A note on parental time allocation

The Generalized Alchian–allen Theorem: A Slutsky Equation for Relative Demand

“…Consider a familiar labor–leisure–child‐care choice model, as presented, for example, in Minagawa and Upmann (). Here, we extend this model by introducing an ad valorem tax (or subsidy) for external child care.…”

“…Consequently, as the price of pure leisure is higher than the price of parental child care by the cost of external child care, a rise in wages lowers the relative price of pure leisure, and therefore raises the relative demand for leisure. Recently, Minagawa and Upmann () acknowledged the applicability of the Alchian–Allen framework for time allocation problems (of parents with young children) and derived a specific version of the Alchian–Allen theorem with income and endowment effects tailored to this particular application.…”

“…For example, when applied to time allocation problems, the GAAT for unit cost components provides predictions for the change of the ratio of any two types of leisure activities in response to an increase in the wage rate. In particular, as mentioned above, Minagawa and Upmann () addressed the time allocation decisions of a parent with young children and explored the wage effect on the demand ratio of pure leisure and parental child care. As we shall see, their result may be regarded as a limiting case of the GAAT (for unit cost components) when the consumer possesses a positive initial endowment of only one good (time) and cannot consume this good (leisure time) in excess of his/her initial endowment.…”

“…Although Ramey and Ramey () found no empirical support for income effects as a possible explanation for why educated parents spend more child care time, several researchers have criticized their methodology (cf., the Comments and Discussion section of Ramey and Ramey ). See also the Discussion section of Minagawa and Upmann ().…”

“…See, for example, Gould and Segall (), Borcherding and Silberberg (), Umbeck (), Leffler (), Bertonazzi, Maloney, and McCormick (), Cowen and Tabarrok (), Sobel and Garrett (), Razzolini, Shughart, and Tollison (), Bauman (), Hummels and Skiba (), Lawson and Raymer (), Nesbit (), Saito (), Liu (), Minagawa (), Minagawa and Upmann (), and Minagawa and Upmann ().…”