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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 (Z i ) in which people are engaged. U=U(Z 1 , Z 2 ,…, Z N )

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Household production model i l.jpg

Household Production Model I:

The allocation of time


Household production model l.jpg

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.


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Example: college attendance

  • College attendance

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


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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.


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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.)


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Time constraint


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Goods constraint


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Constraints

Solving the time constraint for time at work:

Substituting this into the goods constraint results in:


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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.


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Full-income constraint (cont.)

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

  • Where FCi = full cost of Zi:


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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.


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Isoquants

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


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Indifference curves / isoquants

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


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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.


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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.


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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.


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Other isoquants

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


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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.


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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.


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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.


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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.


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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


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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.


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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.)


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Sources of comparative advantage

  • 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.


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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.


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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.


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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.


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Additional worker effect

  • 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.


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Additional worker effect (cont.)

  • 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.


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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.


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Lifetime labor supply decisions

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

  • Market wages vary over time as productivity changes.


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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.


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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.


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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.


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Social Security & Retirement Age

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


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Single-parent households and welfare

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


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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


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Child Support Enforcement Act

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


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Child Support Enforcement Act

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


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