Local Government Part II

1
Local Government Part II

• Chapter 15 16

2
Heterogeneous Households and Voting

• One location. The local government collects a
  head tax to finance local education.
• H unit measure of households.
• Let I be household income.
• Households have heterogeneous income.
• Have preference on two normal goods
• x consumption
• y education
• px 1 and py 1

3
Heterogeneous Households and Voting

• Voting Stage 1
• Each Household decides an optimal head tax T
• y T
• Preference Maximization
• Let y(I) be the optimal education level for
  households with income I.
• y(I) gt 0

4
Heterogeneous Households and Voting

• Voting Stage 2 Households coordinate. A head tax
  winning majority votes will be implemented.
• Let F(I) be the cumulative distributed function
  (CDF) of income type I. Let Imed be the median
  income level.
• Graph

5
Heterogeneous Households and Voting

• In one dimensional elections, the median voter
  rules
• The education level winning the election is
  y(Imed).
• T y(Imed)

6
Alternative Educational Finance Income Tax

• Educational expense is financed by income tax.
  The tax rate is t.
• Total tax revenue Ttotal
• Education level (one child per HH)

Tax paid by a HH with Income equals I
pdf proportion of HHs with income equals I
Number of HHs with income equals I
Equation A
7
Alternative Educational Finance Income Tax

• Median voter picks t that induce y which maximize
  his/her utility.
• Case I Symmetric distribution of income Imed
  Imean
• Eg. Standard normal distribution
• The median voter knows that the tax she pays is
  going to be the education she receives. So,
  picking a tax rate is equivalent to picking a
  head tax

8
Alternative Educational Finance Income Tax

• The equilibrium level of education is the same as
  the case of a head tax y y(Imed)
• Finance is different. There is income
  redistribution as compared to the head tax.
• Individuals with I lt Imed pay less
• Individuals with I gt Imed pay more.

9
Alternative Educational Finance Income Tax

• Case II Asymmetric distribution of income
• Eg. Imed lt Imean
• The median voter knows the tax she pays is less
  than the education she receives. Some people are
  paying education for her.
• Education level is greater than the case of a
  head tax.

10
Jurisdiction Formation A Simple Version of the
Tiebout Model.

• A large number of locations and a large number of
  households.
• HHs are mobile. Can vote with feet.
• Heterogeneous income I
• Utility function U(x, y ?) depends upon taste
  parameter ? such that y(I, ?) is strictly
  increasing in ?, where y(I, ?) is the optimal
  education level in the Robinson Crusoe Economy
  with I and ?.

11
Jurisdiction Formation A Simple Version of the
Tiebout Model.

• px 1 and py 1
• Education determined collectively (voting)
• Head Tax
• No spillovers. U depends upon y but on ymean

12
Tiebout Equilibrium

• Complete sorting on income and taste. Let
• Then ymin, ymax is the range of education
  levels observed and a HH of type (I, ?) moves to
  a community with y y(I, ?).
• First best. First Welfare Theorem.

13
Property Tax instead of Head Tax

• Introduce the third good z, housing, like
  earlier, and utility function is U(x, y, z ?)
• Tax paid is tz
• Wont have complete sorting because of free rider
  problem.
• Suppose sorting was complete, how can a HH with
  high ? and low I improve his/her welfare?

14
Jurisdictional Spillovers and Scale Economies

• Why larger jurisdictions?
• Jurisdictional Spillovers
• Education spillovers may extend beyond a
  jurisdiction.
• Free rider problem.
• Make jurisdiction larger to internalize the
  spillover.
• Education provision may have some sorts of scale
  economy.
• Specialization

15
Jurisdictional Spillovers and Scale Economies

• Drawbacks for having large jurisdictions?
• Less able to accommodate preference diversity
• Less competition

16
Who pays the property tax?

• Depends on the elasticities of supply and demand.
• Property tax annual tax on the property value
• Value structure value land value
• Example A city with mobile homes.
• 100,000 80,000 20,000
• Tax on housing firms at 1 tax rate 1,000
  800 200

17
Land proportion

• Landlords supply land housing firms demand land
• In a very short run (a year), supply is perfectly
  inelastic. Demand is elastic.
• Landlords pay all the tax
• How do they share tax burden, if supply and
  demand have the same elasticity?

18
Structure proportion

• Housing firms supply households demand
• If the technology of making mobile homes is CRS,
  supply is perfectly elastic.
• Households pay all the tax.

19
Intergovernmental Grants

• 2/5 of the revenue of local governments
• 1/2 of grants are spent on education
• Good things about these grants
• Internalize jurisdictional spillovers
• Finance the shortage of local revenue in the
  short run
• Desired spending on local public goods rises
  faster than the local tax base

20
Intergovernmental Grants

• Conditional grants must be spent on a specific
  program.
• One dollar grant will not increase the spending
  on the specific program by one dollar because of
  the income effect.