Relative capital accumulation with heterogeneous individuals

Abstract

The purpose of this paper is to show how differences in individuals’ labour productivitiescause differences in their accumulation of capital, and thereby analysing the evolution of theincome distribution. There are three cases of interest: (i) the high productive accumulaterelatively more capital [growing inequality], (ii) no individual accumulates relatively morecapital [neutrality], (iii) the low productive accumulate relatively more [diminishinginequality]. Which of these cases is generated depends on the price dynamics (the growth rateof wages and the level of the interest rate relative to the rate of time preference), togetherwith the preferences for consumption. The exact conditions for the price dynamics to generate(i), (ii) and (iii) are derived. Furthermore, since the price dynamics is endogenous in generalequilibrium, we find the conditions for preferences and technology that determine relativecapital accumulation. We find (in general equilibrium) that growing economies typically causethe high productive to accumulate more capital than the low productive if preferences areDecreasing Absolute Risk Aversion, and shrinking economies cause the less productive toaccumulate more (i.e. decumulate less). The relations are reversed for Constant and IncreasingRelative Risk Aversion. The final part of the paper analyses the effects of capital taxation onthe income distribution.