1967/05/01 by Lucien Foldes
Economics, Econometrics and Finance · Social Sciences · #Fiscal Policy and Economic Growth #Gender, Labor, and Family Dynamics #Local Government Finance and Decentralization
paper · doi:10.2307/2552486
In an article which appeared in the February issue of this Journal', I considered the problem of income redistribution when the government does not know the preferences of individuals, but must nevertheless take definite decisions as to the quantities of all goods to be transferred. It was shown that, in the two-good case, the preferred optimum can be attained for each of two possible patterns of preference (states) by redistributing both goods and allowing resale, assuming that the price lines through the two optima are not parallel (see Figure 2 in the earlier article); but this cannot be done with three states (unless the price lines meet in one point), nor can it be done with two states if the price lines are parallel (but do not coincide). This Note uses the same geometric technique2 to show that it may in certain cases be possible always to attain the preferred optimum even with parallel price lines or with three states, if the government does not decide definitely the quantities to be transferred, but uses a scheme which allows individuals to choose between suitably defined bundles of goods and forbids resale once a choice has been made3. There is an interesting affinity between this theoretical construction and the so-called voucher schemes which have recently been proposed as alternatives to certain social services. The situation with two states and parallel price lines is depicted in Figure 1. In the state whose contract curve is C, the optimum preferred by the government is P, corresponding to the allocation (xA, YA) = (X,Y), (XB, YB) = (l-X, l-y); for the alternative curve C', the preferred optimum is P', with allocation (xA, YA) (X', Y'), (XB, YB) = (-X', l-y').4 The government can now adopt the following scheme: it decrees that all individuals must surrender their initial endowments, informs each A thathe may choose to receive in exchange either of the bundles (x, y) and (x',y'), and each B that he may choose either (1-x, l-y) or (l-x', l-y'), with-