By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of financial coverage debates this present day. decreasing public debt; financing social defense; taxing capital and bequests; and designing the schooling process indicate enormous inter-generational transfers. The device that economists hire to research those concerns is the overlapping generations version, which displays different sessions of existence. while the version contains capital accumulation, it additionally permits researchers to formalize the improvement of an economic climate, touching on its development route to the mark downs 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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Additional info for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
3. This proposition says that if f (0) > 0 it is possible to produce, and hence accumulate, without capital and 0 is not a steady state. Before analyzing the stability properties of the steady states, we precise two deﬁnitions of stability. 20) with initial capital stock k0 converge to k. ¯ |k0 − k| This corresponds to two situations: r If k¯ is an interior steady state ( k¯ > 0), there exists ε > 0 such that ∀k0 ∈ ¯ [ k¯ − ε, k¯ + ε] the dynamics converge to k. 26 A more precise notion of stability (for both local stability and stability in an interval) requires in addition the following condition (Lyapounov stability): ∀ε > 0, ∃y > 0 such that ∀k0 ∈ [ k¯ − y, k¯ + y], the whole dynamics belong to [ k¯ − ε, k¯ + ε].
3 (Rational inter-temporal equilibrium) A rational inter-temporal equilibrium is an inter-temporal equilibrium with perfect foresight such that there exists no other inter-temporal equilibrium with perfect foresight having the same initial capital stock. Note that in the absence of assumption H3 ensuring the uniqueness of the inter-temporal equilibrium, we end in a logic a` la Arrow–Debreu where the way expectations are formed is not treated. 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.
If we can prove that a result is true from time t to time t + 1, and that it is true for the ﬁrst case (here, k0 is given), we can put together a chain of conclusions: Truth for t = 1 implies truth for t = 2, and so on. Pushing the ﬁrst domino causes all of the other dominoes to fall in succession. , such that there exists k > 0 verifying ω(k) = w. 6. Existence of inter-temporal competitive equilibria. When lim k→0 s(w, f (k)) > 0, savings remain positive even when the interest rate goes to inﬁnity.
A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations by David de la Croix, Philippe Michel