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A Theory of Economic Growth: Dynamics and Policy in by David de la Croix, Philippe Michel

By David de la Croix, Philippe Michel

Inter-generational transfers are on the heart of monetary coverage debates this present day. decreasing public debt; financing social safety; taxing capital and bequests; and designing the schooling method indicate vast inter-generational transfers. The device that economists hire to research those concerns is the overlapping generations version, which displays different sessions of lifestyles. whilst the version comprises capital accumulation, it additionally permits researchers to formalize the improvement of an economic system, bearing on its development route to the rate 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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U (xt+1 ct ) Rt+1 12 A Theory of Economic Growth Using the definition of xt+1 and rearranging, we have e −u dt+1 dRet+1 dRet+1 dxt+1 e = = σ d . t+1 e e xt+1 Ret+1 Ret+1 u dt+1 dt+1 e )/ Hence, the size of the effect of dRet+1 /Ret+1 on dxt+1 /xt+1 is given by u (dt+1 e e [−u (dt+1 )dt+1 ]. The quantity − u (d) ≡ σ (d) > 0 du (d) is the reciprocal of the elasticity of marginal utility evaluated at d in absolute value. The effect of a change in the expected rate of return on consumption is captured by σ (d).

13) It results from the equilibrium in the labor market, from the equality between effective and distributed profits, and from the budget constraint of the households. Indeed, we have Nt (ct + st ) = Nt wt = Nt [ f (kt ) − kt f (kt )] = Yt − Kt f (kt ), Nt−1 dt = Nt−1 Rt st−1 = Rt Kt = Kt f (kt ). The temporary equilibrium can now be defined as follows. 1 (Temporary equilibrium) Given the variables from the previous period {st−1 , It−1 = Nt−1 st−1 } and the expected rate of return on savings Ret+1 , the temporary equilibrium of time t is defined by 1.

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. 20). 20) if and only if ω(0) = 0, or equivalently, if and only if f (0) = 0. (savProof: Assume ω(0) = 0. Then, for k > 0, the inequality 0 < g(k) < ω(k) 1+n ings lower than wage) implies g(0) = 0.

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