By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of financial coverage debates this day. lowering public debt; financing social safety; taxing capital and bequests; and designing the schooling procedure indicate tremendous inter-generational transfers. The instrument that economists hire to research those matters is the overlapping generations version, which displays the several sessions of lifestyles. while the version contains capital accumulation, it additionally permits researchers to formalize the improvement of an economic climate, referring to its progress route to the mark downs 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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Additional resources for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
13. GDP per capita in the world. GDP per capita is increasing from one generation to the next in all countries for all periods. 7 comparison of myopic and perfect foresight Although the assumption of myopic foresight is no longer used in the literature, it has long been viewed as a useful framework in macro-economics. For example, Lucas and Rapping (1969) see myopic foresight as a good approximation when the growth rates of prices are stable. 14. GDP per capita in the most developed countries. The GDP per capita in the most developed countries converges to a similar growth path.
It is possible to analyze these questions in a simple way, which is the following. Considering a given wage w > 0, we look for a capital stock k such that the expectations of the rate of return R(k) = f (k) will lead to a savings decision s(w, f (k)) corresponding to the level of capital accumulation. In other words, given w > 0, we wonder whether it is possible to solve for k the equation19 (k, w) ≡ (1 + n)k − s(w, f (k)) = 0. For the existence, it is enough to prove that the limits of (k, w) when k goes to 0 and when k goes to +∞ are of opposite sign.
3 The Properties of the Savings Function The savings function s(w, R) = arg max[u(w − s) + βu(R s)] will be central in the subsequent analysis. It is thus useful to analyze its properties. It is characterized by the marginal condition φ(s, w, R) ≡ −u (w − s) + βRu (R s) = 0. 9) In models with uncertainty this coefﬁcient σ (d) has another interpretation. It is the reciprocal of the coefﬁcient of relative risk aversion. e. for w > 0 and R > 0. 2) and differentiate φ(s, w, R) = 0: φs ds + φw dw + φR dR = 0, in which φs = u (w − s) + βR2 u (R s) < 0, φw = −u (w − s) > 0, φR = βu (R s) + βR s u (R s) = βu (R s) 1 − 1 , σ (R s) where σ (R s) = u (R s) −R s u (R s) is the inter-temporal elasticity of substitution evaluated at d = R s.
A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel