The Optimal Wage Share in Adam Smith

Abstract

Adam Smith explains the origin and causes of the wealth of nations through the operation of a set of institutions within which the growth of average labor productivity is positively related to that of profit. The paper studies this relationship in the simplest case, when it is linear, within a multi-year production model that produces a single good. To simplify, the wage and profit shares of net product are referred to respectively as wage and profit. Since the model doesn’t include rents, the sum of these two variables is always equal to one. In addition, real wage is defined as the amount of the good that the average wage per labor unit can buy and optimal wage as the one with the highest real wage. In this context, the percentage increase in average labor productivity obtained when profit increases from zero to a given level above zero, divided by the given level of this variable, gives the same result for all levels of profit above zero. This quotient depends on productivity growth during the reference period and is referred to as the productivity/profit rate. The main result states that if this rate is less than or equal to one, every increase in profit causes a decrease in real wage, while if it is greater than one, the opposite is true for a certain interval of possible values of profit. Moreover, the optimal wage corresponds to a profit equal to zero in the first case, but higher than zero in the second. Consequently, the economic interest of all wage-earners, which consists of obtaining wages with the greatest possible purchasing power, doesn’t always coincide with the aim of obtaining the largest possible wage, nor with the equivalent purpose of reducing the exploitation rate to its lowest possible level.