Rules for a Just and Optimal Taxation
Two significant developments on taxation are to be found in the 1793 paper “Sur l,impot progressif” - they do not explicitly use mathematics but they entail an implicit formalization.
The first consists in providing a theoretical proof of the fact that a progressive income tax complies with justice: this is done in the “equal absolute sacrifice” perspective, assuming a decreasing marginal utility of wealth (one of Daniel Bernoulli’s hypotheses) and an elasticity of the utility of marginal income with respect to income greater than unity (Faccarello 2006: 26-30).The second 1793 development on taxation consists in the determination of what is called today the optimal volume of public expenses and taxation, with a reasoning that is probably the first to refer to an equilibrium at the margin. A question debated at that time was that a theory of public finance cannot be limited to the affirmation that the state should not spend too much and that the normal financing of its expenditure should be made through taxation in a quid pro quo perspective. It is also important to determine what public goods and services should be produced, and in which quantities. The list of the goods and services useful to society could be long and it is generally impossible to provide them at once. Choices must be made, and, in a given period, a criterion to determine the optimal volume of public spending is needed. The essence of Condorcet’s answer is the following (Faccarello 2006: 19-21). Amounts of public expenses may be classified according to the decreasing order of utility they produce. One might then imagine (although Condorcet does not do so explicitly) a plan in which one would have, as abscissa, the successive volumes of public spending, and as ordinate, the levels of utility engendered by each supplementary volume of expense (the curve of decreasing “marginal” utility of public spending).
But public spending must be financed by taxes, taxation meaning a diminution of the disposable income. As Condorcet accepted Bernoulli’s hypothesis of a diminishing marginal utility of wealth, successive increases in public spending necessarily entail an increasing marginal disutility of taxation. As a consequence, it is also possible to imagine an increasing “marginal” disutility curve for public expenditure; in the same schema as before, this disutility is shown along the ordinate while the successive volumes of taxation (equal to those of public spending) is represented along the abscissa. The two curves cross. Public expenses “have a limit: the point where the utility of the expense becomes equal to the evil generated by the tax” (Condorcet 1793, in 1847-49, XII: 629). In other words, their volume is determined by the point at which their marginal utility is equal to the marginal disutility they entail, the “margins” being here broadly defined.But in a modern state, all these decisions about public expenses and taxation are taken by an elected assembly. How to choose its members and which decision-making process should they follow in order to take just and true decisions?