Aggregation with two-member households and home production

This note explores the problem of family labor supply decision in an economy with two-member households, joint home production, and fixed cost of joint labor supply. Even though the labor supply decisions are not indivisible per se, the presence of such fixed cost and partners with unequal labor productivity create non-convexities. The note shows how lotteries as in Rogerson (1988) can again be used to convexify consumption sets, and we perform aggregation over individual preferences. The main result demonstrated in the paper is that aggregate preferences of males do not differ from individual level ones. However, for females, the disutility of non-market work at the aggregate becomes separable from market work, but keeps its original (logarithmic) form, while the female labor elasticity of the market hours supply increases from unity to infinity.