A neo-classical theory of distribution and wealth (Q1075233)

This book presents a class of neoclassical models for the determination of wealth and its distribution between workers and capitalists. Chapter 1 is an introduction to the issues involved in income and wealth distribution. Chapter 2 contains a brief survey of the literature, including the models of Lancaster, Hoel, Pohjola, Machacvzek and Burk. Chapter 3 presents the main results concerning distribution and wealth for an economy where the population is constant. Chapter 4 extends the models to allow for population growth. The implications of the results obtained in chapter 3 and 4 are further discussed in chapter 5. The models presented in chapter 3 distinguish two classes of agents in the economy - workers and capitalists. Workers receive wages as well as dividends for their savings. The residual between output and payments to workers becomes the incomes of capitalists. The production function is neoclassical. The first model assumes that both groups of agents cooperate perfectly to maximize the utility of the stream of aggregate consumption over a specified horizon, which can be either finite or infinite. The optimality conditions are shown to require that the net marginal product of capital equal the rate of change in the marginal utility of aggregate consumption. The second model assumes that workers control wages and they choose a sequence of wages so as to maximize the utility of the stream of wages over the specified horizon. The author shows that the optimality conditions for this economy coincide with those for the cooperative case only under rather restrictive conditions. Thus it is surprising that the optimality conditions for an economy in which capitalists choose a sequence of investments so as to maximize the utility of residual incomes support the cooperative equilibrium under a much less restrictive set of conditions. An interesting question that is raised in section 3.4 is how well the wage policies chosen by workers and the investment policies chosen by capitalists fit together. The author answers this question by considering whether there exists a Nash equilibrium of the investment \((u^ 0)\) and wage \((w^ 0)\) rates such that (i) given \(u^ 0\), \(w^ 0\) constitutes the optimal wage policy for workers, and (ii) given \(w^ 0\), \(u^ 0\) constitutes that optimal policy for capitalists. The author shows that if capitalists and workers are maximizing the present values of consumable residuals and wages, respectively, then for constant savings and investment rates, such a Nash equilibrium exists and coincides with the cooperative equilibrium. That is, the Nash equilibrium values of \((u^ 0,w^ 0)\) maximize the present value of total consumption. Moreover, workers will consume the entire total consumption while capitalists consume nothing. A similar result is shown to hold also in a Nash equilibrium in which capitalists control investment and workers control savings, and can be extended to the case where the role of the state is explicitly taken into account.