiebout Model

Pareto efficient allocation is given by the following optimization:

Read More in: Theory of Public Finance

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