By David de la Croix, Philippe Michel
Inter-generational transfers are on the heart of financial coverage debates this present day. decreasing public debt; financing social safeguard; taxing capital and bequests; and designing the schooling process suggest monstrous inter-generational transfers. The software that economists hire to research those matters is the overlapping generations version, which displays different sessions of existence. while the version comprises capital accumulation, it additionally permits researchers to formalize the advance of an financial system, concerning its development route to the discounts habit of younger brokers. the purpose of this booklet is an in-depth research of this version that incorporates its significant coverage implications.
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Extra info for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
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). The assumption H3 implies that for any ﬁxed w the curve (k, w) does not intersect the horizontal axis at more than one point.
10 (Stability of monotonic dynamics) Assume H1, H2, and H3, and consider a steady state k¯ > 0. ¯ ≥ 0 (monotonic dynamics with myopic foresight), k¯ In the case where m ( k) is respectively stable, unstable, or non-hyperbolic for the two dynamics when m (k) is respectively <1, >1, or = 1. ¯ < 0, k¯ is stable for the rational dynamics, but it may be In the case where m ( k) stable (m (k) > −1) or unstable (m (k) < −1) for the myopic dynamics. ¯ ≥ 0, we have |m ( k)| ¯ = m ( k) ¯ and the ﬁrst-order stability Proof: When m ( k) ¯ < 0, we have s ω < conditions for the two dynamics are identical.
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. 20) are deﬁned on R+ . 4 (Steady state) ¯ = k. 20) if g( k) particular value k¯ = 0, when g(0) = 0, we say that 0 is a corner steady state.