1. Public Choice
Chapter 6 (Part 2)

2. Market Failures and Government Intervention
How do governments and state bureaucrats actually behave?
Efficiency of providing the public goods
Government failures leading to an inefficient level of government expenditure

3. Efficient Provision of Public Goods
A trade-off between private and public goods is just like a tradeoff between two private goods
The indifference curves for the public goods are also downward-sloping (more of one good must be obtained to compensate for a reduction in the availability of the other good for the consumer to remain indifferent)
Indifference curves are also strictly convex to the origin (as more private goods are consumed, the household is willing to give up fewer and fewer units of the public good to obtain successive additional units of the private good)
The further away from the origin the indifference curve is located, the higher overall utility it represents

4. Existence Value
An individual may derive satisfaction from the provision of a public good even if he or she himself or herself does not consume the good
Examples include charity, contributions for preserving wild nature
Some people attribute value just to the fact that something exists: the existence value

5. Compensating Variation
Suppose the household is only consuming the private good: in the space of the private and public goods the price of the public good is infinite so that the budget line is a horizontal line
Suppose the government provides a certain amount of public good
What is the most the household is willing to pay for the opportunity to consume that amount of public good?
The reduction in quantity of the previously consumed private good that leaves the household on the same indifference curve is called compensating variation

6. Compensating Variation
Private good A
Initial budget line C CV B
Public good

7. Marginal Willingness to Pay
Private good CV
Public good

8. Adding MWTP Curves for Public Goods
Re-cap: one individual’s consumption of a public good does not reduce the other person’s ability to consume the public good
Therefore, we add MWTP-s for a public good vertically rather than horizontally, to obtain the aggregate MWTP

9. Aggregate MWTP $
MWTP2
Aggregate MWTP
MWTP1
Public good

10. How Large Should the Provision of the Public Good Be?
Re-cap: one individual’s consumption of a public good does not reduce the other person’s ability to consume the public good
Therefore, we add MWTP-s for a public good vertically rather than horizontally
Suppose the marginal cost curve (MC) of producing an extra unit of a public good is increasing upwards
The optimal supply is obtained when the sum of the marginal willingness to pay over all households is equal to the marginal cost of provision
Since both households can consume the unit simultaneously, we just add up the households’ marginal willingness to pay for the public good in order to obtain total (aggregate) MWTP

11. Adding MWTP for Public Goods$
Hshld 2
Aggregate MWTP
MWTP household 1
Hshld 1
Public good

12. Adding up MWTP for Public Goods
For a supply less than the equilibrium amount, the sum of the marginal willingness to pay over all households is greater than the marginal cost of producing an extra unit of a public good
For levels above the equilibrium amount households are not willing to give up a sufficient amount of consumption of other goods (or their income) to cover the cost of producing the final unit of the public good, so that reduction in supply adds to social welfare

13. Provision of Public Goods and Pareto Efficiency
A pure public good is efficiently supplied when the sum of each individual’s marginal willingness to pay is equal to the marginal cost of supplying the good
Pareto efficiency in private markets requires that an individual’s MWTP is equal to the marginal cost (p=MC)
The difference arises because public goods can be consumed simultaneously by many individuals

14. Public Goods Provision and Pareto Efficiency
Private goods: MRS1=MRS2=p1/p2=MRT
Public goods: MRS1+MRS2=MRT

15. How can Pareto Efficient Provision of Public Goods can be Attained?
Assume the voter is paying a tax price to cover the provision of public goods (the individual’s share of a dollar of government expenditure)
With uniform taxation of H individuals the uniform tax price is $1/H
The tax paid by the individual is p*z, where z is the amount of the public good
In this case the budget constraint for a particular individual is given by y=qx+pz, where qx is price times quantity of the private good, y is income and pz is price times quantity of the public good

16. Deriving the Demand Curve for Public Goods
By varying the tax price for the public good provision we can derive the demand curve for a public good
If the public good is normal as opposed to inferior an increase in the voter’s income shifts the demand curve to the northeast
Therefore, individuals with different incomes will vote for different levels of public goods (lower income people will vote for a smaller amount of public goods)
If taxation is proportional, the tax price is an increasing function of income so that in this case we cannot be sure whether higher incomes will lead to an increase of decrease of the demand for a public good

17. Deriving the Demand Curve for a Public Good
Budget Line with a Smaller Tax Price
Budget Line with a Higher Tax Price

18. Lindahl Equilibrium
Assume there are only two individuals in the economy
Let those individuals pay for the public goods according to their respective demand curves
Obtain equality between the sum of their tax prices and the marginal cost of producing the public good
In the Lindahl equilibrium P1+P2=MC, and the two individuals are consuming the same amount of the public good

19. Lindahl Equilibrium and Pareto Efficiency
Lindahl equilibrium is Pareto efficient in the sense that price (i.e. the sum of individual tax prices) is equal to the marginal cost
However, because individuals realize their tax prices depend on their willingness to pay for the public goods provision may try to cheat by under- or over-stating their true willingness to pay for the public good
This problem may be seen as a special case of the free rider problem illustrated by means of the prisoners’ dilemma
In general, it is necessary to reveal individual preferences in order to arrive at Lindahl equilibrium, but it is not clear how to do that

20. Revealing Preferences for Optimal Taxation
In general, it is necessary to reveal individual preferences in order to arrive at Lindahl equilibrium, but it is not clear how to do that
In the case of private goods, individuals reveal their preferences in market place
In the case of public goods there is no similar market mechanism so we need to reveal preferences
Possibilities
Ask people about their willingness to pay for public goods
Hypothetical payment experiments (contingent valuation methodology)
Use some voting mechanism

21. The Majority Voting Rule
Majority voting rule: the alternative (among two alternatives) that receives the majority of votes wins
Does the majority voting rule produce a Pareto-efficient allocation?
Each level of the public good provision results in different levels of utility so we can plot utility schedules against the various levels of public good provision

22. Classes of Individuals according to their Most Preferred Level of Public Good Provision
Utility
The Rich
Middle Class
The Poor
Public Good

23. The Median Voter
The median voter is the one for whom the number of individuals preferring more expenditure is exactly equal to the number of individuals preferring less expenditure
In the example before, the median voter’s most preferred level of public good provision gets adopted according to the majority voting rule
Under uniform taxation, majority voting results in the Pareto efficient level of public good provision since the median voter prefers an expenditure level such that his MWTP is equal to the marginal costs
If taxation is proportional and the median voter’s income is smaller than the average income in the society, his tax price will be small and he will vote for a greater amount of public good compared to the one where price is equal to marginal costs

24. Majority Voting and Pareto Efficiency
Majority-voting can, but need not be Pareto efficient
Sometimes majority-voting equilibrium will not exist (remember the Coase theorem discussion)

25. Why do Voters Vote?
With millions of voters in the society, each individual’s impact on the voting outcome is negligible
Why do people continue to vote?
Interdependent utilities (e.g. some people may care about the poor or clean environment)
In democratic societies, children are taught that voting is a duty

26. Bureaucrats and Voters
Bureaucrats seek to maximize the size of their agencies so they choose the level of public good provision that is too high compared to the efficient one
Forcing the voters to choose between too little and too much of the public good, the bureaucrats have a good chance of getting the permission to produce too much of the public good (e.g. police force in a criminal city)
The economic policy may reflects interests of those in power
Size of agricultural sector is way too large in most industrialized powers
In short, government intervention into public goods provision does not necessarily move the economy closer to the Pareto efficient allocation