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Library Introduction to The Economic Theory_1

Trong mô hình của Mirrlees "với các tiện ích phụ gia, là tốt nhất đầu tiên có tất cả các cá nhân với mức tiêu thụ bình đẳng, và những người có năng suất cao hơn, có một disutility thấp hơn để tạo ra một thu nhập nhất định, được phân công làm việc nhiều hơn và do đó có một tiện ích thấp hơn. | Utilitarian Pricing of Annuities 111 Figure 13.1. First-best allocation of utilities. while Vh 1 ph ph L y Eh 1 1 ph Thus the utilitarian first best has inequality in expected utilities but may have equality in consumption levels Arrow 1992 . This result is similar to Mirrlees 1971 optimum income tax model where individuals differ in productivity.2 The first best allocation provides higher expected utility to those with a higher capacity to produce utility. In the appendix to this chapter it is shown that 0 1 pn h -1 ch dph 13.7 while dch dpj Ệ 0 for j h h j 1 2 . . . n. 2 In Mirrlees model with additive utilities the first best has all individuals with equal consumption and those with higher productivity having a lower disutility for generating a given income are assigned to work more and hence have a lower utility. 112 Chapter 13 Concavity of u and 13.7 imply d V dứ u ch 1 pn u cn Ị 0 13.8 Ơ ph d pn while d V. dpj Ệ 0 j h j 1 2 . H.3 Thus with the given total resources an increase in one individual s survival probability decreases his or her optimum consumption but the positive effect of higher survival probability on expected utility dominates. The effect on the welfare of other individuals facing only resource redistribution depends on the shape of the social welfare function. 13.2 Competitive Annuity Market with Full Information In a competitive market with full information on the survival probabilities of individuals and a zero rate of interest the price of a unit of second-period consumption c2h is equal to the survival probability of each annuitant. Individuals maximize expected utility subject to a budget constraint C1h phC2h yh h 1 . H 13.9 where yh is the given income of individual h. Demands for first- and second-period consumption annuities C1h and c2h are given by C1h C2h Ch yh 1 ph . The first-best allocation can be supported by a competitive annuity market accompanied by an optimum income allocation. Equating consumption levels under competition Ch