Lindahl Equilibrium

What Is a Lindahl Equilibrium?

Lindahl equilibrium is a state of equilibrium in a quasi-market for the pure public good. As in competitive market equilibrium, the supply and demand for the good are balanced, in addition to the cost and revenue to produce the good. Lindahl equilibrium depends on the possibility of implementing an effective Lindahl tax, first proposed by the Swedish economist Erik Lindahl.

Understanding a Lindahl Equilibrium

At Lindahl equilibrium, three conditions must be met:

A Lindahl tax is a type of taxation proposed by Swedish economist Erik Lindahl in 1919, in which individuals pay for the provision of a public good according to the marginal benefit they receive to determine the efficient level of provision for each public good.

In the equilibrium state, all individuals consume the same quantity of public goods but will face different prices under the Lindahl tax because some people may value a particular good more than others.

Under this paradigm, each individual’s relative share of the total tax revenue is proportional to the level of personal utility they enjoy from a public good. In other words, the Lindahl tax represents an individual’s share of a given economy’s collective tax burden. The actual amount of the tax paid by each individual is this proportion times the total cost of the good.

The equilibrium quantity will be the amount that equates the marginal cost of the good with the sum of the marginal benefits to consumers (in monetary terms). The Lindahl price for each individual is the resulting amount paid by an individual for their share of public goods. Lindahl prices can thus be viewed as individual shares of the collective tax burden of an economy, and the sum of Lindahl prices equals the cost of supplying public goods — such as national defense and other common programs and services — that collectively benefit a society.

Problems with the Lindahl Tax

The Lindahl equilibrium has more of a philosophical application than a practical use due to various issues that restrict the Lindahl equilibrium's real-world function. Due to the infeasibility of actually implementing a Lindahl tax to achieve Lindahl equilibrium, other methods such as surveys or majority voting are normally used to decide the provision and financing of public goods. 

In order to implement a Lindahl tax, the taxing authority must know the exact shape of every individual consumer's demand curve for each public good. However, without a market for the good, there is no way for consumers to communicate what these demand curves look like. Because it's not possible to evaluate how much each person values a certain good, the marginal benefit cannot be aggregated across all individuals. 

Even if consumers could communicate their preferences and the taxing authority could aggregate them, consumers might not even be aware of their own preferences regarding a given public good, or how much they value it depending on whether, how much, or how often any given consumer actually consumes the public good. 

Even if consumer preferences are known, communicated, and aggregated, they may not be stable at the individual level or in the aggregate. Estimates of consumer demand curves might need to be continuously updated in order to adjust both the total quantity of each public good produced and the rate charged to every single individual. 

Problems of the equity of a Lindahl tax have also been raised. The tax charges each individual an amount equal to the benefit they receive from the good. For certain public goods, such as social safety nets, this obviously makes no sense. For example, it would require charging welfare beneficiaries a tax at least equal to the transfer payments they receive, which would seem to defeat the entire purpose of the program. 

It might also be the case that some consumers receive negative utility from a given public good, and providing the good actually causes them harm. For example, a devout pacifist who deeply opposes the very existence of an armed military for national defense. A Lindahl tax for this individual would necessarily be negative. This would lead to a lower equilibrium quantity (since total demand is lower) and a higher Lindahl price for everyone else in society (since the total revenue required would include the price of "buying off" the pacifist). 

In the extreme, this could even lead to a case where a small minority group or even a single individual with strongly contrary preferences could completely prevent the production of a given public good regardless of how much it would benefit the rest of society — if the price to buy them off is higher than the amount that others are willing to pay. In this case, it might make more sense to simply ignore the interests of the contrarian minority, to divide the political body along the lines of preferences for public goods, or to physically remove the contrarian minority from the economy.