Redistribution in cash rather than kind is traditionally advocated by economists for the simple reason that cash preserves the option of buying the in-kind transfer on the open market and hence is never inferior from the viewpoint of the consumer. Yet, this proposition only aggregates up for society as a whole when there are no distortionary wedges between the private and social benefits of individual behaviour. In particular, if lump-sum taxation is not feasible, then transfers in-kind and other quantitative restrictions may raise welfare above the levels achievable via taxation alone (see Guesnerie and Roberts (1984) or Blackorby and Donaldson (1988) for instance). This possibility is analysed here, by examining the optimality of a stylised form of one common type of transfer: the self-selection scheme. Along with a full set of linear taxes and a universal lump-sum tax, the government offers consumers a bundle of goods, accompanied by a flat rate charge (which may be zero). For these goods, consumers choose between the private market where they can buy unrestricted amounts, or the fixed ration provided by the government. If they opt in for the government product they are unable to top it up in the private sector, even if an identical good is available. Healthcare, education and public sector housing programmes are often of this kind. In the UK health sector, for instance, consumers choose between a more or less set level of provision in the public sector, supplied at zero charge or buy in the private market. As relatively simple adjuncts to linear taxes, in-kind transfer schemes may make it possible to achieve some of the welfare gains of non-linear taxes. Examining transfers in-kind also enables us to bridge the gap between the conditions governing optimal linear taxes and those representing non-linear taxes. Previous articles, by Nichols and Zeckhauser (1982), Blinder and Rosen (1985) and Blackorby and Donaldson (1988) look at simple examples in two good economies. In the Nichols and Zeckhauser model, the government aims to redistribute income between two agents, using a mixture of cash and an inferior good, given in-kind, plus a cap on pre tax income. No charge is levied, but as the proportion of the total aid given in-kind increases, the attractiveness of the package diminishes for high income agents. Thus low income families remain in while high income households opt out into the private sector. Blinder and Rosen's paper compares the excess burden of subsidies with'notches' or sharp jumps in budget constraints. If agents consume more than a fixed amount of a favoured good they receive a lump-sum, otherwise, they get

* This paper is based on part of my D. Phil thesis on transfers in-kind. Thanks are due to my supervisor, David Bevan, two anonymous referees, seminar participants at the Universities of McMaster and Stirling and the sixth World Congress of the Econometric Society, Barcelona, and the editors of this JOURNAL for their helpful comments. A technical appendix is available from the author upon request.