Invisible hand equilibrium in family: the gravitation between men and women in marriage markets

The marginal analysis of consumer and producer behavior under wage and price dispersion discovers some previously unknown properties of optimality. Both parts in transaction are making satisficing choices, which unintentionally optimize their allocation of time, for a seller between production and services and for a buyer between labor, search, and leisure. This implicit optimization process results in a particular equilibrium, which can be regarded as the proof for the Invisible hand. Marriage markets can also produce the Invisible hand equilibrium close to the mating of unlikes but with some important differences. On commodity market corner solutions simply limit consumer behavior, but in marriage market they actively work and result in disequilibria of unhappy families, where either a husband or a wife starts to search leisure time with another partner and create the implicit polygamy. But Becker’s conclusion on polygamy as a substitution of one superior mate by several inferiors is true only for female polygamy or polyandry. For male polygamy, the optimal choice represents the total of opposite corner solutions, when an unattractive woman is complemented by an attractive lady, who cannot be chosen alone. While the ambiguous substitution effect of dowry can escape from corner solution, the substitution effect of bride price moves the family to the corner solution and results in the phenomenon of Femme Fatale Fate. Wealthy men and beautiful women really attract each other due to strong gravitational fields of both parts in transaction. But at the equilibrium a beautiful woman reduces the attractiveness of her partner’s wealth and cuts the time horizon of happy family. If the husband tries to support his attractiveness by gifts, the equilibrium fails, and a beautiful wife comes to the corner solution and searches for another partner. It is therefore not surprising that the common family position for a beautiful woman is the role of ‘beloved wife’ in the polygamy, either explicit or implicit, where she can efficiently use her strong gravitational field.