The seminal papers by Mirrlees (1971) and Sheshinski (1972) laid the foundations of the modern theory of income taxation for the cases of non-linear and linear taxes respectively. Their fundamental contribution was to formalise the idea of the trade-off between equity and efficiency in redistributive taxation, and to show how this determines, in conjunction with social preferences for redistribution, the structure of a tax system. This trade-off defines in effect a cost function for redistribution, which conditions the extent to which a ‘social planner’ would find it desirable to carry it out.
Their analytical framework, the behavioural model which defines the relationships between tax rates, labour supply, tax revenue and welfare, is that of the individual worker/consumer dividing his time between work and leisure, and using the income from labour supply to buy consumption goods. It is perhaps arguable that this model is a reasonable abstraction for the type of household that overwhelmingly characterised developed economies up to the late 1950s and early 60s, in which the male spouse specialised in market work and the female in household work. If the assumption is made that the within-household income distribution is made just as the ‘social planner’ would wish, and the value of untaxed household production is constant across households and independent of the tax system, then the results of the Mirrlees/Sheshinski optimal tax analysis could be applied to the problem of taxation of these ‘traditional’ households, in which only one market labour supply is relevant. Even then, however, there are issues such as gender discrimination and the determinants of the distribution of productivities in market work, taken as exogenous in the optimal tax models, that could lead one to dispute this.