Lindahl tax

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A Lindahl tax is a form of taxation in which individuals pay for the provision of a public good according to their marginal benefits. So each individual pays according to his/her marginal benefit derived from the public good. e.g. If A loves scenic beauty and likes to be close to nature he might be ready to pay 5 dollars per day for sitting in a park, whereas a college student who does not visit the park very often will not be ready to pay so much, but might agree to pay 1 dollar. So a person who values the good more pays more.

Lindahl taxes are sometimes known as benefit taxes. A Lindahl equilibrium is a state of economic equilibrium under such a tax. Individuals in a society have different preferences based on their nature, personal choice etc. So an individual's willingness to pay for a public good is a function of many factors, like income, preference etc. So a student will want to pay just 1 dollar for entering a museum but a business man will be ready to pay 10 dollars for the same museum. So in such cases the problem of supply of the public good, at optimal levels arises. Lindahl taxation is a solution for this problem.[1]

Definition

A Lindahl tax is an individual share of the collective tax burden of an economy. The optimal level of a public good is that quantity at which the willingness to pay for one more unit of the good, taken in totality for all the individuals is equal to the marginal cost of supplying that good. Lindahl tax is the optimal quantity times the willingness to pay for one more unit of that good at this quantity.[2]

Lindahl equilibrium

A Lindahl equilibrium is a method for finding the optimum level for the supply of public goods or services.This idea was given by Erik Lindahl in 1919. The Lindahl equilibrium happens when the total per-unit price paid by each individual equals the total per unit cost of the public good. It can be shown that an equilibrium exists for different environments.[3] Hence the Lindahl equilibrium describes how efficiency can be sustained in an economy with personalised prices. Johansen (1963) gave the complete interpretation of the concept of "Lindahl equilibrium". The basic assumption of this concept is that every household's consumption decision is based on the share of the cost they must provide for the supply of the particular public good.[4]

The importance of Lindahl equilibrium is that it fulfills the Samuelson rule and is therefore said to be Pareto Efficient,[3] despite the good in question being a public one. It also demonstrates how efficiency can be reached in an economy with public goods by the use of personalised prices. The personalised prices equate the individual valuation for a public good to the cost of the public good.[citation needed]

Background

Main article: Erik Lindahl

Erik Lindahl was deeply influenced by his professor and mentor Knut Wicksell and proposed a method for financing public goods in order to show that consensus politics is possible. As people are different in nature, their preferences are different, and consensus requires each individual to pay a somewhat different tax for every service, or good that he consumes. If each person's tax price is set equal to the marginal benefits received at the ideal service level, each person is made better off by provision of the public good and may accordingly agree to have that service level provided.

Problems

Lindahl pricing and taxation requires the knowledge of the demand functions for each individual for all private and public goods.When information about marginal benefits is available only from the individuals themselves, they tend to under report their valuation for a particular good, this gives rise to a "preference revelation problem." Each individual can lower his tax cost by under reporting his benefits derived from the public good or service. This informational problem shows that survey-based Lindahl taxation is not incentive compatible. Incentives to understate or under report one's true benefits under Lindahl taxation resemble those of a traditional public goods game.

Preference revelation mechanisms can be used to solve that problem,[5][6] although none of these have been shown to completely and satisfactorily address it. Among others the Vickrey–Clarke–Groves mechanism is an example of this, ensuring true values are revealed and that a public good is provided only when it should be.[7] The allocation of cost is taken as given and the consumers will report their net benefits (benefits-cost) The public good will be provided if the sum of the net benefits of all consumers is positive. If the public good is provided side payments will be made reflecting the fact that truth telling is costly. The side payments internalize the net benefit of the public good to other players. The side payments must be financed from outside the mechanism. In reality these preference revelation mechanisms are difficult to implement as the size of the population makes it costly both in terms of money and time.[8]

A second drawback to Lindahl prices is that they may be unfair. Consider a television broadcast antenna that is arbitrarily placed in an area. Those living near the antenna will receive a clear signal while those living farther away will receive a less clear signal. Those living close to the antenna will have a relatively low marginal value for additional wattage (thus paying a lower Lindahl price) compared to those living farther away (thus paying a higher Lindahl price).[9]

Mathematical representation

We assume that there are two goods in a n economy:the first one is a "public good," and the second is “everything else.” The price of the public good can be assumed to be Ppublic and the price of everything else can be Pelse.

• α*P(PUBLIC)/P(EVERY) = MRS(PERSON1)

This is just the usual price ratio/marginal rate of substitution deal the only change is that we multiply Ppublic by α to allow for the price adjustment to the public good. Similarly, Person 2 will choose his bundle such that:

• (1-ɑ)*P(PUBLIC)/P(EVERY)= MRS(PERSON2)

Now we have both individuals' utility maximizing. We know that in a competitive equilibrium, the marginal cost ratio (price ratio)should be equal to the marginal rate of transformation, or

• MC(PUBLIC)/MC(EVERY)=[P(PUBLIC)/P(EVERY)]=MRT