Lindahl tax
In other words, they pay according to the amount of satisfaction or utility they derive from the consumption of an additional unit of the public good.
Lindahl taxation is designed to maximize efficiency for each individual and provide the optimal level of a public good.
Knut Wicksell was one of the most prominent economists who studied this concept, eventually arguing that no individual should be forced to pay for any activity that does not give them utility.
[2] Erik Lindahl was deeply influenced by Wicksell, who was his professor and mentor, and proposed a method for financing public goods in order to show that consensus politics is possible.
A Lindahl equilibrium is a state of economic equilibrium under a Lindahl tax as well as a method for finding the optimum level for the supply of public goods or services that happens when the total per-unit price paid by each individual equals the total per-unit cost of the public good.
Leif Johansen gave the complete interpretation of the concept of "Lindahl equilibrium", which assumes that household consumption decisions are based on the share of the cost they must provide for the supply of the particular public good.
[5] The importance of Lindahl equilibrium is that it fulfills the Samuelson condition and is therefore Pareto efficient,[3] despite the good in question being a public one.
Fain, Goel and Mungala[6] present a specialized definition, for the case in which there are only public goods.
The mechanism that, given agents' utilities, computes the Lindahl equilibrium, is not strategyproof, even in the setting with only public goods.
Fain, Goel and Mungala[6]: Thm.2.2 present an algorithm for computing the Lindahl equilibrium using convex programming, in the special case in which agents have scalar-separable non-satiating utilities.
Particularly: Peters, PIerczynski, Shah and Skowron[8] present an adaptation of the concept of Lindahl equilibrium to a market with indivisible public goods.
If the definition is strengthened to require that the total payment for each public good exactly equals its cost, then the stronger Lindahl equilibrium notion is equivalent to a concept they call strict stable priceability.
In theory, Lindahl pricing and taxation leads to an efficient provision of public goods.
In doing this, an individual can lower his or her tax cost by under reporting the benefits derived from the public good or service.
The incentive to lie is associated with the free rider problem; if an individual reports a lower benefit, he or she will pay less taxes, but only see a marginal decrease in the public good.
Incentives to understate or under report one's true benefits under Lindahl taxation resemble those of a traditional public goods game.
[5] Preference revelation mechanisms can be used to solve that problem,[9][10] although none of these has been shown to completely and satisfactorily address it.
If the public good is provided side payments will be made reflecting the fact that truth telling is costly.
In reality, preference revelation is difficult as the size of the population makes it costly both in terms of money and time.
This is especially true for public goods that individuals do not interact with on a day-to-day basis, like fireworks and national defense.
[11] Even if individuals know their marginal willingness to pay, and are honest in their reporting, the government can have extreme difficulties aggregating this into a social value.
However, in the case of national defense in the United States, compiling the marginal willingness to pay for this public good of each individual would be nearly impossible.
