will be higher when individuals in the model work more than is optimal, social welfare will tend to be lower than optimal This is for two reasons: The hours that individuals work in excess of the optimal number may be hours for which the disutility of work is high(the disutility of work may grow as the number of hours left in the day diminishes) the extra output may be unevenly distributed, contributing relatively little to an individual's utility if he already has substantial output Socially optimal outcome is achievable under property rights: where each individual has rights in his own output. If each individual has possessory rights in the output he produces, he will work the socially optimal amount and social welfare will be maximized. This is one of the classic arguments for the desirability of property rights. In particular, an individual with possessory rights will know that he will be able to consume what he produces and thus he will compare the utility from the output he produces by orking an extra hour to the disutility of work effort. In Example 1, individuals will hoose to work two hours, the optimal amount. another way of expressing why social optimality will result is that the goal of each individual will coincide with the social goal Socially optimal outcome is achievable under property rightS: where a supervisory entity has rights in an individuals output. a different regime in which the socially optimal outcome may result involves an entity that enjoys possessory rights individuals'output and that can supervise individuals'work. Such a supervisory entit might, for example, be a single-person owner of a farm. If a supervisory entity can monitor individuals'work, then, through use of appropriate rewards or punishments, it may be able to ensure that they work the optimal amount. Whether a supervisory entitys incentives will lead it to choose the optimal outcome, and how a regime with supervisory entities compares to a regime with individuals as possessors of property rights in their Notice here that an individual gains most of his utility from the first unit of output (interpreted as that of what they produce, so that it would take two hours to obtain one unit of output, an individual woul talf necessary for subsistence)and that working one hour is socially optimal. But if individuals would lose work two hours: his welfare would then be 40-10=30. whereas if he would work one hour his welfare would be only 20-2=18(assuming the utility from 5 unit of output is 20) IThis is the case in the example of the previous note, where the second hour of work creates output that would be worth only 5 but involves extra disutility of 8 STo demonstrate the latter possibility, let us assume that individuals are identical and that there is a probability p that each person will lose a fraction a of his output and an equal probability of the independent event that he will obtain a of someone else's output. Then(using the notation from note 4)an individual's expected utility will be Pu p)u(w)-dw); the terms correspond to the events that he loses a of his output and gains a of another person's, that he does not lose any of his but gains a of another persons, and so forth. Because he will select w to maximize his expected utility, and because w =w in equilibrium, we obtain the equilibrium conditionp(I-au(w)+(1- p)pu(1+a)+ (1-a)(1-p)pu((1-a))+(1-p)(w)=d (w). Now the third term on the left side of this condition can be arbitrarily higher than u (w), for(1-a)w<1. Hence, the left side may exceed d(w*), implying hat w>w"*is possible; that is, the equilibrium may be such that individuals work more and produce more than is optimal. They are also worse off than in the optimal situation. To see explicitly why this is so, note hat, as is readily shown, if they work w and retain their entire output for sure, individuals are better off than in the risky situation, but we know that when they retain their output, they are better off working w* Chapter 7-Page 5will be higher when individuals in the model work more than is optimal, social welfare will tend to be lower than optimal. This is for two reasons: The hours that individuals work in excess of the optimal number may be hours for which the disutility of work is high (the disutility of work may grow as the number of hours left in the day diminishes);7 the extra output may be unevenly distributed, contributing relatively little to an individual=s utility if he already has substantial output.8 Socially optimal outcome is achievable under property rights: where each individual has rights in his own output. If each individual has possessory rights in the output he produces, he will work the socially optimal amount and social welfare will be maximized. This is one of the classic arguments for the desirability of property rights. In particular, an individual with possessory rights will know that he will be able to consume what he produces and thus he will compare the utility from the output he produces by working an extra hour to the disutility of work effort. In Example 1, individuals will choose to work two hours, the optimal amount. Another way of expressing why social optimality will result is that the goal of each individual will coincide with the social goal. Socially optimal outcome is achievable under property rights: where a supervisory entity has rights in an individual’s output. A different regime in which the socially optimal outcome may result involves an entity that enjoys possessory rights in individuals’ output and that can supervise individuals’ work. Such a supervisory entity might, for example, be a single-person owner of a farm. If a supervisory entity can monitor individuals’ work, then, through use of appropriate rewards or punishments, it may be able to ensure that they work the optimal amount. Whether a supervisory entity’s incentives will lead it to choose the optimal outcome, and how a regime with supervisory entities compares to a regime with individuals as possessors of property rights in their Notice here that an individual gains most of his utility from the first unit of output (interpreted as that necessary for subsistence) and that working one hour is socially optimal. But if individuals would lose half of what they produce, so that it would take two hours to obtain one unit of output, an individual would work two hours: his welfare would then be 40 ! 10 = 30, whereas if he would work one hour, his welfare would be only 20 ! 2 = 18 (assuming the utility from .5 unit of output is 20). 7 This is the case in the example of the previous note, where the second hour of work creates output that would be worth only 5 but involves extra disutility of 8. 8 To demonstrate the latter possibility, let us assume that individuals are identical and that there is a probability p that each person will lose a fraction " of his output and an equal probability of the independent event that he will obtain " of someone else’s output. Then (using the notation from note 4) an individual’s expected utility will be p2 u((1 ! ")w + "we ) + (1 ! p)pu(w + "we ) + p(1 ! p)u((1 ! ")w) + (1 ! p) 2 u(w) ! d(w); the terms correspond to the events that he loses " of his output and gains " of another person’s, that he does not lose any of his but gains " of another person’s, and so forth. Because he will select w to maximize his expected utility, and because w = we in equilibrium, we obtain the equilibrium condition p2 (1 ! ")u'(we ) + (1 ! p)pu'((1 + ")we ) + (1 ! ")(1 ! p)pu'((1 ! ")we ) + (1 ! p) 2 u'(we ) = d'(we ). Now the third term on the left side of this condition can be arbitrarily higher than u'(we ), for (1 ! ")we < we . Hence, the left side may exceed d'(w*), implying that we > w* is possible; that is, the equilibrium may be such that individuals work more and produce more than is optimal. They are also worse off than in the optimal situation. To see explicitly why this is so, note that, as is readily shown, if they work we and retain their entire output for sure, individuals are better off than in the risky situation; but we know that when they retain their output, they are better off working w* than we . Chapter 7 - Page 5