By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of financial coverage debates at the present time. lowering public debt; financing social safeguard; taxing capital and bequests; and designing the schooling approach indicate immense inter-generational transfers. The software that economists hire to investigate those concerns is the overlapping generations version, which displays the several sessions of existence. while the version contains capital accumulation, it additionally permits researchers to formalize the advance of an economic climate, touching on its progress route to the reductions habit of younger brokers. the purpose of this e-book is an in-depth research of this version that comes with its significant coverage implications.
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Extra resources for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
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.
6. Existence of inter-temporal competitive equilibria. When lim k→0 s(w, f (k)) > 0, savings remain positive even when the interest rate goes to inﬁnity. When lim k→0 s(w, f (k)) = 0, savings go to zero when the interest rate goes to inﬁnity. In all cases, (k, w) takes positive values for large k and takes negative values for small k. As (k, w) is continuous with respect to k, there always exists at least one k > 0 such that (k, w) = 0. Assumption H3. For all w > 0 and all k > 0, (k, w) = 0 =⇒ k(k, w) > 0, where (k, w) = (1 + n)k − s(w, f (k)), k(k, w) = 1 + n − sR (w, f (k)) f (k).
1+n 1+n The assumption implies that for all small enough k, say 0 < k < ε, we have ω(k) < 1 + n, and thus g(k) < k. k A necessary condition is the following: If 0 is a catching point, then ω(0) = 0. Indeed, if ω(0) > 0, then when k → 0, g(k) = h(ω(k)) converges to h(ω(0)) > 0, and ω(0) > 0 implies that 0 is not an equilibrium. Another necessary condition is obtained under the assumptions A4 and f (0) > 1/β. 2 (Necessary condition for a catching point) Assume A4 and f (0) > 1/β. Then, if 0 is a catching point,29 we have lim k→0 29 ω(k) 1+β ≤ (1 + n) .
A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel