By Peter A. Diamond
During this publication Peter Diamond analyzes social protection as a specific instance of optimum taxation concept. Assuming a global of incomplete markets and uneven details, he makes use of various uncomplicated versions to light up the industrial forces that undergo on particular social defense coverage concerns. the focal point is at the measure of progressivity fascinating in social safety and the layout of incentives to hold up retirement past the earliest age of eligibility for merits. earlier than studying those versions, Diamond offers introductions to optimum source of revenue tax thought and the idea of incomplete markets. He comprises fresh theoretical advancements equivalent to time-inconsistent personal tastes into his analyses and indicates that distorting taxes and a degree of progressivity in merits are fascinating. Diamond additionally discusses social safety reform, with a spotlight on Germany.
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Extra info for Taxation, incomplete markets, and social security
Schmidt-Hebbel (1999) ﬁnds little impact except relatively in Chile, which also cut its payroll tax rate signiﬁcantly, thereby making it impossible to separate the effects of the change in type of system from the change in tax rate. 2. For an analysis of social security with some examples of time inconsistent preferences and a discussion of normative criteria, see I˙mrohorog˘lu, I˙mrohorog˘lu, and Joines (2000). 34 Chapter 4 Chapter 3 considered a model that could be interpreted as giving the optimal progressive earnings tax and optimal social security beneﬁts for a model with no savings, but rational labor supply decisions.
This suggests that higher earners have lower discount rates. Again using a two-types model, we brieﬂy review his argument to see how it results in a gain from taxing savings. We now use separable utility (with the same function each period) but with different discount rates: u i ½x; c; z=ni ¼ v½x þ di v½c À w½1 À z=ni : ð3:23Þ With full nonlinear taxation, and assuming that the only binding moral hazard constraint is type 1 considering imitating type 2, we can write the problem as follows: Maximizex; c; z f1 ðv½x1 þ d1 v½c1 À w½1 À z1 =n1 Þ þ f2 ðv½x2 þ d2 v½c2 À w½1 À z2 =n2 Þ subject to E þ f1 ðx1 þ rc1 À z1 Þ þ f2 ðx2 þ rc2 À z2 Þ a 0; v½x1 þ d1 v½c1 À w½1 À z1 =n1 b v½x2 þ d1 v½c2 À w½1 À z2 =n1 : ð3:24Þ Income Taxation with Time-Consistent Preferences 31 The ﬁrst-order conditions are as follows: f1 v 0 ½x1 þ mv 0 ½x1 ¼ l f 1 ; f1 d1 v 0 ½c1 þ md1 v 0 ½c1 ¼ l f 1 r; f1 w 0 ½z1 =n1 =n1 þ mw 0 ½z1 =n1 =n1 ¼ Àlf 1 ; f2 v 0 ½x2 À mv 0 ½x2 ¼ l f 2 ; f2 d2 v 0 ½c2 À md1 v 0 ½c2 ¼ l f 2 r; f2 w 0 ½z2 =n2 =n2 þ mw 0 ½z2 =n1 =n1 ¼ Àlf 2 : ð3:25Þ ð3:26Þ ð3:27Þ ð3:28Þ ð3:29Þ ð3:30Þ As in the previous case where everyone had the same (nonseparable) preferences considered above, there is no implicit marginal taxation of savings for the highest skill, as can be seen from the ﬁrst two conditions: v 0 ½x1 d1 ¼ : v 0 ½c1 r ð3:31Þ From the two conditions for type 2: ð f2 À mÞv 0 ½x2 d2 ¼ : 0 ð f2 À mðd1 =d2 ÞÞv ½c2 r ð3:32Þ If and only if d2 ¼ d1 is there no taxation of savings for type 2.
Therefore, having individuals ignore second-period consumption does not change labor supply. The solutions to the ﬁrst-order conditions are not generally the same since the government would choose second-period consumption differently than would a rational saver. That is, the social ﬁrst-order condition G 0 vc ¼ lr ð4:19Þ is generally not the same as the private ﬁrst-order condition vc ¼ r; ð4:20Þ since G 0 varies with n in general. However, if, in addition G 0 is a constant, then, since retirement beneﬁts would not vary, the two models are the same.