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Income Sustainability

Some Heroic Assumptions Our task here is very ambitious, being nothing less than rigorously elucidating a strong quantitative theoretical relationship among the four fundamental economic concepts of: (1) Department of Economics, Harvard University (mweitzman@harvard.edu). As will become clear, this paper is in the nature of an essay that attempts to enlarge upon, clarify, and unify my own approach to what might be called ìthe pure theory of perfectly complete national income accounting.î I do not attempt to do a proper survey or evaluation of the many other views on this vast subject. 1 ìwealthî; (2) ìincomeî; (3) ìsustainabilityî; (4) ìaccountingî. In the course of dealing with these four fundamental economic concepts, we will be forced to deal also with such background concepts as ìconsumptionî, ìinvestmentî, ìinvestment pricesî, ìcapitalî, ìthe rate of returnî(on investment, in units of consumption), and so forth. We will not get very far in the analysis without making several heroic assumptions that greatly simplify the problem under consideration via a particular ìtoy model.î I believe that the heroic simplifying assumptions behind this toy model may be acceptable at a high level of abstraction because they will allow us to obtain sharp neat results, which can then serve as a conceptual point of departure for further analysis and applications.1 First of all, for utmost simplicity, I assume in this toy model that there is just one consumption good. (More generally the single consumption good could be interpreted as the ìgainîor ìpayo§îof the system.) The assumption of a single consumption good allows for an unambiguous measure of ìtheîrate of return along a consumption-e¢ cient trajectory, which, when this rate of return is additionally assumed to be constant over time, will play an important role in what follows. The rate of return in any period (along an e¢ cient trajectory) is the extra consumption that could be obtained next period from curtailing consumption in this period by one unit, but otherwise leaving the rest of the e¢ cient trajectory as is.2 The strong assumption of a single composite consumption good is stark, but it might be approximately appropriate for an ideal index number of aggregate consumption. In any event, I need this assumption, along with the further assumption of a constant rate of return, to get very sharp results. E§ectively I am assuming the situation is ìas ifîthe utility function is linear in consumption and the welfare criterion is ìas ifîit is present discounted consumption at the given constant rate of return. The more complicated general case of multiple consumption goods and a nonlinear utility function is treated in Weitzman (2003, Chapter 6, ìThe Pure Theory of Perfectly Complete National Income Accountingî), which the interested reader might consult.3 Here I am aiming at expositional simplicity.