Exponential Income Distribution and General Equilibrium Growth: A Survey for the United Kingdom

Abstract

We provide a theoretical demonstration that an exponential income distribution will emerge spontaneously in a standard Arrow-Debreu general equilibrium model, which is intended to describe the income structure of the low- and middle-class in a well-functioning free-market country. Furthermore, we find, theoretically, that a parameter μ in the exponential income distribution has a linear relationship with unemployment compensation. In this paper, we test this relationship for the United Kingdom from 2001 to 2015. Our empirical investigation confirms that the income structure of low and middle class exactly obeys exponential distribution, in which the fitting parameter μ is exactly in line with the evolution of unemployment compensation in the United Kingdom. In particular, our analyses indicate that, at each time point of economic evolution, the technological choice in industries should match the existing labor and capital stock; otherwise, general equilibria will be broken. Based on this finding, we propose an index for measuring the potential deviation from general equilibria. For the United Kingdom, we empirically observe a significant deviation from general equilibria around 2008.

Keywords: General equilibrium; Income distribution; Economic growth; Technological progress

JEL Classification: D31; D51; O40