The Economic Theory of Annuities by Eytan Sheshinski 1 pdf
The Economic Theory of Annuities by Eytan Sheshinski_1 pdf
... the following. August 18 , 2007 Time: 11 :22am chapter14.tex 12 4 • Chapter 14 Rewrite (14 .19 ) in the more familiar form: ˆ tS =− 1 1 + λ 1( λ ˆ X + ˆ K ˆ Q) ˆ Q 1 , and substituting from (14 .15 ), ˆ tS ... = R − 1. The indirect utility, ˆ u,is therefore ˆ u(p 1 , p 2 ; α) = ln α p 1 α 1 − α p 2 1 α + R − 1. (15 .3) August 18 , 2007 Time: 11 :22...
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The Economic Theory of Annuities by Eytan Sheshinski_3 ppt
... associated with (11 .18 ). Equations (11 .18 )– (11 . 21) jointly determine positive amounts ˆ a( p a , p x a ; α), ˆ a x (p a , p x a ; α), and ˆ b(p a , p x a ; α). Note first that from (11 .19 )– (11 . 21) , it follows ... dG(α) (11 .28) August 18 , 2007 Time: 10 :40am chapter 11. tex 86 • Chapter 11 To see this, observe that the solution ˆ p a and ˆ p b = 1 satisfying (11 .6) and...
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The Economic Theory of Annuities by Eytan Sheshinski_4 ppt
... 0.0009 01 0.003699 0.008094 0. 014 519 10 6 0.000538 0.002309 0.005 216 0.009766 10 7 0.000 311 0.0 013 94 0.00 318 9 0.006259 10 8 0.00 017 5 0.000 813 0.0 018 30 0.003784 10 9 0.000094 0.000455 0.000974 0.00 213 1 11 0 ... 0.000473 0.0 011 00 11 1 0.000025 0.00 012 5 0.000206 0.000 510 11 2 0.000 012 0.0000 61 0.000078 0.000206 11 3 0.000005 0.000028 0.000024 0.000068 11 4 0.0000...
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The Economic Theory of Annuities by Eytan Sheshinski_5 doc
... because the annuities held by individuals in this class are worth more because of the 5 The change in r(z)is ˙ r(z) = δr 1 δr 1 + (1 − δ)r 2 f 1 (z) f 1 (z) + (1 − δ)r 2 δr 1 + (1 − δ)r 2 f 2 (z) f 2 (z) . The ... firms cannot condition the rate of return on annuities on the level of these expenditures by annuitants. Let the rate of retur...
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The Economic Theory of Annuities by Eytan Sheshinski_6 pdf
... analysis of these unintended bequests (and endowments) see chapter 12 . 5.8 No Annuities: Risk Pooling by Couples It has been observed by Kotlikoff and Spivak (19 81) that, in the absence of an annuity ... 2p 2 u(c 1 /2) + 2p (1 − p)u(c 1 ), where c 0 is per-capita consumption in the first period and c 1 is total consumption in the second period. The second term is th...
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The Economic Theory of Annuities by Eytan Sheshinski_8 potx
... 0, ˆ a 1 = 0, p ≤ p < p b . (16 .14 ) August 18 , 2007 Time: 11 :25am chapter16.tex Chapter 16 • 15 1 Denote by ϕ expected profits in the period -1 market for annuities, ϕ(q 1 1 ) = p p a (q 1 1 − ... that ˆ a 1 and ˆ b 1 depend implicitly on q 1 1 and q 2 1 and on ˜ y 1 1 (p) and ˜ y 2 1 (p), defined above. Thus, the existence and uniqueness of ( ˆ q 1...
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THE ECONOMIC THEORY OF ILLEGAL GOODS: THE CASE OF DRUGS doc
... Henry and Chaloupka, Frank J. The Demand for Illicit Drugs,” Economic Inquiry, 37, No. 3, July 19 99, pp. 4 01- 411 . The Economic Theory of Illegal Goods: the Case of Drugs Gary S. Becker, Kevin ... 13 marginal enforcement costs are zero. Then the RHS of this equation equals zero, which simplifies to 12 b) V q = MR ≡ P (1+ 1/ε d ), or V q /P = 1+ 1/ε d , an...
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The Economic Theory of Annuities_1 pptx
... Pricing of Annuities 11 3 Appendix 11 6 Chapter 14 Optimum Taxation in Pooling Equilibria 11 8 14 .1 Introduction 11 8 14 .2 Equilibrium with Asymmetric Information 11 9 14 .3 Optimum Commodity Taxation 12 2 14 .4 ... Taxation 12 2 14 .4 Optimum Taxation of Annuities 12 5 Appendix 12 9 Chapter 15 Bundling of Annuities and Other Insurance Products 13 1 15 .1 I...
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The Economic Theory of Annuities_2 pptx
... Time: 11 :22am chapter14.tex 12 4 • Chapter 14 Rewrite (14 .19 ) in the more familiar form: ˆ tS =− 1 1 + λ 1( λ ˆ X + ˆ K ˆ Q) ˆ Q 1 , and substituting from (14 .15 ), ˆ tS = λ 1 + λ 1 ˆ X − 1 ˆ K. (14 .20) Equation ... ε 11 = ˆ q a s 11 / ˆ a, ε 12 = ˆ q a s 12 / ˆ a, ε 21 = ˆ q b s 21 / ˆ b, ε 22 = ˆ q b s 22 / ˆ b: ε 11 ˆ t a + ε 12 ˆ t b =−θ − ˆ...
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The Economic Theory of Annuities_3 pdf
... the text. August 18 , 2007 Time: 11 :06am chapter13.tex Chapter 13 • 11 7 Differentiating (13 A .1) with respect to p 2 , (1 + p 2 ) c ∗ 2 ∂c ∗ 1 ∂p 2 = 1 (1 + p 1 ) (1 + p 2 )[ W 11 u (c ∗ 1 ) 2 − ... p 1 ) , (13 A.2) where (using (13 A .1) ) =− (1 + p 1 ) (1 + p 2 )λ 2 W 2 1 W 2 2 [ W 11 W 2 2 − 2W 12 W 1 W 2 + W 22 W 2 1 ] − (1 + p 1 ) W...
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