By David de la Croix, Philippe Michel
Inter-generational transfers are on the middle of monetary coverage debates this day. decreasing public debt; financing social safeguard; taxing capital and bequests; and designing the schooling approach indicate mammoth inter-generational transfers. The instrument that economists hire to investigate those concerns is the overlapping generations version, which displays different classes of existence. while the version comprises capital accumulation, it additionally permits researchers to formalize the advance of an economic system, pertaining to its progress route to the reductions habit of younger brokers. the purpose of this booklet is an in-depth research of this version that comes with its significant coverage implications.
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Extra info for A Theory of Economic Growth: Dynamics and Policy in Overlapping Generations
20) is a monotonic sequence. This sequence converges either to a steady state or to a boundary of the interval on which g(k) is deﬁned. The consequence of this proposition is that the dynamics of kt converges either ¯ The equilibrium trajectory never goes to 0, or to +∞, or to a steady state k. from one side of a steady state to the other. We shall thus consider the three ¯ 0) successively. Let us ﬁrst show that unlimited growth of possible cases (∞, k, capital is excluded, which excludes the convergence of kt to +∞.
3 Uniqueness of the Steady State We have seen that when the utility function is logarithmic and the production function is CES with ρ ≤ 0, the positive steady state k is unique and globally stable under perfect foresight. 1). We have also seen a simple case with either multiple positive steady states or no positive steady states; this case arises when the utility function is logarithmic and the production function is CES with ρ > 0. To 44 A Theory of Economic Growth study the number of steady states we can of course use the results on the myopic dynamics, which are simpler.
Savings are smaller than wage income and the ratio of wage to capital tends to zero as capital goes to inﬁnity. In other words, as Jones and Manuelli (1992) stress, the young individuals do not have sufﬁcient income to acquire a stock of capital large enough to sustain long-run growth. 5, we shall see that the allocation chosen by a benevolent planner can display sustained growth. In this case, Jones and Manuelli (1992) argue that income redistribution from the old to the young can ﬁght against the declining wage to capital ratio and achieve sustained growth.