The first part of this chapter gives a self-contained exposition of the theory of nonlinear taxation, as a prelude to the extension of the theory to the case of two-person households. Our aim is to present as simply and clearly as possible the main ideas and results of the theory in a reasonably rigorous way. In doing this, we set up an analytical framework based on specific utility and social welfare functions. We provide references to the literature for those who would like to see a more general treatment.
The two-type case
In a seminal paper, the importance of which extends well beyond public economics, James Mirrlees analysed the implications for optimal taxation of an informational constraint on the planner's ability to use lump sum taxation to redistribute income from high- to low-productivity individuals. One reason often given for the impossibility of lump sum taxation relates to the difficulty of finding a tax base which is truly non-distortionary. Taxing wage income distorts labour supply decisions; taxing wealth distorts saving and consumption decisions; taxing goods distorts the pattern of expenditures. On the other hand, if we really know or can observe a consumer's innate productivity type, there is nothing to rule out the simple instruction: pay the tax collector T*i units of income. We do not need to relate the tax to anything except the productivity type of the individual. But this, according to Mirrlees, is the problem. If the planner cannot observe the productivity type of the individual, then lump sum taxation of this kind becomes infeasible.