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2000-02-10T09:45:23+00:00
2010-11-12T17:30:13+00:00
2017-10-03T20:13:09+00:00
MARTIN L. WEITZMAN
2010-11-12T17:30:13Z
The linearised Hamiltonian as comprehensive NDP
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https://www.cambridge.org/core/product/93F59F338515984725F062852C5E346E
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(C)Tj
/F1 1 Tf
0.717 0 TD
(\()Tj
/F2 1 Tf
0.3328 0 TD
(t)Tj
/F1 1 Tf
0.3328 0 TD
-0.0002 Tc
(\)\) )Tj
/F2 1 Tf
0.9405 0 TD
(dt)Tj
/F1 1 Tf
0.8328 0 TD
[(,)-11618.2(\(2\))]TJ
-19.7887 -2.3158 TD
(where )Tj
/F2 1 Tf
3.2657 0 TD
0 Tc
(U)Tj
/F1 1 Tf
0.7778 0 TD
(\()Tj
/F2 1 Tf
0.3328 0 TD
(C)Tj
/F1 1 Tf
0.667 0 TD
-0.0001 Tc
0.2476 Tw
(\) is a concave, smoothly differentiable instantaneous utility)Tj
-5.0433 -1.1579 TD
-0.003 Tw
(function with positive rst derivative, while )Tj
/F4 1 Tf
19.7182 0 TD
0 Tc
0 Tw
()Tj
/F1 1 Tf
0.7471 0 TD
-0.0004 Tc
-0.0027 Tw
(is the rate of pure time pref-)Tj
-20.4653 -1.1579 TD
-0.0002 Tc
0 Tw
(erence.)Tj
6.27 0 0 6.27 95.2065 243.9755 Tm
0 Tc
(4)Tj
9.5 0 0 9.5 75.1929 229.8405 Tm
-0.0001 Tc
0.1139 Tw
(As is well known, any instantaneous utility function that is a positive)Tj
-1 -1.1579 TD
0.0884 Tw
(afne transformation of )Tj
/F2 1 Tf
11.0192 0 TD
0 Tc
0 Tw
(U)Tj
/F1 1 Tf
0.7778 0 TD
(\()Tj
/F2 1 Tf
0.3328 0 TD
(C)Tj
/F1 1 Tf
0.667 0 TD
-0.0001 Tc
0.0884 Tw
(\) gives the same welfare ordering as \(2\). For)Tj
-12.7967 -1.1579 TD
0.3403 Tw
[(this reason, the magnitude of \(2\) depends on how utility is scaled.)]TJ
T*
0.128 Tw
(Typically, nothing much is made of this observation because we do not)Tj
T*
0.0259 Tw
(usually attribute importance to such a magnitude. However, in this paper)Tj
T*
0.025 Tw
(it will play a critical role.)Tj
1 -1.1579 TD
0.2979 Tw
[(Consider next the standard optimal growth problem: Maximise)-548(\(2\))]TJ
-1 -1.1579 TD
0.0439 Tw
[(subject to constraints)-294(\(1\))-294(and )]TJ
/F2 1 Tf
13.1 0 TD
0 Tc
0 Tw
(K)Tj
/F1 1 Tf
0.367 0.2105 TD
()Tj
0.4 -0.2105 TD
(\()Tj
/F2 1 Tf
0.3328 0 TD
(t)Tj
/F1 1 Tf
0.3328 0 TD
-0.0002 Tc
(\) )Tj
/F4 1 Tf
0.6267 0 TD
0 Tc
()Tj
/F3 1 Tf
1.1267 0 TD
(I)Tj
/F1 1 Tf
0.3889 0 TD
(\()Tj
/F2 1 Tf
0.3328 0 TD
(t)Tj
/F1 1 Tf
0.3328 0 TD
(\))Tj
/F2 1 Tf
0.3328 0 TD
(,)Tj
/F1 1 Tf
0.5439 0 TD
-0.0001 Tc
0.0439 Tw
[(and obeying the initial condition)]TJ
/F3 1 Tf
-18.2171 -1.1579 TD
0 Tc
0 Tw
(K)Tj
/F1 1 Tf
0.7778 0 TD
-0.0002 Tc
(\(0\) )Tj
/F4 1 Tf
1.4405 0 TD
0 Tc
()Tj
/F3 1 Tf
1.1078 0 TD
(K)Tj
/F1 1 Tf
6.27 0 0 6.27 104.6805 138.7056 Tm
(0)Tj
9.5 0 0 9.5 107.8155 141.8405 Tm
-0.0002 Tc
0.0251 Tw
(, where)Tj
/F3 1 Tf
3.5681 0 TD
0 Tc
0 Tw
(K)Tj
/F1 1 Tf
6.27 0 0 6.27 149.1016 138.7056 Tm
(0)Tj
9.5 0 0 9.5 154.8492 141.8405 Tm
-0.0002 Tc
0.0251 Tw
[(is given.)]TJ
-9.3849 48.8549 TD
0 Tc
0 Tw
(56)Tj
/F2 1 Tf
2 0 TD
-0.0001 Tc
0.025 Tw
(Martin L. Weitzman)Tj
/F1 1 Tf
5.61 0 0 5.61 65.6929 117.1567 Tm
0 Tc
0 Tw
(2)Tj
8.5 0 0 8.5 71.1929 114.3517 Tm
-0.0001 Tc
0.025 Tw
(Mler \(1991\) includes a good discussion of some of the relevant issues here.)Tj
5.61 0 0 5.61 65.6929 107.1567 Tm
0 Tc
0 Tw
(3)Tj
8.5 0 0 8.5 71.1929 104.3517 Tm
-0.0001 Tc
-0.0332 Tw
(For some treatment of the time-dependent case, see Weitzman \(1997\) or Weitzman)Tj
0 -1.1765 TD
-0.0002 Tc
0.0008 Tw
(and Lfgren \(1997\) and the further references cited there. Time dependence intro-)Tj
T*
-0.0001 Tc
(duces a host of unpretty complications, but a modied \(and messy\) version of the)Tj
T*
-0.0002 Tc
0.025 Tw
(result presented here will hold.)Tj
5.61 0 0 5.61 65.6929 67.1567 Tm
0 Tc
0 Tw
(4)Tj
8.5 0 0 8.5 71.1929 64.3517 Tm
-0.0001 Tc
0.0699 Tw
(This particular functional form can be defended on \(what to me is\) a reasonable)Tj
T*
0.025 Tw
(axiomatic basis. See, e.g., Koopmans \(1960\).)Tj
ET
Q
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