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What is the Lindahl Equilibrium?
A Lindahl tax is a form of taxation that is calculated according to the amount of satisfaction or benefit individuals receive from using an additional unit of the public good. So, the optimal level for producing a public good is the point at which an individual is willing to pay an amount equal to the marginal cost of supplying that good. To produce more than that equilibrium amount means the cost of production is more than value received (and thus the willingness of the consumer of the good to pay).
A Little More on What is the Lindahl Equilibrium
Lindahl equilibrium is the method used for finding the equilibrium point for the level of supply against the highest amount consumers are willing to pay for public goods.
As expressed by Leif Johansen, the Lindahl equilibrium is the comparison of how much individuals are willing to pay for a particular public good affects their consumption decisions.
The theory is applied to public taxation. It centers around benefit taxation as individuals are taxed based on what they think is the benefit received from the provision of public benefits. According to this theory, individuals are prepared to pay taxes for the quantity of public goods received or consumed. Supplying more (or a larger number of) public benefits than an individual is willing to pay results in total benefits of a lower value than individuals are willing to pay. The Lindahl equilibrium is important because it shows how productivity can be achieved in an economy by equating individual appraisal for a public good to the cost of the public good.
Despite leading to a systematic provision of public goods, the Lindahl tax has three main problems in implementation.
Preference Revelation Problem – Individuals are prone to lie about and under report their appraisal of the value of a particular good and the benefits derived. This to them paying lower taxes. This tendency of humans is associated with the free rider problem and is not incentive compatible. Though preference revelation mechanisms such as the Vickrey-Clarke-Groves mechanism can be used to solve the issue as it ensures the true value is revealed and that the public good is provided only when it should be, they have been unable to eradicate the problem entirely.
Preference Knowledge Problem – Another problem with the Lindahl solution is that some individuals may honestly have no idea of the value of the public goods they do not interact with on a day to day basis.
Preference Aggregation Problem – Governments may have problem accumulating the marginal willingness to pay of their citizens except if few individuals are affected by the public good.
References for Lindahl Equilibrium
Academic Research on Lindahl Equilibrium
The core and the Lindahl equilibrium of an economy with a public good: An example, Muench, T. J. (1972). Journal of Economic Theory, 4(2), 241-255. This makes use of an example in discussing the core and the Lindahl Equilibrium in an economy with a public good
Equivalence of Lindahl equilibrium with participation prices and the core, Wooders, M. H. (1997). Economic Theory, 9(1), 115-127. This article tries to compare the core and equilibrium outcomes of an economy with only one public good and that of an economy with multiple public goods and differentiated crowding.
The sale of development rights and zoning in the preservation of open space: Lindahl equilibrium and a case study, Wolfram, G. (1981). Land Economics, 57(3), 398-413. Using the United States as a case study, this journal tries to determine the Lindahl equilibrium in the sale of development rights and zoning in the preservation of open space.
Double implementation of the Lindahl equilibrium by a continuous mechanism, Peleg, B. (1996). Economic Design, 2(1), 311-324. This paper attempts a consideration of economies with public goods that have some properties. It does this by providing a continuous and feasible mechanism that implements the Lindahl equilibrium by Nash equilibria.
Existence of Lindahl equilibrium with a measure space of consumers, Roberts, D. J. (1973). Journal of Economic Theory, 6(4), 355-381. The author examines the usage of the Lindahl equilibrium within a measured space of consumers.
Manipulating Lindahl equilibrium via endowments, Sertel, M. R. (1994). Economics Letters, 46(2), 167-171. The author makes a case for the fact that the Lindahl equilibrium can be individually and coalitionally manipulated with various examples to buttress his point.
Tax progression in Lindahl equilibrium, Snow, A., & Warren Jr, R. S. (1983). Tax progression in Lindahl equilibrium. Economics Letters, 12(3-4), 319-326. This paper demonstrated tax progression in Lindahl equilibrium and discussed some conflicting empirical evidence against it.
Efficiency and nonlinear pricing in nonconvex environments with externalities: A generalization of the Lindahl equilibrium concept, Vega-Redondo, F. (1987). Journal of Economic Theory, 41(1), 54-67.This article defines and studies a ‘Generalized Lindahl Equilibrium’ that attains local Pareto efficiency.
Lindahl equilibrium versus voluntary contribution to a public good: The role of the income distribution, Buchholz, W., Cornes, R., & Peters, W. (2006). FinanzArchiv: Public Finance Analysis, 62(1), 28-49. This is a discussion of some inequalities that arose in the use of Lindahl equilibrium which may make it equal to the voluntary contribution Nash equilibrium and what benefits lie in a move from the former to the latter. The potential applications concerning international cooperation on global public good provision is also examined in the work.
Lindahl and equilibrium, van den Nouweland, A. (2015). (pp. 335-362). Springer, Berlin, Heidelberg. This paper carries out a reassessment of the ideas expressed by Lindahl in 1919 and the current definition of Lindahl equilibrium, finding some discrepancies within. It also examines the ratio equilibrium and its suitability to the original Lindahl ideas.
Coalitional instability of the distributive Lindahl equilibrium, Asdrubali, P. (1996). Economic Theory, 8(3), 565-575. This is an argument against the need of a distributive Lindahl equilibrium to satisfy coalitional stability supported by examples.
Optimality and Lindahl equilibrium, Yates, A. J. (1999). Journal of Economic Research, 4, 37-60. The article discusses the need for optimality of the public goods in determining Lindahl equilibrium.