Question

19. Consider a household where the husband can earn a market wage of $15 per hour and has a marginal productivity in the household that is the equivalent of $12. The wife can earn a market wage of $20 and has a marginal productivity in the household that is the equivalent of $15. Suppose initially that their marginal household productivities do not depend on the time that the otherspouse spends at home.

19a. If the couple decides to have only one of them work for pay outside the home, who should it be?

19b. Would it make sense for both the husband and wife to work for pay outside of the home?

19c. Assuming both members of the couple are working, how would an increase in the wife’s wage affect her work hours? Would an increase in the wife’s wage cause the husband to increase or decrease his work hours?

19d. How would your answer to 20c be different if you knew that the couple were substitutes in household production?

19e. How would your answer to 20c be different if you knew that the couple were complementary in household consumption?

Answer 1

19a. A household’s total production will be maximized when the spouse with the highest net gain from market work is the one who works for pay. Even though the wife is more productive at home than the husband, the net gain to the household of having the wife work is $5, while the net gain to having the husband work is $3. For every hour the wife works and the husband stays at home, the household produces the equivalent of $32, while having the husband work and the wife stay at home would result in only $27.

19b. Yes, since an extra hour of market work allows each to buy at least enough goods and services to compensate for the hour of lost production time at home.

19c. An increase in the wife’s wage would decrease her work hours if the income effect of the wage increase dominated the substitution effect. On the other hand, work hours would increase if the substitution effect of the wage increase dominated the income effect. Empirical studies suggest that the latter is the more common occurrence for women. The income effect associated with the wife’s wage increase reduces the husband’s incentive to work for pay provided there are no cross effects on the husband’s household marginal productivity or the marginal utility that the husband derives from household consumption.

19d. If the husband and wife are substitutes in household production, an increase in the wife’s work hours will increase her household marginal productivity, creating an incentive for the husband to spend more time in household production and less time in market work.

19e. If the husband and wife are complements in the consumption of household commodities, an increase in the wife’s work hours will decrease the utility the husband derives from the additional consumption of household commodities and create an incentive to spend more time in market work.