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Abstract
We characterize the equilibrium of simple dynamic economy with linear production and redistribution, where agents face arbitrary sequences of after tax returns on wealth. This allows us to study the dynamics of the distribution of wealth. We apply our analytical method to illustrate that for an agent with wealth less than or equal to the median, there may be no tradeoff between growth and equality, while there could be a tradeoff between growth and welfare.
Notes
Therefore, if τ = 0 and
produces complete non-distortionary equality in one step.
For ,
is increasing in
, and decreasing in τ because
See also the last sentence of this section to note that letting in the continued fraction also yields the correct solution, x = 0.
More generally, see also Seneta, Theorem 4.14, page 150, and Exercise 4.38, p. 158, and in particular Chatterjee and Seneta, Corollary of Theorem 5, p. 93. Note in particular that the index 2 is the single essential class of indices of , which is aperiodic.