Allocating Time: Individuals' Technologies, Household Technology, Perfect Substitutes, and Specialization

In an efficient household if the spouses' time inputs are perfect substitutes, then spouses will "specialize" regardless of their preferences and the governance structure. That is, both spouses will not allocate time to both household production and the market sector. The perfect substitutes assumption implies that spouses' "unilateral" production functions (i.e., the household production function when only one spouse allocates time to home production) are closely related, satisfying a highly restrictive condition that I call "compatibility." I introduce the "correspondence assumption", which postulates that the unilateral production functions in a newly formed household coincide with individuals' production functions before they enter marriage. The correspondence assumption provides a plausible account of the genesis of household technology and simplifies its estimation. I introduce the "additivity assumption" which postulates that the household production function is the sum of the spouses' unilateral production functions and argue that additivity is implicit in much of the new home economics. Together, the correspondence and additivity assumptions imply that individuals' technologies reveal the entire household technology. I show that perfect substitutes, additivity and concavity imply that the household production function is of the same form as the unilateral production functions, exhibits constant returns to scale, and depends on the spouses' total time inputs, measured in efficiency units.