The point of departure of the theory of optimal income taxation is the proposition that, ideally, a tax should be levied on an individual's innate productivity endowment, which determines the utility level he can achieve on the labour market. Since this is, however, unobservable, a tax must instead be levied on money income. The underlying model of behaviour, whether in the theory of non-linear taxation first developed by Mirrlees (1971), or in the theory of linear taxation formulated by Sheshinski (1972), is that of a utility-maximizing individual who divides his time optimally between market labour supply and leisure, given his net wage. The gross wage measures his productivity. There is a given distribution of wage rates over the population, and the problem is to maximize some social welfare function defined on individual utilities.
In Mirrlees's non-linear tax analysis, the problem is seen as one in mechanism design. An optimally chosen menu of marginal tax rates and lump sum tax/subsidies is offered, and individuals select from this menu in a way that reveals their productivity type. As well as the government budget constraint, therefore, a key role is played by incentive compatibility or self-selection constraints.
In Sheshinski's linear tax analysis, the attempt to solve the mechanism design problem is abandoned. All individuals are pooled, and the problem is to find the optimal marginal tax rate and lump sum subsidy over the population as a whole, subject only to the government budget constraint.