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(2) Single life: a lock of options and/or a choice? Imagine a world with both men and women in which males are all the same, but there are two types of women. These women differ by their productivity in the market, (Pi. and at home, 13;, for j: 1, 2, with (:52 > 4b] and :72 :a VI . The fraction of women of each type is given by Xi- A male's productivity at home and in the market is 1. Each sex has one unit of time. An efficiency unit of labor supplied to the market earns the wage rate w,- i.e., if a person's productivity in the market is n, then they will earn war for each unit of labor supplied. Suppose that tastes for a single person are given by 9c+ (1 9) ln(n), with 0 :9 q 1, where c is the individual's consumption of market goods and n is the consumption of home goods. A single person produces household goods according to the home production function Mal-\"(u)", with 0 q q 1, where l is the household's labor at home, d represents the inputs of goods into home production, and A is the person's productivity at home. Suppose that d is xed and can be purchased at the price 9'. (Assume that Wm } q.) A married household has tastes represented by 9c/2+ (1 9) rum/2*), again with 0