A note on parental time allocation

• The Alchian–Allen theorem may be applied to time-allocation decisions.
• A wage increase well raises the demand for leisure relative to parental child care.
• Empirical estimates together with the GAAT imply asymmetries in income elasticities.
• The income elasticity of parental child care must largely exceed that of leisure.
• Our findings impose restrictions on reasonable specifications of utility functions.

We explore the implications of the generalised Alchian–Allen theorem for the labour-leisure-child-care decision of a mother with young children. In this framework we find: (i) For mothers who work only a few hours a week, a rise in wages arguably increases the demand for leisure relative to parental child care; (ii) given empirical evidence that an increase in wages induces mothers to spend less time on leisure and more with children, the generalised Alchian–Allen theorem implies that this requires the income elasticity of parental child care to be substantially higher than that of leisure. This finding, though, imposes substantial restrictions on reasonable specifications of a mother's utility function.