Divine Proportion of the Invisible Hand: a new look at Adam Smith’s natural theology
Recent research on labor-search-leisure model has described local multiple equilibria of Invisible hand under wage and price dispersion. This paper analyzes the general competitive equilibrium, where the Invisible hand creates harmonic proportions of mutually beneficial exchange. The analysis results in the rigorous mathematical proof that at the general competitive equilibrium both the marginal rate of substitution of leisure for consumption and marginal rate of transformation of production into services are equal to the golden ratio conjugate, whereas both the intensity of consumption and the sales-costs of production ratio are equal to the golden ratio itself, also called the divine proportion. On commodity market the golden ratio conjugate equalizes the gravitation or attractiveness of both seller and buyer. Local monopoly and monopsony disappear, and the competitive equilibrium really becomes perfect. In marriage markets the golden ratio conjugate equalizes the attractiveness of both man and woman and creates the ideal family. These results bring us back to the theological grounds of Adam Smith’s works; it gives a new view on his idea of natural rates of both wages and profit. It really can be argued that there was a good reason to apply the natural theology approach to the analysis of exchange at times of the ‘Wealth of Nations’.