THE use of withholding taxes on a pay-asyou-go basis is by now accepted and permanent, at least in the English-speaking countries. introduction of this system in the United Kingdom, during World War II, had certain effects which are measured statistically in this article and which are of theotetical and historical interest. effects on output of reductions in the tax rates under the pay-as-yougo system are also measured. To date, the literature on the subject of taxation and individual-worker incentive has been largely theoretical, but not empirical. With respect to the theoretical discussion of taxes and individual incentive, Professor Frank Knight early submitted the hypothesis that for rational men the effect of a direct income tax is to induce increased effort to overcome lost income.' Were this hypothesis true, modern governments would face no major incentive problem. government could operate in confidence that the collecting arm would not depress output in the course of tax collection. However, Professor Lionel Robbins expanded the formal analysis of this problem some years ago.2 In the course of his argument, Robbins pointed out that the relation of work to income depends upon the elasticity of demand for income in terms of effort, and that this elasticity is not always less than unity. If it is less than unity the Knight hypothesis holds, for a tax on wages will then induce an increase in work done. But if it is greater than unity, the opposite effect holds. Whether it will be greater or less than unity depends upon the subjective utility valuation placed upon work as opposed to leisure by the individual worker. It is implicit that this in turn depends at least in part on such external objective conditions as the availability of incentives or inducement to overcome wages lost by taxes. It is further conditioned by the sociological and cultural milieu in which workers' attitudes are formed. A working class which aspires to an ever-increasing share of the world's goods will conceivably be more prone to work to overcome a tax than one which has no such aspirations. Dr. Richard Goode has expressed the same idea in other terms. . . imposition of an income tax is equivalent to a reduction in the price of leisure and . . . like other price reductions, it has a substitution effect and an income effect. substitution effect suggests that more leisure will be bought at a lower price. income effect, however, is less clear. 3 Since the theoretical formulation, particularly Robbins', is, of course, purely formal and a rather obvious truism, it is not possible a priori to predict the effect of a direct income tax on leisure or incentive. tax might (i) induce a reduction of the amount of work done and an increase in the consumption of leisure, (2) have the opposite effect, or (3) have no effect on the work-leisure relationship depending upon the elasticity conditions premised above. Actually, some individuals will respond one way, some another, to tax changes. Empirical measurements are needed to show how many responses in each direction take place. Non* assistance of the Social Science Research Council, under whose auspices a study of the United Kingdom cotton industry was conducted by Mr. Rolfe, of which this paper is a by-product, is gratefully acknowledged. Helpful suggestions from Professors Milton Friedman, William Baumol, Ely Devons, and Dr. Gideon Rosenbluth are also acknowledged. Errors of fact or judgment remain the authors' responsibility, as usual. 1 Cf. Frank Knight, Risk, Uncertainty and Profit, ist ed. (Boston, I92I), II7-II8. hypothesis was based on the assumption of declining marginal utility of incremental income. elasticity of demand for income was assumed to be less than unity. 2Lionel Robbins, On the Elasticity of Demand for Income in Terms of Effort, Economica (June I930), 123-29. Reprinted in Readings in the Theory of Income Distribution (Philadelphia, I946), 237-44. Richard Goode, The Income Tax and the Supply of Labor, Journal of Political Economy, LVII (October I949),
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