1. Household Production and Life-Cycle and Labor Supply

2. Household Production
As in the study of labor demand, we can alter the variables to explore the impacts of utility maximization and the accompanying income and substitution effects of labor supply.
In the previous analysis, we ignored household production. Household production of goods and services is an alternative to participation in the labor force and purchased goods and services that flow from that participation.

3. Assumptions
Two alternatives: Purchased goods and services that come from working for pay and home produced goods and services that come from hours spent at home.
Hours spent at home are directly related to home produced goods.
Assume that leisure is zero
Single decision-maker
Household does not save or borrow

4. Graphical Model
Value of purchased goods and services on Y axis and hours spend at home on the X axis (proxies value of home production)
Hours spent at home = 16 hours - Hours spent working for pay
Hh = 16 – H
Value of purchased goods and services is equal to Y = W x H
Constraint is similar to previous model with a slope of -W
Indifference curves or utility isoquants assume that home produced goods (GS) and services and substitutes for purchased goods and services (Hh)
The utility isoquants are convex reflecting that:
High GS and low Hh : ΔGS/ΔHh is high or isoquant is steeper
Low GS and high Hh : ΔGS/ΔHh is low or isoquant is flatter

5. Ray from the origin reflects ration of GS to Hh
If GS/Hh is high, ΔGS/ΔHh is also relatively high. When you an extra hour of Hh one has to give up a lot of purchased goods and services to remain equally well off. Why? At low levels of Hh time spend at home is more highly valued relative to GS.
If GS/Hh is low, ΔGS/ΔHh is also relatively low. When you an extra hour of Hh one has to give up only a few purchased goods and services to remain equally well off. Why? At high levels of Hh time spend at home is less highly valued relative to GS.
Work preferrer has a flatter isoquant.
Home preferrer has a steeper isoquant.

6. Figure 7.1 The Production of Child Care

7. Changes in Wages
Changes in wages changes the “income/wage” constraint and produces income and substitution effects.
The choice between time spent in the household and the time spent at work depends upon income and substitution effects
The observed increases in participation rate of women and the convergence of participation rates with men indicates that the substitution effect has outweighed the income effect but the relatively strength of the substitution effect has been diminishing as participation rates approach those of men.

9. Tripartite Choice
The analysis can be expanded by including the labor-leisure choice. Households must decide between time at work, time in household production and time spent in leisure.
Two income and substitution effects as wages change. For example, as wages rise,
Substitute time in household for time at work
Initially, time at household can more easily be given up through labor-saving devices and childcare. However, as participation rates and hours worked of breadwinners rises, this becomes more difficult.
Substitute leisure for time at work
Leisure activities usually require time so it is more difficult to substitute for them
This may explain the initial rapid increase in participation and hours worked and why the trend is diminishing.

10. Figure 7.2 Large versus Small Substitution Effects Attendant to a Wage Increase

11. Joint Labor Supply Decisions
Dropping the assumption of one decision-maker, economists have looked at models of joint labor supply:
Retain single decision-maker either home dictator or identical preferences.
Bargaining process with resources determining bargaining power.
Act independently, but consider the impacts of their actions on the other party.

12. Figure 7.3 Home versus Market Productivities

13. Specialization: household utility maximization with different productivities.
Productivity in work place
Productivity at home (household productivity and satisfaction from child-rearing).
Some studies demonstrate the division of housework depends on the relative wage
Many households maximize utility with both individuals working. See graph.
Cross effects: Spouse’s decision to work more for pay affects the other spouse household productivity in production or consumption.
If spouses are substitutes in household production, if one spouse works more the other may become more productive and increase the amount of time they stay at home. If they are complements, the other may work more.
If spouses are complements in consumption, the other may work more. Substitutes in consumption reflect a problematic marriage so…

14. Household Productivity in Recessions
Recession causes spouse to become unemployed:
The unemployed workers productivity at work drops and the opportunity cost of working at home goes down.
The relative productivity of the worker’s spouse rises if their potential wages do not change.
Substitute unemployed worker for spouse’s participation in household production and the spouse goes to work.
As family income falls, less goods and services and less leisure time are demanded.
This creates an “additional worker” effect.

15. On the other hand, the expected wage of either spouse may have also fallen.
Decreases in expected wages create a substitution effect towards less work and more leisure.
This would tend to create a “discouraged worker” effect.
Discouraged and part-time workers are part of “hidden” unemployment.

16. Life Cycle Aspects
Dynamic preferences or labor productivity at home and changing labor participation patterns
Presence of young children can make an indifference curve steeper and the absence of younger children make the indifference curve flatter.
Presence of a disabled child, parent or spouse could also have similar effects.

17. Figure 7.4 Household Productivity Can Change over the Life Cycle

18. Figure 7.5 Life-Cycle Allocation of Time

19. An individual or household unit strives to maximize its present discounted wealth, which includes both wages from work and the value of household production.
Individuals will work the most in those years with the greatest difference between wages and productivity at home.
Scheduling vacations with market wage and household productivity. (e.g. Chile in the summer)
Once time is considered, life-time wealth and the expected wage path that generates the life-time wealth may become more important that current wages.
If wage increase is expected, meaning that it follows the expected wage path, it will not change life-time wealth. Therefore, the change in expected wages will create only a substitution effect.
If the wage increases is unexpected, meaning the expected wage path changes, it will change life-time income. This will generate both a substitution and an income effect.

20. Choice of Retirement Age
The budget constraint: See spreadsheet.
Increases in social security benefits:
Increase in the fixed amount of benefits in each retirement year
No substitution effect and retirement would be accelerated.
Decrease in penalties from delaying retirement retirement (higher net wages in later years)
Create a substitution effect towards later retirement
Create an income effect to retire earlier
If the decision is between participation and non-participation, the substitution effect is likely to dominate

22. Figure 7.6 Choice of Optimum Retirement Age for Hypothetical Worker (based on data in Table 7.2)

23. Child Care
Forty percent of US families pay for child care and cost about 7% of family income.
Child care costs involve fixed costs so that the average cost for limited child care is more than for full child care.
Reducing the fixed costs of care:
Assume a level of non-earned income
Cover the fixed cost of child care
Person not working chooses to work
Person not working chooses to continue not to work
Person working will choose to work less

24. Figure 7.7 Labor Supply and Fixed Child-Care Costs: A Parent Initially out of the Labor Force

25. Figure 7.8 Labor Supply and Fixed Child-Care Costs: A Parent Initially Working for Pay

26. Reducing the costs of hourly care
The hourly child care costs are like a tax rate on wages
A subsidy that reduces hourly wages would act like a wage increase
Substitution effect towards more work
A strong substitution effect for those out of the labor force and likely to increase participation rates
Income effect towards more work
Subsidy that reduce both the fixed and hourly costs increase participation rates but have an ambiguous effect on hours worked among those in the labor force.

27. Child Support Assurance
Many children in poverty live in single-parent households. One persistent problem is that the absent parent often does not contribute to the children’s financial support.
Programs that guarantee government support when private support is not forthcoming are likely to affect the labor supply decision of the single-parent.
The budget constraint:
Work
Work and welfare guaranteeing a given income
Work and welfare and guaranteed child support regardless of income.

28. Figure 7.10 A Single Parent Who Joins the Labor Force after Child Support Assurance Program Adopted

29. Figure 7.9 Budget Constraints Facing a Single Parent before and after Child Support Assurance Program Adopted