By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of monetary coverage debates this day. lowering public debt; financing social safeguard; taxing capital and bequests; and designing the schooling process indicate significant inter-generational transfers. The instrument that economists hire to research those matters 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, concerning its development route to the discounts habit of younger brokers. the purpose of this e-book 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
4. 8. Rational inter-temporal equilibrium. In the left panel, there is a multiplicity of solutions kt+1 ; agents do not know what will be the expectations of the others and thus face non-unique Rt+1 with perfect foresight. In the right panel, for any level of kt , there is always a unique solution kt+1 , and there is thus a rational inter-temporal equilibrium. 6 capital dynamics at a rational inter-temporal equilibrium With the assumptions H1, H2, and H3 there exists a unique inter-temporal equilibrium with perfect foresight given the initial capital stock k0 : the rational inter-temporal equilibrium.
When the factors of production are poorly substitutable (CES production function with ρ > 0), there are either no or two non-trivial steady states (plus the case of one steady state when the function is tangent to the 45◦ line, which is not illustrated). When the corner steady state is the only steady state, it is globally stable. If there are two non-trivial steady states, the higher one is locally stable and so is the corner one. 3 The Behavior Near 0 We have deﬁned g(0) = g(0+), allowing us to obtain a function g(k) increasing and continuous on R+ and differentiable on R++ .
This demand scheme results from the assumption of constant returns to scale. 18 A Theory of Economic Growth The equilibrium on the goods market is Yt = Nt−1 dt + Nt (ct + st ). 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.
A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel