In the following section, an indifference curve describes the preferences of an individual for numbers of two goods, X and Y, which might be chocolates and apples. An individual may be indifferent to whether he has 2X plus 10Y, or 5X plus 5Y, or 10X plus 2Y, or various other combinations.

7. The Individual's Supply Of Labour In this chapter we apply the theory of choice to aspects of the supply of a productive service - labour. In particular, we consider the choice of an individual member of the labour force as to how many hours per week he will undertake. As always, we need to know about three factors in order to set the problem up in manageable form - the objects of choice, the constraints upon choice, and the tastes which govern the choice. Once these are properly defined subsequent analysis is straightforward. Consider first the objects of choice. At first glance one might think of each member of the labour force being faced with a choice between work and leisure but a moment's reflection makes it apparent that only one item is in fact being chosen. When hours to be worked have been selected, the number of hours available for leisure are already determined and vice versa. In mentioning work and leisure we are specifying one of the objects of choice, and in our analysis it is convenient to deal explicitly with leisure and hence implicitly with work. As our individual gives up leisure, he receives wage payments in recompense for his efforts. He gains income - the ability to purchase consumption goods - and the objects of choice for him are therefore income and leisure. We measure income along the vertical axis of figure 7.1 and leisure along the horizontal axis. Now let us consider the the constraint upon the individual's choice. First of all there is the obvious physical constraint that limits the number of hours of leisure available in a week to the number of hours that there are in the week. This point is given by L0 on the horizontal axis of figure 7.1. Working is only one source of income, there is no reason why any person cannot also receive unearned income. Such income receipts are common indeed in a modern economy in which the state provides a number of services to individuals. Free education for children, health insurance - and so forth, are all part of income but receipt of them does not depend in any way upon hours worked. More Figure 7.1 The choice between combinations of income and leisure. Note that hours worked may be measured moving to the left from L0. Viewed in this way the diagram depicts the choice of the best available of a 'good' (income) and a 'bad' (work). The individual here chooses to work L0 - L2 for a wage income y2 - y0. traditional forms of unearned income accruing from ownership of wealth belong here as well. Thus there is no reason to suppose that the level of income associated with not working, i.e. with L0 hours of leisure per week, is zero. In figure 7.1 it is assumed to be y0 and the budget constraint is drawn vertically up to this level of income. Beyond this point, however, more income can only be obtained by working and hence by sacrificing leisure. Each hour worked increases income by the hourly wage the individual can command. Hence the slope of the budget constraint above point L0y0 is given by the wage rate, with a negative sign of course, showing the rate at which income can be substituted for leisure. It is clearly not possible to continue the constraint to cut the vertical axis since no individual can work every hour of the week without some 'leisure' time being devoted to eating and sleeping. Thus there is a cut-off at some minimum amount of leisure L1 and an associated maximum income level of y1. Thus the constraint on the choice we are analysing is characterised by a kinked relationship such as shown in figure 7.1. The continuity of the constraint over the range L0y0-L1y1 does imply that the individual may choose the length of his own work week. This is obviously too simple for direct application to modern labour market institutions. Despite this degree of simplification, however, the analysis is of some interest. Figure 7.2 The indifference map implicit in the assumption that, after a certain point, leisure becomes a 'bad'. Moving to the left from L0 the individual would be willing to pay for permission to work for the first few hours. As to the individual's tastes, if income and leisure are both goods in the sense that more of one of them without sacrifice of the other increases satisfaction, then we are safe in characterising them by a conventional indifference map. One may object to this on the grounds that perhaps the first few hours of work a week may actually be a pleasant alternative to the boredom implicit in complete idleness, and prefer indifference curves that actually become upward sloping at high levels of leisure as in figure 7.2. But because this extra complication adds nothing to the analysis that follows we ignore it from now on. This is not to say, though, that the assumption underlying it lacks plausibility..... David Laidler. Introduction to Microeconomics. 1974.