By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of financial coverage debates at the present time. decreasing public debt; financing social safeguard; taxing capital and bequests; and designing the schooling method suggest enormous inter-generational transfers. The instrument that economists hire to research those matters is the overlapping generations version, which displays the several classes of existence. whilst the version comprises capital accumulation, it additionally permits researchers to formalize the advance of an financial system, concerning its progress 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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Additional info for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
A rise in the return on savings has two effects for the consumer: (1) an income effect, as the revenue from savings will be higher, all other things being equal; (2) a substitution effect, making it proﬁtable to substitute consumption today for consumption tomorrow. When the inter-temporal elasticity of substitution is lower than 1, the substitution effect is dominated by the income effect. In that case, a rise in the rate of return has a negative effect on savings. When the inter-temporal elasticity of substitution is higher than 1, the households are ready to exploit the rise in the remuneration of savings by consuming relatively less today.
However, the proof applies to the limit superior (lim sup) when the limit does not exist. 3). 36 A Theory of Economic Growth Proof: s(w, 1/β) is solution of u (w − s) = u (s/β), which implies w − s = s/β and s(w, 1/β) = βw . 1+β For small k > 0, f (g(k)) > 1/β and g(k) = 1 1 s(ω(k), f (g(k))) ≥ s(ω(k), 1/β), 1+n 1+n as sR ≥ 0 (A4). Hence, g(k) ≥ βω(k) , (1 + β)(1 + n) from which we deduce that g(k) < 1 =⇒ k ω(k) 1+β < (1 + n) . k β The necessary condition for 0 to be a catching point can be converted into a sufﬁcient condition for 0 not to be a catching point.
F (k) Hence, the degree of inter-temporal substitution between consumption when young and consumption when old should not be too small, so that the substitution effect will not be dominated too much by the income effect in the face of changes in the rate of return. Under H3, there exists a function h deﬁned on R++ with values in R++ which satisﬁes, for w > 0, k = h(w) ⇐⇒ (k, w) = 0. 18) In addition, at any point w > 0, we have k(h(w), w) = 0 and we can apply the implicit function theorem: the function h(w) is continuously differentiable at w > 0, with derivative h (w) = − As k(h(w), w) w (h(w), w) = k(h(w), w) sw (w, f (h(w))) .
A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel