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Becker's (1965) paper, 'A Theory of the Allocation of Time' revolutionised the modelling of household behaviour, by unifying Marshallian demand functions for goods with labour supply and related time use decisions within the household. In this article, we first summarise Becker's time allocation model and associated key contributions, then we show how his original framework extends to modern collective household models. Becker, G.S. (1965). 'A theory of the allocation of time', Economic Journal, vol. 75(299), pp. 493–517.
Chiappori et al. (Sun,) studied this question.