Family Utility Maximization

1. Family Utility Maximization The goal of the family is to maximize utility by choosing a combination of home work and market work.

2. Household production You can cook and eat a steak at home or you can go out to eat a steak. The household production takes time to prepare. The way we will look at household production is to say for every hour devoted to household production, like cooking a steak at home, the person generates a certain dollar amount of goods and services. In order to go out and have a steak we will assume the person has to work first to generate the income to make the purchase in the market. So the wage rate indicates the purchasing power of the person.

3. Jack and Jill Jack and Jill live in the same house. Jack can make $20 an hour in the labor market, but only $10 an hour worth of stuff if he works in the household. Jill can make $15 an hour outside the house and $25 an hour inside the house. Let’s assume that each will only work a total of ten hours a day at either work in the house or in the labor market. Thus the household will have a total of 20 hours of work. Let’s look at a new graph - one with market goods on the vertical axis and household goods on the horizontal axis.

4. Household opportunities - budget market goods $ 3 1 2 Jack’s Jill’s Households 4 5 6 Household goods $

5. Household budget If Jack spent all his time working in the market he could make $200 and be at point 1. If he spent all his time in the household he could make $100 and be at point 4. If Jill spent all her time working in the market she could make $150 and be at point 2. If she spent all her time in the household she could make $250 and be at point 5. Let’s combine the two. If they both spend all their time outside the house they would be at point 3. Now say they would have one of them stay home for 1 hour a day. Who should do it? Jill would give up a $15 wage, but make up $25 at home. Jack would give up a $20 wage and make $10 at home.

6. Household budget For each dollar in wage given up, Jill makes back $1.67 while Jack only makes back only $0.50. So to have the greatest opportunities Jill would spend the first hour at home. In fact she would always spend time at home first, if they decide they want less market goods. The household budget is parallel to hers up to the point where she stays at home for her whole ten hours. Then the budget rotates and becomes parallel to Jacks.

7. Who works where? Market goods $ Depending on the households preferences (which influence the shape of the indifference curves), the house could be at points like a, b, or c. I have shown this house as being best off at point b. b c a Household goods $

8. Who works where? At points like a Jill works totally in the house and Jack splits his time between house and work. At points like b Jill splits her time (maybe not evenly) between house and work and Jack totally works. At point c Jill is totally at home and Jack is totally at work.

9. Indifference curves Market goods $ Households with steep indifference curves value household relatively more because in order to have the same utility as it has at the start they must be given much more market goods than on a flat indifference curve. Household goods $

10. Increase Jack’s wage An increase in Jack’s wage rotates his and the household opportunity set. If the house started at point a, the higher wage may induce Jack to withdraw from household production all together. This seems like the old days in America. market goods $ b 3 1 2 Jack’s Jill’s Households a 4 5 6 Household goods $

11. Change in culture Market goods $ Indifference curves used to reflect our relatively strong desire for household production. With no change in wage, but change in shape of indifference curves we she the Jills of the world begin to work outside of the home, like at point b. b a Household goods

12. Increase in Jill’s wage As Jill’s wage increases the household utility can be increased because of the greater opportunities available to the household. market goods $ 3 b 1 2 a Jack’s Jill’s Households 4 5 6 Household goods $

13. Household production The household production is design to highlight features about the labor market that have lead to the increase in the number of women who participate in the labor market. The two main points are women are earning more per hour than they used to make and indifference curves seem to be coming flatter, i.e., our society is putting les emphasis on household production.

14. Market $ One specializes in market work and one does some market work Point of specialization Person with comp. Adv at home does first amount of home work If additional home work is desired it will come from person with comparative advantage in market work Home $ The PPF shows the combinations the family can have.

15. Market $ Steep indifference curves are for families with relatively strong preference for home produced goods. The logic is because to get them to give up a $1’s worth of home goods they have to be given back a relatively large amount of market value. What is needed in return. Give up $1 Home $

16. Market $ u1 u2 u3 u4 Here the family can not get to u4. u1 or u2 can be had, but the family is happier at u3. Note at u3 the indifference curve is just tangent to the ppf – the slopes are equal or the curves touch at one point Home $ The family here, with steep indifference curves, has a relative preference for home production.

17. The previous screen has a family that has a relatively strong preference for home production. The best choice for them is to have one person totally specialize in home production (the one with the comparative advantage in home production) and the other to do some home production along with some market work. The next screen has a family that has a relatively strong preference for market production. The best choice for them is to have one person totally specialize in market production (the one with a comparative advantage in market production) and the other to do some home production along with some market work.

18. Market $ u1 u2 u3 u4 Home $

19. Market $ u1 u2 u3 u4 This family has complete specialization. One does only market work and one does only home work. Home $

20. Market $ u1 u2 u3 u4 Here we show a family with the same preferences over time. But market wages have risen. The family has changed from complete specialization to having only one worker specialize and the other worker do some of both types of work. after before Home $

21. Market $ u1 u2 u3 u4 The solid indifference curves represent a family in an earlier time. The dashed curves represent the same family, but after a change in preferences. after before Home $ The family has changed from complete specialization to having only one worker specialize and the other worker do some of both types of work.

22. In this section we have viewed the economic way of thinking about the family decision to allocate time between market work and home work. In the end we saw that either a change in wages or preferences at the family level could have the family change form complete specialization to having both adults in the family participate in the labor market.