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 safety; taxing capital and bequests; and designing the schooling approach suggest vast inter-generational transfers. The instrument that economists hire to investigate those concerns is the overlapping generations version, which displays different classes of lifestyles. while the version comprises capital accumulation, it additionally permits researchers to formalize the improvement of an financial system, touching on 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 incorporates its significant coverage implications.
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Additional resources for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
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.
17) is then equivalent to (kt+1 , ω(kt )) = 0, which is equivalent to kt+1 = g(kt ). The derivative of g is g (k) = h (ω(k))ω (k) = sw (ω(k), f (g(k)))ω (k) . 1 + n − sR (ω(k), f (g(k))) f (g(k)) Competitive Equilibria 25 One important difﬁculty for applications is that the hypothesis H3 is not directly formulated in terms of preferences and technologies and depends on the equilibrium values of k and w. Thus, it is useful to have the following sufﬁcient condition for uniqueness. Assumption A4. The utility function veriﬁes ∀c > 0, u (c) + cu (c) ≥ 0.
K. S. 2. K. S. 6 38 A Theory of Economic Growth A ﬁrst conclusion that we can drawn from these ﬁgures is that savings rate of the post-war (World War II) period in most of the countries are well above their pre-war level. Notice that the post-war period is also the period that experienced the highest growth rate in output per head. As stressed by Maddison (1992), “there is a general positive relationship between the faster post-war growth period in output per head and the acceleration in savings rate, and a similar positive relation in the post 1973 slowdown.