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The aim of the optimal income taxation literature is to make precise the limits to redistribution implied by behavioural responses to progressive taxation. In its modern form, as expressed by Mirrlees (1971), the optimal tax problem is essentially a problem of hidden information. The taxation authority wishes to tax individuals on the basis of ability, but is not privy to this information. The best it can do is tax labour income, a quantity that depends on both ability and effort. Mirrlees (1971) and Guesnerie (1981) have shown that the planner can do no better than to invite individuals to report their ability, and to design a mechanism such that it is in each person's interest to do so.
While the standard optimal income taxation paradigm has provided many insights into the incentive effects of tax policies, it may be criticised for not taking into account the complete arsenal of policy instruments that governments may (and actually do) use for redistributive purposes.(1) One such instrument, of current theoretical and policy interest, is workfare. The incentive effects of workfare programmes have been studied in detail by Besley and Coate (1992, 1995). They consider a world in which required work is of no productive value. Among their conclusions is that workfare may play a part in optimal income maintenance schemes. Nevertheless, work requirements are not desirable if the planner wishes to design a least-cost utility maintenance programme.
That work requirements are optimal only in non-welfarist settings appears to be somewhat paradoxical. In both the nonlinear income tax model and the income maintenance model, the labour supply of low-ability individuals is distorted downward. However, Guesnerie and Roberts (1984) have shown that it is almost always optimal to impose a small, personalised increase in a good whose allocation is subject to a downward distortion. Of course, this apparent paradox is easily resolved by recognising that market labour supply and unproductive required work are different goods. In the absence of information asymmetries, the former has marginal social value equal to the wage rate, whilst the latter has a zero shadow price. It seems reasonable, therefore, to interpret the utility maintenance results of Besley and Coate (1995) as stating that the marginal value of workfare as a screening device is insufficient to overcome the initial discrepancy between the value of market work and the value of required work.
This study has two aims: to identify how productive required work must be in order for it to become part of an optimal policy mix; and to identify who should be required to take part in workfare programmes. I employ the standard nonlinear taxation model of Guesnerie and Seade (1982), with the addition of a third good, required work.(2) Required work produces some output, but its marginal product may differ from that of market work. The taxation authority is assumed to maximise some Paretian, inequality-averse social welfare function, subject to self-selection constraints and a materials balance constraint.
After spelling out the general features of optimal nonlinear taxation with work requirements, I present a special case of the model, the two-agent economy. I show that it is optimal to implement a workfare scheme for low-ability workers when required work is sufficiently productive. When low-ability workers supply a positive amount of labour, required work need not be as productive as the market work. However, when low-productivity workers are out of the labour force, required work must produce enough output to compensate these workers for their foregone leisure. This value is determined by preferences and not by productivity. Given that much of the policy debate focuses on workfare for those out of work, this finding is potentially of much importance.
The remainder of the paper is organized as follows. The next section describes the model, and gives some general properties of its solution. An analysis of the two-agent version of the model is presented in Section 3. The fourth and final section contains some comments on the relationship of this study to the policy debate on workfare. Proofs are gathered in an Appendix.
2. The model
The most general form of economy considered in this paper consists of H individuals, who may be partitioned into n types according to their productivity. The number of individuals of type i is denoted by [[Pi].sub.i]. The productivity of an individual of type i is given by [w.sub.i]. Types are ordered such that [w.sub.1] [less than] [w.sub.2] [less than] ... [less than] [w.sub.n]. The production sector is assumed to exhibit constant returns to scale, and the labour market is perfectly competitive. Under these assumptions, the before-tax labour income of an individual i is given by
[y.sub.i]: = [w.sub.i][l.sub.i] (1)
where [l.sub.i] is the supply of market labour by person i.
In addition to market work, the planner may require an amount of workfare, [r.sub.i], from each individual of type i. Although the total amount of after-programme consumption enjoyed by an individual may depend on participation in the workfare scheme, required work is not paid a wage at the margin. One unit of required work is assumed to produce [Gamma] units of output, regardless of the individual providing the work.(3) Each person has preferences over a consumption good, x, and time spent working, t, represented by
u(x, t): = x - h(t) (2)
The function h([center dot]) is assumed to be increasing, strictly convex and twice continuously differentiable. This form of utility function is exactly the one adopted by Besley and Coate (1995), and is maintained here to allow for comparisons of the present study with theirs. Moreover, it is widely known that quasi-linear utility functions add much to the tractability of screening problems, especially when there are more than two types of individuals. For some of the results below, the following regularity condition is assumed.
Assumption 1 h[double prime](t)/h[prime](t) is non-increasing in t.
Assumption 1 restricts the curvature of h([center dot]), limiting it to grow no faster than an exponential function. It is satisfied by the often-used quadratic function.
For any individual of type i, the planner can observe [y.sub.i], but not [w.sub.i]. The …