Abstract
The dynamics of inequality are studied in a model of human capital accumulation with credit constraints. This model admits a multiplicity of steady state skill ratios that exhibit varying degrees of inequality across households. The main result studies equilibrium paths. It is shown that an equilibrium sequence of skill ratios must converge monotonically to the smallest steady state that exceeds the initial ratio for that sequence. Convergence is “gradual" in that the steady state is not achieved in finite time. On the other hand, if the initial skill ratio exceeds the largest steady state, convergence to a steady state is immediate.
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This paper is based on unpublished notes from 1990; see http://www.econ.nyu.edu/user/debraj/DevEcon/Notes/incdist.pdf. Two considerations suggest that these results may be worth reporting in print. First, the existence of a sizeable recent literature indicates that these relatively early notes may have value outside a filing cabinet or a private webpage. Second, Mukul Majumdar’s own research on economic growth with a nonconvex technology is an even earlier precursor to some of this literature, so the current outlet – a special issue in his honor – seems appropriate. Conversations with Glenn Loury simplified the proof of the main result. I thank Dilip Mookherjee for many useful discussions, and two anonymous referees for helpful comments on an earlier draft. Funding from the National Science Foundation under grant number 0241070 is acknowledged. This paper is dedicated with much affection and warm admiration to Mukul Majumdar – or to Mukulda, as I always think of him – on the occasion of his 60th birthday.
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Ray, D. On the dynamics of inequality. Economic Theory 29, 291–306 (2006). https://doi.org/10.1007/s00199-005-0021-2
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DOI: https://doi.org/10.1007/s00199-005-0021-2