Several theories of taxation exist in public economics. Governments at all levels (national, regional and local) need to raise revenue from a variety of sources to finance public-sector expenditures. Adam Smith in The Wealth of Nations (1776) wrote:
"The subjects of every state ought to contribute towards the support of the government, as nearly as possible, in proportion to their respective abilities; that is, in proportion to the revenue which they respectively enjoy under the protection of the state. The expense of government to the individuals of a great nation is like the expense of management to the joint tenants of a great estate, who are all obliged to contribute in proportion to their respective interests in the estate. In the observation or neglect of this maxim consists what is called the equality or inequality of taxation." The Wealth of Nations#Book V: Of the Revenue of the Sovereign or Commonwealth In modern public-finance literature, a whole economy of the tax system has developed (tax system economics), which can be defined as "the overall management of public revenue of a state or integration grouping's public revenues and expenditures in order to shape smart economic policies that stimulates economic growth and development and safeguards against functional risks for present and future generations." A narrower view of the theory of taxation reduces the system to two issues: who can pay and who can benefit (Benefit principle). Influential theories have been the ability theory presented by Arthur Cecil Pigou and the benefit theory developed by Erik Lindahl. There is a later version of the benefit theory known as the "voluntary exchange" theory. Under the benefit theory, tax levels are automatically determined, because taxpayers pay proportionately for the government benefits they receive. In other words, the individuals who benefit the most from public services pay the most taxes. Here, two models adopting the benefit approach are discussed: the Lindal model and the Bowen model.
Lindahl's model
Erik Lindahl was a Swedish economist and professor of economics at Uppsala University, as well as an advisor to the Swedish government and central bank. Lindahl approached the financing of public goods through the lens of individual benefits, ensuring that the total marginal utility equated to the marginal cost of their provision, thereby addressing the number of public goods. The necessary and sufficient conditions for such an equilibrium are:
the sum of the declared willingness be greater than the cost of the provision the minimum willingness to pay is positive & non-zero Lindahl was deeply influenced by his professor and teacher Knut Wicksell and proposed a method of financing public goods that shows that consensus politics is possible. Because people are naturally different, their preferences differ, and consensus requires that each pay a slightly different tax for each service or good they consume. Suppose the price of everyone’s tax is set at the equivalent of the marginal utility he receives. In that case, everyone will be better off by the provision of the public good and may accordingly agree to be provided with that level of service. Lindahl tries to solve three problems:
Extent of state activity Allocation of the total expenditure among various goods and services Allocation of tax burden
Lindahl's model
In the Lindahl model, if SS’ is the supply curve of state services it is assumed that production of social goods is linear and homogenous. DDa is the demand curve of taxpayer A, and DDb is the demand curve of taxpayer B. The Horizontal summation of the two demand curves results in the community’s total demand schedule for state services. A and B pay different proportions of the cost of the services which is vertically measured. When ON (O = graph origin, at axes intersection) is the amount of state services produced, A contributes NE and B contributes NF; the cost of supply is NG. Since the state is non-profit, it increases its supply to OM. At this level, A contributes MJ and B contributes MR (the total cost of supply). Equilibrium is reached at point P on a voluntary-exchange basis.
Lindahl's equilibrium The Lindahl equilibrium proposes that individuals pay for the provision of a public good according to their marginal benefits in order to determine the efficient level of provision for public goods. In the equilibrium state, all individuals consume the same quantity of public goods but may face different prices because some people may value a particular good more than others. The Lindahl equilibrium price is the resulting amount paid by an individual for his or her share of the public goods. The significance of the Lindahl equilibrium is that it satisfies Samuelson's rule and is therefore said to be Pareto efficient, even though there are public goods. It also sets out how efficiency can be achieved in an economy with public goods by using personalized prices. Personalized prices are equal to the individual estimate for the public good and the public good's cost.
Lindahl tax and Pareto optimality
It's essential to consider whether the Lindahl Pareto tax stands as an optimal equilibrium. A Pareto optimal allocation occurs for a public good when the sum of the marginal rates of substitution (MRS) equals the marginal rate of transformation (MRT). Thus, if this can be shown to hold in a Lindahl equilibrium, it can be conveniently said to be Pareto optimal. Demonstrating this can be achieved through the following steps: let's examine Figure 1. Considering the demand curve for public goods. With the lower price of public goods, the X will want to consume more.
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