By David de la Croix, Philippe Michel

ISBN-10: 0511041780

ISBN-13: 9780511041785

ISBN-10: 0521806429

ISBN-13: 9780521806428

Inter-generational transfers are on the middle of financial coverage debates this day. lowering public debt; financing social safeguard; taxing capital and bequests; and designing the schooling approach indicate colossal inter-generational transfers. The device that economists hire to investigate those matters is the overlapping generations version, which displays the various sessions of existence. while the version contains capital accumulation, it additionally permits researchers to formalize the improvement of an economic climate, referring to its development route to the discount rates 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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Then the limit of the continuous function g(k) = h(ω(k)) is h(ω(0)) > 0. 3. This proposition says that if f (0) > 0 it is possible to produce, and hence accumulate, without capital and 0 is not a steady state. Before analyzing the stability properties of the steady states, we precise two deﬁnitions of stability. 20) with initial capital stock k0 converge to k. ¯ |k0 − k| This corresponds to two situations: r If k¯ is an interior steady state ( k¯ > 0), there exists ε > 0 such that ∀k0 ∈ ¯ [ k¯ − ε, k¯ + ε] the dynamics converge to k.

Assume ω(0) > 0. Then the limit of the continuous function g(k) = h(ω(k)) is h(ω(0)) > 0. 3. This proposition says that if f (0) > 0 it is possible to produce, and hence accumulate, without capital and 0 is not a steady state. Before analyzing the stability properties of the steady states, we precise two deﬁnitions of stability. 20) with initial capital stock k0 converge to k. ¯ |k0 − k| This corresponds to two situations: r If k¯ is an interior steady state ( k¯ > 0), there exists ε > 0 such that ∀k0 ∈ ¯ [ k¯ − ε, k¯ + ε] the dynamics converge to k.

25 In contrast, a recent literature has developed in macroeconomics that exploits the presence of multiple equilibria to understand cycles and growth phenomena. Benhabib and Farmer (1999) survey this approach. 28 A Theory of Economic Growth Let us re-deﬁne the function g for the dynamics to be deﬁned on R+ . The function g(k) is increasing and non-negative. As a bounded and monotonic function on R++ admits a limit, there exists a limit of g(k) when k > 0 goes to 0 and this limit is non-negative: g(0+) = lim k→0, k>0 g(k) ≥ 0.

### A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel

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