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# Household Production Model I: - PowerPoint PPT Presentation

Household Production Model I:. The allocation of time. Household production model. In the household production model, utility is derived from the activities (Z i ) in which people are engaged. U=U(Z 1 , Z 2 ,…, Z N )

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## Household Production Model I:

The allocation of time

### Household production model

• In the household production model, utility is derived from the activities (Zi) in which people are engaged.

• U=U(Z1, Z2,…, ZN)

• Each final commodity is produced and consumed within the household by combining time and purchased inputs.

### Example: college attendance

• College attendance

• Requires time as well as purchased inputs (tuition, books, supplies, etc.)

### Full cost

• The full cost of an activity includes the opportunity cost of time as well as the opportunity cost of purchased inputs.

• Example – college enrollments often increase during recessions due to lower opportunity cost of time.

### Assumptions

• U=U(Z1, Z2,…, ZN)

• Zi=fi(ti,xi)

• Where:

• ti = amount of time devoted to producing and consuming commodity i.

• xi = amount of purchased inputs devoted to producing and consuming commodity i. (This is a composite commodity that is an index of all purchased inputs used in producing final commodities.)

### Constraints

Solving the time constraint for time at work:

Substituting this into the goods constraint results in:

### Full-income constraint

• After a little algebraic manipulation, the full income constraint is given by the formula below.

• The first time is the opportunity cost of goods, the second is the opportunity cost of time.

### Full-income constraint (cont.)

• The full-income constraint may also be expressed as:

• Where FCi = full cost of Zi:

### Applications

• Individuals are assumed to minimize the full cost of consuming any commodity. This model may explain:

• the growth of the fast-food industry,

• why convenience stores can survive while charging higher prices than grocery stores,

• the decline in fertility, and

• why many people do not use coupons in grocery stores.

### Isoquants

• This diagram illustrates the possible combinations of time and purchased inputs to provide a given quantity and quality of meals.

### Indifference curves / isoquants

• An isoquant is also an indifference curve since Zi is held constant.

### Points on an isoquant

• At point A, an individual may prepare meals using basic ingredients such as flour, vegetables, meat, etc.

• the individual is using a large quantity of time, but a relatively low level of purchased inputs.

### Points on an isoquant (cont.)

• At point B, the individual prepares meals of the same quality using prepackaged mixes, frozen meals, and other preprocessed ingredients.

### Points on an isoquant (cont.)

• The individual uses less of his or her own time and more purchased ingredients when producing and consuming meals at point C.

• This may involve meals consumed in restaurants or meals delivered to the home from restaurants.

### Other isoquants

• Points that lie above an isoquant correspond to the production of a higher level of Zi.

### Isocost curves

• Isocost curves have a slope equal to -w/p (the negative of the real wage).

• The level of total costs increase as the level of time and purchased inputs increase.

### Cost minimization

• The least costly combination of time and purchased inputs occurs at the point of tangency between the isoquant curve and an isocost curve.

• This occurs at point E.

### Wage increase: substitution effects

• First type:

• As the wage rate increases, the relative price of time rises and households substitute purchased inputs for time in the production and consumption of a given level of each commodity.

### Substitution effects

• Second type:

• Some activities are inherently more time-intensive than other activities. When the wage rate increases, the relative price of time-intensive activities increases. In response, goods-intensive activities are substituted for time-intensive activities.

• Under both types of substitution effect, a higher wage reduces the quantity of time used in household production and increases the amount of time spent at work.

### Income effect

• An increase in the wagealso increases the quantity of final commodities (Zi) consumed.

• This income effect tends to increase the amount of time required for the production and consumption of these commodities.

x

C

x

B

t

t

B

C

### Backward-bending labor supply curve

• The labor supply curve is upward sloping if the substitution effects are larger in magnitude than the income effect.

• An individual operates on a backward-bending portion of his or her labor supply curve if the income effect is larger than the substitution effects.

### Specialization

• If a household wishes to produce output efficiently, each individual should specialize in those tasks in which he or she possesses a comparative advantage.

• a household member possesses a comparative advantage in an activity if the opportunity cost of the activity is lower for this individual than for any other member of the household.)

• A comparative advantage may exist if:

• an individual is more productive in an activity than other members of the household (in this case an “absolute advantage” is said to occur), or

• because the individual’s time is relatively less valuable in alternative activities.

### Gender division of labor

• Historically, married women have tended to specialize in household production and married males have tended to specialize in market production.

• Comparative advantage for women in household production in the past?

• Possible reasons:

• high completed fertility rates,

• high infant mortality rates, and

• labor market discrimination.

### Evolving gender roles

• As infant mortality and completed fertility rates decline and as female wage rates rise, it is expected that this division of labor between spouses will be altered.

• In recent years, married women have substantially increased the amount of time spent in the paid labor market and have spent slightly less in household production).

• Married men now spend slightly more time in household production than in the past.

### Specialization or shared activities?

• Both spouses will tend to work together in household production tasks in which their time is complementary

• Individuals will specialize (according to comparative advantage) when one spouse’s time is a substitute for that of the other spouse.

• The labor force participation rate generally declines during recessions as a result of an increase in the number of discouraged workers.

• In a household, however, one spouse may increase his or her labor supply (or enter the labor market) if the other spouse becomes unemployed.

• This “additional worker effect” partly offsets the “discouraged worker effect” discussed earlier.

• The additional worker effect is smaller in magnitude than the discouraged worker effect.

• The additional worker effect is relatively small because the expected wage declines during a recession:E(w) = pw

where: E(w) = expected wage

p = probability of employment

w = wage rate if employed

As the unemployment rate rises during a recession, the probability of being employed, p, declines, leading to a reduction in the expected wage.

### Female labor supply and divorce

• Married women tend to increase their labor supply when a divorce becomes more likely.

• This is partly to prepare for the reduction in the division of labor that occurs after the divorce.

• Empirical evidence suggests that the level of per capita consumption declines by a larger amount in the portion of the splitoff household headed by divorced women.

• The productivity of time in the paid labor force varies over the lifecycle.

• Market wages vary over time as productivity changes.

### Lifecycle labor supply

• individuals are expected to spend more time working in the paid labor market (and less time in household production) when market wage rates are relatively high.

### Labor force participation and childrearing

• Historically, many married females chose to reduce the quantity of labor supplied or leave the labor force during their childbearing years.

### Changes in LFPR for married women

• As fertility levels have declined and market wage rates have increased, a smaller proportion of married working mothers exit the labor force during the childbearing years today than in past decades.

### Social Security & Retirement Age

• an increase in the level of retirement benefits induces individuals to retire earlier.

### Single-parent households and welfare

• Many single parents (typically female) remain out of the labor force

### Child Support Enforcement Act

• the budget constraint facing the custodial parent shifts vertically upward.

• reduces state welfare expenditures even if there is no effect on labor supply

### Child Support Enforcement Act

• Increases labor supply for some welfare recipients who were initially out of the labor force.

### Child Support Enforcement Act

• is expected to reduce labor supply if the custodial parent is initially working.