Public Choice through Mobility

© Allen C. Goodman, 2009

Issues with Optimal Amount

• Optimal literature on choosing the amount of public goods was pretty pessimistic.

• If you ask people how much they want, and you tell them they will be taxed, they will “lowball” their responses.

• If they don’t think it will be related to taxes, they will “highball” their responses.

• Tiebout wrote a “response” in 1956.

Tiebout Model

• You have a bunch of municipalities.

• Each one offers different amounts of public goods.

• Consumers can’t adjust at the margin like with private goods, but ...

Tiebout Model

• They vote with their feet.

• If they don’t like what’s being provided in one community, they move to another.

• Assumptions

– Jurisdictional Choice -- Households shop for what local governments provide.

– Information and Mobility -- Households have perfect information, and are perfectly mobile.

– No Jurisdictional Spillovers -- What is produced in Southfield doesn’t affect people in Oak Park.

– Community size – City manager seeks to reach average minimum cost of producing goods.

– Head Taxes -- Pay for things with a tax per person – all pay, no one is subsidized.

• We get an equilibrium. People’s preferences are satisfied.

Eq’m occurs when people stop moving!

What happens if people keep movingFrom Community 1 to Community 2?

Note on returns to scale

• If public goods can be produced with constant returns to scale exact satisfying of preferences.

• This assumption kind of assumes away part of what’s public about public goods!

Is this sensible?

Fisher points out:In 1950s and 1960s, approx 20% of the population moved each year.Currently, it’s about 14%, but this is still over 40 million people per year.Local moves tend to be for housing related reasons.Renters move more often than home-owners.

Tiebout Model• Critique

– People aren’t perfectly informed.– There may not be enough jurisdictions to meet

everyone’s preferences.– Income matters. Someone from Detroit cannot

move to Bloomfield Hills to take advantage of public goods in Bloomfield Hills.

– Where you work matters.– It’s probably a better model for suburbs than for

central cities.– Very few places have a “head tax.”

Lots of Tiebout Literature

• We have to make things more realistic.

• In most places local public goods are financed by property taxes.

• Property taxes are a constant percentage of the value of the property.

Rent and Value

y is the annual value of housing services (the amount of rent you would pay. r is interest rate.

How is this converted into the price P of a house?

P = y/(1+r) + y/(1+r)2 + … y/(1+r)n

Why?

Rent and ValueP = y/(1+r) + y/(1+r)2 + …+ y/(1+r)n-1 + y/(1+r)n (1)

multiply both sides by (1+r)

(1+r)P = y + y/(1+r) + … + y/(1+r)n-1 (2)

Subtract (2) – (1)

rP = y - y/(1+r)n (3)

As n gets infinite, we lose the second term.

rP = y P = y/r (3′)

Rent and Value

So, with y as the annual value of housing services.

P = y/r.

We can rewrite this as P = Dy, where D = 1/r

If r is 0.05, then D = 20,

and P = 20y.Houses don’tlast infinitely,So D < 20.

If Asset is taxed at Rate t

Price = Stream of Returns – Stream of Tax Liabilities

P = Dy – D(tP), where tP = tax liabilitiesP(1 + Dt) = Dy P = Dy / (1 + Dt)Price falls because the asset is taxed, butIf the taxes buy X, thenP = Dy + DX – D(tP) P = D(y + X)/(1 + Dt)

Higher y, X increased price!

Higher taxes decreased price!

Equations

Pni = Dyn + D (Xi – tiPni) Value of House

Bi = Pni/n Tax Base per house (type

n in municipality i)

Xi = ti Bi $ worth of public good/house

in municipality i.

PV of Housing Services

PV of FiscalSurplus (Deficit)

Example

Suppose we had a community ONLY of small houses worth $150,000 each.

If the community wanted Xi = $5,000 worth of public goods (schools, police, fire, etc.) they would have to tax themselves.

How much?

Xi = ti Bi

5,000 = ti * 150,000 ti = 5,000/150,000 = 0.033

Why?Tax rate of 3.33%

Value of the House

What happens to the value of the house?

It stays at $150,000.

Why? Because you are paying $5,000 in taxes for something worth $5,000 to you.

In a sense buying the public good is no different than buying groceries.

Example

Suppose we had a second community ONLY of big houses worth $300,000 each.

If the community wanted Xi = $5,000 worth of public goods (schools, police, fire, etc.) they would have to tax themselves.

How much?

Xi = ti Bi

5,000 = ti * 300,000 ti = 5,000/300,000 = 0.0167

Why? Tax rate of 1.67%, or

HALF the tax rate of the othercommunity.

Example

Suppose that someone who can only afford a small house, would like to pay lower taxes, like 1.67% rather than 3.33%, to get $5,000 worth of public goods.

Builds a house in the community of larger houses.

It would seem that by building in the community of larger houses, he/she would get a fiscal surplus.

It looks like he/she is getting $5,000 worth of services, while only paying 0.0167 * 150,000, or $2,500. This generates a fiscal surplus.

BUT, a couple of things happen

Pni = Dyn + D (Xi – tiPni) Value of House1. The fiscal surplus is an asset. Anyone else

would love to get hold of this fiscal surplus. Price will be bid up until someone buying a small house will be no better off in the community of large houses, than they were in the community of small houses. [Paying less for services BUT more for housing]

2. The tax base in the community of large houses has fallen. Why? Because the “average house” is now slightly smaller.

A bunch of things happen

Property tax rate in community of “big houses” rises (slightly).

Value of other houses in “big” community falls.

Land values for small houses in big community rise.

Is this stable?

No.

Another Exampley Dy P Orig LV New LV2 30 68.7931 6 44.793 45 78.62069 9 42.624 60 88.44828 12 40.455 75 98.27586 15 38.286 90 108.1034 18 36.107 105 117.931 21 33.938 120 127.7586 24 31.769 135 137.5862 27 29.59

10 150 147.4138 30 27.4111 165 157.2414 33 25.2412 180 167.069 36 23.0713 195 176.8966 39 20.9014 210 186.7241 42 18.7215 225 196.5517 45 16.5516 240 206.3793 48 14.3817 255 216.2069 51 12.21 Base = 9.5

Tiebout-Hamilton Capitalization (X=5)

0

50

100

150

200

250

300

0 2 4 6 8 10 12 14 16 18

Units of Housing

Hou

sing

and

Lan

d Va

lues

Dy

P

Orig LV

New LV

W/ no capitalization Land Value/unit = 3 for all parcels

W/ capitalization Land Value/unit is LARGEST for smallest parcels

WhatWill

Happen???

WhatWill

Happen???AssumeD = 15

So, what then …

• Does this explain “large lot zoning?”

• Is this the way that developers develop?

• Are there enough different communities for this to occur.

• We’ll look at some empirical stuff next time.