I would like to thank Paul Zarembka for pointing out what is apparently a very careless mathematical error in my paper. In actual fact, however, my carelessness was not so much a failure to make a correct algebraic substitution as a failure to explain briefly why I changed the form of my analytical equilibrium model equation (8) from that directly implied by the underlying behavioural model-i.e. why I did not use Zarembka's equation (8a). The model set forth in my paper represented an attempt to provide a concise and mathematically rigorous formulation of a phenomenon which was described verbally, in considerably more detail, in an earlier paper published in the Yale Economic Essays. Unfortunately, in my desire to be concise I carelessly forgot to point out in the sentence before equation (8) that for analytic as well as policy purposes I was separating the employment probability variable, 7r(t), from the percentage urbanrural wage differential variable, a(t), so that each could be treated independently-i.e., the sentence should have read, Next we specify an aggregate labor supply equation which is a simplified version of equation (1) in the sense that only a one-period time horizon is assumed and the probability variable ('r) for analytical and policy purposes is treated separately from the wage differential variable. Now, having expressed my mea culpa for this carelessness, let me turn to Zarembka's correction and show why he also has been very careless in greatly exaggerating the quantitative significance of my apparent mathematical error. I shall then show why I feel that my equation (8) is a much better way of formulating the labor supply function than is Zarembka's (8a). Briefly, Zarembka shows that if I had made the proper substitution in equation (8) on the basis of my earlier equations (2) and (3), then my equilibrium employment rate could be closely approximated by

Although the starting point for modern discussions of the optimum division of income is the classic formulation of the problem given by A. P. Lerner, it is difficult to find an unambiguous statement of his analysis in the recent literature of welfare economics. Various interpreters, claiming equally the authority of Lerner, have offered differing and often contradictory statements of Lerner's argument and its implications. Lerner himself has noted this fact, remarking somewhat wistfully, that though he feel[s] very pleased . . . with his argument it is nevertheless . . . the least successful of my inventions.' Our purpose in this paper is to show that the puzzlement and suspicion surrounding the Lerner theorem given in chapter 3 of The Economics of Control probably derives from his ambivalent statement of conclusions that allegedly follow from a single argument. For, as we shall see, there is not one Lerner theorem but two, and Lerner proves his case for only one conclusion (and here only under the most restrictive assumptions) and not the other. However the unsubstantiated Lerner conclusion can still be salvaged through a modified conceptualization of the problem. In Section I, we shall summarize Lerner's statement of his theorem on income distribution under conditions of diminishing marginal utility of income and extend the model to accommodate the possibility of increasing marginal utility as well. In Section II, we shall review a recent revision of the theorem in terms of a voting model and suggest how the unanimity conclusion of this model can be preserved even with the existence of risk takers. In Section III, we shall indicate difficulties encountered when it is realized that Lerner's proof applies only to a mild version of his theorem and not to his bolder conclusion that allegedly follows from his argument. Section IV will be devoted to showing that Lerner's egalitarian conclusion can be rigorously vindicated leaving his basic strong theorem intact.