NPTEL--Public Economics

Module 4 Lecture 19

Topics 4.24 Lindahl Pricing: Advantage

4.25 Graphical Representation of Lindahl Equilibrium 4.26 Lindahl Pricing: Practical Constraints 4.27 Public Provision of Public

4.28 Alternative Way of Financing Public Goods: Lotteries (Morgan 2000)

4.29 Lottery Model 4.30 Public Provision of Public Goods (Contd.) 4.31 Mechanisms for Aggregating Individual 4.32 Majority Voting: When it Works 4.33 Majority Voting 4.34 Majority Voting: When it Works (Contd.)

4.35 Majority Voting: When it doesn’t Work

4.24 LINDAHL PRICING: ADVANTAGE

Lindahl pricing corresponds to the concept of benefit taxation, which occurs when individuals are being taxed for a according to their valuation of the benefit they receive i.e. paid by individual h is the MB that she derives from G.

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Figure19.1 The Lindahl equation is a set of shares and a public good provision such that

Household 1’s function can be thought of as curve for G at different . 4.25 GRAPHICAL REPRESENTATION OF LINDAHL EQUILIBRIUM

such that

Figure19.1

With Lindahl pricing, the government does not need to know the functions of individual voters: it gets the voters to reveal their preferences by stating their willingness to pay for different levels of the public good.

Lindahl Equilibrium: Challenges

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Lindahl equation leaves every one better off.

: Honest Equilibrium Dishonest Equilibrium

Figure19.2

By under reporting for G, individual 2 secures a lower tax.

Announcing and adjusting tax shares with many consumers Incentive for truthful demand revelation Assumed max U taking as given – i.e. honest But depends on his reported demand, can increase by strategically misrepresenting demand – Assume 1 is honest, 2 knows this and Honest eqm= – Report instead of (i.e. max given Eqm= Therefore should focus on mechanisms that are not open to strategic manipulation in this way if we want efficiency.

4.26 LINDAHL PRICING: PRACTICAL CONSTRAINTS

Must be able to exclude a consumer from using the public good.

– Does not work with non-excludable public good

– Must be able to exclude since otherwise those with WTP=0 will also end up consuming

Must know individual preferences to set personalized , τh

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– Preference revelation problem: Agents have no incentives to reveal their preferences. Individuals may behave strategically and pretend their willingness to pay is low in order to get others to bear a larger cost of the public good.

Preference knowledge problem: It is hard for people to properly goods they do not shop for on a regular basis.

Preference : Aggregating millions of voters’ preferences is difficult in reality. Direct democracy, whereby voters directly cast ballots in favour of or in opposition to particular public projects, is one way of aggregating preferences.

Difference between Lindahl equilibria and standard equilibria:

– No decentralized mechanism for deriving prices; no forces that will generate the right vector 4.27 PUBLIC PROVISION OF PUBLIC GOODS

How do we actually determine level of PGs in practice?

– Voting on bundles of PGs and taxes

– Does voting lead to the first best solution? 4.28 ALTERNATIVE WAY OF FINANCING PUBLIC GOODS: LOTTERIES (MORGAN 2000)

Benchmark model with quasi linear preferences :( No Lottery)

2 identical players Each with income , consuming private goods, P and public goods G. H’s utility function is

Where

Outcomes: Efficient: 2

And Private:

Private charities and Governments often use lotteries in lieu of voluntary contributions to finance public goods

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Lottery funding – Rather than buying public good directly, suppose each individual buys lottery tickets for a chance to win some prize – One person picked at random to win, probability of being picked equals the share of lottery tickets bought – Lottery revenues used to finance prize and public goods

4.29 LOTTERY MODEL h buys lottery tickets His probability of winning prize R is

Note that G =

he’s expected utility is

Outcome: h then buys such that

When R=0, G is private provision level When R>0, G is more than private provision level, since The prize provides an additional incentive to purchase public goods. More efficient as: Positive (G) offset by negative externality (Lottery).

4.30 PUBLIC PROVISION OF PUBLIC GOODS (CONTD.) In practice, three problems emerge: – Determining the public’s preferences. – Measuring costs and benefits. – Crowd-out. So how do we actually determine level of PGs in practice? – Voting on bundles of PGs and taxes. – Does voting lead to the first best solution?

4.31 MECHANISMS FOR AGGREGATING INDIVIDUAL PREFERENCES

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This section discusses how voting can serve to aggregate individual preferences into a social decision.

For now, we focus on direct democracy, whereby voters directly cast ballots in favor of or in opposition to particular public projects. 4.32 MAJORITY VOTING: WHEN IT WORKS

The Lindahl pricing scheme had a very high standard for coming to a consensus: only when citizens are unanimously in agreement would the government achieve Lindahl equilibrium.

A common mechanism used to aggregate individual votes into a social decision is majority voting, in which individual policy options are put to a vote, and the option that receives the majority of votes is chosen.

Majority voting does not always provide a consistent means of aggregating preferences.

To be consistent, an aggregation mechanism must satisfy three goals:

– Dominance: If one choice is preferred by all voters, then the aggregation mechanism must be such that this choice is made by society.

– Transitivity: Choices must satisfy transitivity (If A>B & B>C, then A>C).

Independence of Irrelevant Alternatives: The introduction of a third choice does not change the ranking of the first two choices 4.33 MAJORITY VOTING

It turns out that with these three conditions, majority voting can only produce a consistent aggregation of individual preferences if preferences are restricted to take a certain form. 4.34 MAJORITY VOTING: WHEN IT WORKS (CONTD.) Taxes are assumed to be not-regressive Suppose a town is deciding on education taxes (and spending). There are 3 possibilities: high, medium, and low spending. There are also 3 groups, represented in equal proportions-low, middle & high income parents. Quality of Public schools < Quality of Private schools: implies they are not really substitutable since very different goods

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Low income parents have the highest stake since they will send their children to public schools: hence the above choice High income: just the opposite. They can put their children in private schools so don’t care for public schools Mid Income: Moderate taxes since they still want to send their children to good public schools but at the same time choosing high means they will have to pay a lot, out of pocket. Then they might be better off sending children to private. So low is the next choice. Social ordering implies an unambiguous : M Condorcet Paradox: where majority voting does not work. Now consider a different set of preferences as shown in table 2 Low income is same choice as before. Mid income is also same choice. But for the high income now, either no public school required, or if all public school then better be good Collective preferences can be cyclic (i.e. not transitive), even if the preferences of individual voters are not. This is paradoxical, because it means that majority wishes can be in conflict with each other. When this occurs, it is because the conflicting majorities are each made up of different groups of Individuals Condorcet Paradox: majority voting does not lead to a stable outcome. Condorcet's paradox, which shows that majority preferences can become intransitive with three or more options—it is possible for a certain electorate to express a preference for A over B, a preference for B over C, and a preference for C over A, all from the same set of ballots.

Majority vote share (number of times one outcome is preferred to another)

Table 1: Majority voting delivers a consistent outcome

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Cycling in social ordering: H > M > L > H

Table 2 : Majority voting doesn’t deliver a consistent outcome 4.35 MAJORITY VOTING: WHEN IT DOESN’T WORK

In the example above the second set of outcomes is problematic because there is no clear winner. These results violate the principle of transitivity resulting in cycling–when majority voting does not deliver a consistent aggregation of individual preferences.

Note that the failure to get a consistent winner from majority voting does not reflect a failure on the part of individuals–each group has a sensible set of preferences.

The problem is aggregation–we are unable to use voting to aggregate these individual preferences into a consistent social outcome. Public good provision by Banerjee & Somanathan, 2003 (caste heterogeneity).

This creates the problem of the agenda setter, the person who decides the sequencing of the votes.

In the second situation, he can affect the outcome.

– For low spending to win, for example, first set up a vote between H and M. H wins. Then a vote between L and H means L will win.

– Any outcome can win with appropriate ordering: so the agenda setter will follow the order that leads to his preferred outcome.

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