What is a "collective" model of household decision-making? How does a collective model ...

The collective model of household decision-making has partners with their own individual utility functions who bargain over the allocation of each other's time to household production and market work.  Couples in this model determine which partner is relatively more productive at home and which is relatively more productive at market work.  Historically, female wage rates have been less than male wage rates, implying a relatively larger loss in income if the husband stays home to do the household production.  Because of socialization, it has also been the case that wives have been more productive at household activities than husbands.  Both factors account for wives spending more time engaged in household production.  In the future, these roles may change if and to the extent wage inequality between men and women disappears and to the extent that social/cultural attitudes change with respect to gender based differences in relative household productivity.