Here an individual will not even work the first hour because he will be able to keep and consume only 5 units of output, and therefore enjoy utility of only 5, which is less than the disutility of work of 6, and so forth /l In this example, individuals decide not to work at all, so that social welfare is zero. If, however, the example is altered and individuals lose a smaller fraction of their output, they will work a positive amount. This also means that a positive amount would be taken from them, which raises two complications. First, whoever takes output will have it to consume - in other words what is taken will still contribute to social welfare Second the incentives to work of whoever takes from others have to be reexamined. Bu neither of these complications changes the conclusion that the amount of work and the ut level of social welfare will generally deviate from the optimal Another point to be noted in the absence of property rights is that it is possible that individuals will choose to work more than the optimal number of hours, not less Suppose that having a certain minimum amount of output to consume is important for subsistence. Then, to guarantee that he will retain this amount after others have taken some output from him, an individual might well be inclined to work more than he otherwise would. Although total output Suppose, for instance, that the individuals in the model are identical to one another and each has the opportunity not only to work and produce, but also freely to take a fraction of the output of another person. Then an individual's incentives to work will remain undesirable, for it will still be true that in deciding whether to work an extra hour, the individual will know that he will not be able to keep the full amount of what he produces in the hour Formally, we can show that individuals will work too little under certain assumptions. Let a be the fraction of the output that is taken, w be hours of work and also output produced, u( w) be utility from utput consumed, where u/ (w)>0 and u(w)<0, and d(w) be disutility of work, where d ()>0 and d(w >0. It is socially optimal for w to maximize u)-dow), implying that the optimal w satisfies u(w) d (w): let w* be the optimal w. If a fraction a is taken from individuals, however, then if w is the work the identical individuals generally choose, each particular individual will be able to take aw from another Hence, each individual will select his w to maximize u(aw +(1-a)w)-dw), implying that(1-a)u(at +(1 - w)=d(w). But in equilibrium, w=w so that we must have(1-a)u(w)=d (w ). This means that w <w*(implicit differentiation of (1-a)u (w)=d(w)with respect to a shows that w is decreasing n a, and w* corresponds to a=0) This possibility, that individuals might work more in the absence of property rights than in their presence, is occasionally -and mistakenly--interpreted as an argument against property rights. As I am about to explain, when individuals do work more in the absence of property rights, social welfare still tends to be lower than in the presence of property rights. The issue in question is whether the absence of property rights affects work incentives in such a way as to reduce social welfare, not whether work effort and production themselves fall or rise. Consider the foll situation Hours of work Output Utility from output Disutility from Social welfare 0 Chapter 7-Page 4Here an individual will not even work the first hour because he will be able to keep and consume only .5 units of output, and therefore enjoy utility of only 5, which is less than the disutility of work of 6, and so forth.// In this example, individuals decide not to work at all, so that social welfare is zero. If, however, the example is altered and individuals lose a smaller fraction of their output, they will work a positive amount. This also means that a positive amount would be taken from them, which raises two complications. First, whoever takes output will have it to consume -- in other words, what is taken will still contribute to social welfare. Second, the incentives to work of whoever takes from others have to be reexamined. But neither of these complications changes the conclusion that the amount of work and the level of social welfare will generally deviate from the optimal.4 Another point to be noted in the absence of property rights is that it is possible that individuals will choose to work more than the optimal number of hours, not less.5 Suppose that having a certain minimum amount of output to consume is important for subsistence. Then, to guarantee that he will retain this amount after others have taken some output from him, an individual might well be inclined to work more than he otherwise would.6 Although total output 4 Suppose, for instance, that the individuals in the model are identical to one another and each has the opportunity not only to work and produce, but also freely to take a fraction of the output of another person. Then an individual=s incentives to work will remain undesirable, for it will still be true that in deciding whether to work an extra hour, the individual will know that he will not be able to keep the full amount of what he produces in the hour. Formally, we can show that individuals will work too little under certain assumptions. Let " be the fraction of the output that is taken, w be hours of work and also output produced, u(w) be utility from output consumed, where u'(w) > 0 and u''(w) < 0, and d(w) be disutility of work, where d'(w) > 0 and d''(w) > 0. It is socially optimal for w to maximize u(w) ! d(w), implying that the optimal w satisfies u'(w) = d'(w); let w* be the optimal w. If a fraction " is taken from individuals, however, then if we is the work the identical individuals generally choose, each particular individual will be able to take "we from another. Hence, each individual will select his w to maximize u("we + (1 ! ")w) ! d(w), implying that (1 ! ")u'("we + (1 ! ")w) = d'(w). But in equilibrium, w = we , so that we must have (1 ! ")u'(we ) = d'(we ). This means that we < w* (implicit differentiation of (1 ! ")u'(we ) = d'(we ) with respect to " shows that we is decreasing in ",and w* corresponds to " = 0). 5 This possibility, that individuals might work more in the absence of property rights than in their presence, is occasionally -- and mistakenly -- interpreted as an argument against property rights. As I am about to explain, when individuals do work more in the absence of property rights, social welfare still tends to be lower than in the presence of property rights. The issue in question is whether the absence of property rights affects work incentives in such a way as to reduce social welfare, not whether work effort and production themselves fall or rise. 6 Consider the following situation. Hours of work Output Utility from output Disutility from work Social welfare 0 0 0 0 0 1 1 40 2 38 2 2 45 10 35 Chapter 7 - Page 4