By David de la Croix, Philippe Michel
Inter-generational transfers are on the heart of financial coverage debates this day. decreasing public debt; financing social defense; taxing capital and bequests; and designing the schooling process indicate massive inter-generational transfers. The instrument that economists hire to research those concerns is the overlapping generations version, which displays the various sessions of existence. whilst the version contains capital accumulation, it additionally permits researchers to formalize the advance of an economic climate, bearing on its progress route to the discounts habit of younger brokers. the purpose of this publication is an in-depth research of this version that comes with its significant coverage implications.
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Additional info for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
Proof: We ﬁrst study the sign of (k, w) when k tends to +∞. We have the following inequality bearing on the savings function: 0 < s(w, f (k)) < w, 18 19 An extension of the two-period overlapping generations model to uncertain environments is proposed by Demange and Laroque (1999) and (2000). 17) to ﬁnd a function kt = (kt+1 ). , savings are positive and smaller than ﬁrst-period income. This implies 0< w s(w, f (k)) < . k k For a ﬁxed w > 0 the limit of w/ k when k → ∞ is 0. This implies20 lim k→+∞ s(w, f (k)) = 0.
The quantity − u (d) ≡ σ (d) > 0 du (d) is the reciprocal of the elasticity of marginal utility evaluated at d in absolute value. The effect of a change in the expected rate of return on consumption is captured by σ (d). 14 σ (d) measures the percentage change in the ratio dt+1 /ct associated with a one percent change in the rate of return. It measures the willingness of the consumer to shift consumption across time in response to changes in the expected rate of return. 7) is e dt+1 = βRet+1 ct σ , and the parameter σ is the inter-temporal elasticity of substitution, which is independent of d.
1). We have also seen a simple case with either multiple positive steady states or no positive steady states; this case arises when the utility function is logarithmic and the production function is CES with ρ > 0. To 44 A Theory of Economic Growth study the number of steady states we can of course use the results on the myopic dynamics, which are simpler. The savings function s(ω(k), f (k)) is deﬁned by u (ω(k) − s) = β f (k)u ( f (k)s). It depends on the ﬁrst derivatives of u and f . A general condition which is sufﬁcient for uniqueness, like the concavity of g, involves the third derivatives of u and f (see Galor and Ryder (1989)).