By Peter A. Diamond
During this e-book Peter Diamond analyzes social protection as a selected instance of optimum taxation conception. Assuming an international of incomplete markets and uneven info, he makes use of numerous uncomplicated types to light up the industrial forces that endure on particular social safeguard coverage matters. the point of interest is at the measure of progressivity fascinating in social protection and the layout of incentives to hold up retirement past the earliest age of eligibility for advantages. earlier than studying those versions, Diamond offers introductions to optimum source of revenue tax conception and the idea of incomplete markets. He comprises contemporary theoretical advancements reminiscent of 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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3:4Þ Income Taxation with Time-Consistent Preferences 25 Note the assumption that everyone has the same investment opportunities (r does not vary with n). 4), we can examine the pattern of the optimal consumption replacement rate, c=x, in terms of the degrees of risk aversion when young and when old. 6), we can relate the consumption replacement rate to the level of ﬁrst-period consumption: dðcn =xn Þ cn dcn dxn ¼ À dn xn cn dn xn dn cn R1 ½xn dxn À1 : ð3:7Þ ¼ xn R 2 ½cn xn dn We need to recognize that the indices of risk aversion are evaluated at different consumption levels.
To consider the sign of this relationship, let us examine the derivative of the intertemporal MRS with respect to labor supply: d ux ½x; c; z=n uc uxz À ux ucz uxz =ux À ucz =uc ¼ : ð3:22Þ ¼ dz uc ½x; c; z=n nux uc nðuc Þ 2 Assuming the contemporaneous impact is larger (in percentage terms), we would expect that the absolute value of uxz =ux was larger than that of ucz =uc . But the expression is still ambiguous, depending on the signs of uxz and ucz . 5 Heterogeneous Preferences Saez (2000a) has argued that workers with higher earnings save more relative to earnings, at least in the United States.
Then we would have cn increase with xn but less than one-for-one. 3 Special Case of Second-Period Utility Depending Solely on the Replacement Rate6 An extreme version of the standard-of-living approach is that only relative consumption matters: 6. Another interesting special case would be constant returns to scale for v. 7 The FOC for cn is now G 0 ½xn þ f½cn =xn þ w½1 À yn f 0 ½cn =xn =xn ¼ lr: ð4:13Þ Since xn þ w½1 À yn and xn are increasing in n, it follows that f 0 ½cn =xn is increasing in n, implying that the replacement rate is decreasing in n.