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Allocation of time in ideal family: golden ratio as a means of survival in preindustrial societies and its applications in modern family

Malakhov, Sergey (2021): Allocation of time in ideal family: golden ratio as a means of survival in preindustrial societies and its applications in modern family.

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Abstract

The paper analyzes the model of the preindustrial family where the hunter and the housewife share the quarry and leisure. The model discovers multiple equilibria in marriage markets, where mating of unlikes results in unequal allocation of leisure time, while mating of likes equalizes leisure time of spouses, but the allocation of homework time stays unfair for both inferior and superior partners. There is a unique equilibrium solution when the hunter fairly supplies both leisure and consumption in exchange for housewife’s attractiveness and home productivity. The proportions of the allocation of time in this ideal family match with the properties of golden ratio. However, golden ratio leaves for spouses only six hours and a half for common leisure. This result corresponds to field studies of natural sleep in African and Latin American preindustrial societies and to the historical analysis of sleeping habits before the industrial revolution in Europe, when people went to sleep after sunset and awakened before sunrise, breaking the sleep at midnight for household activities, praying, and conceiving. The correspondence between the model and results of applied and historical studies provides a basis for the hypothesis, that in preindustrial societies the family was a means of survival, and leisure was limited by the vital need in sleeping time. The need in six hours and a half is also confirmed by actual statistics of sleeping time in France. In general, the model of ideal family challenges modern trends in allocation of time, but its analytics discovers the difference between economic viability and feasibility, when the mating of likes gets an additional time with respect to limits of working hours and raises the total leisure time to current leisure habits of working spouses.

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