In this chapter, I have considered the design of a BI/Fr scheme, given that one has been introduced. The purpose has been, not to say that the tax rate should be 30 per cent or 40 per cent, nor to derive simple policy rules, but to explore the structure of the arguments. We have seen some of the consequences of different distributional judgements; we have given a characterization of the equity/efficiency trade-off. In the next chapter, I turn to the choice between the BI/FT scheme and the more complex structure of social insurance and graduated income tax found in most countries.
The special case considered in this Appendix is, like that in the main text, highly simplified, but it does allow for an income effect on labour supply:
where. This function is a version of that used by Deaton ( 1983) to obtain an explicit solution of the optimum linear income tax (see also Tuomala 1990: 77), and has the property that gross earnings are a linear function of the wage rate and lump-sum income. With the linear income tax, this means that net income
w(1 - t)L + B = w(1 - t)L* + (1 - δ)B (A2.2)
It may be noted that this labour supply function is the same as the Cobb-Douglas form where L* = (1 - δ); this form was used in the original article by Mirrlees ( 1971) and in Atkinson ( 1972).
An increase in the basic income reduces labour supply, as recipients 'spend' part of their additional income on increased leisure. The extent of the reduction is measured by the parameter δ, which represents the fraction by which net of tax earnings are reduced for a marginal increase in the basic income (or any other lump sum income). So that δ equal to 0.3