... convenience stores can survive while charging highe

1
Household Production Model I

• The allocation of time

2
Household production model

• In the household production model, utility is
  derived from the activities (Zi) in which people
  are engaged.
• UU(Z1, Z2,, ZN)
• Each final commodity is produced and consumed
  within the household by combining time and
  purchased inputs.

3
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.

5
Assumptions

• UU(Z1, Z2,, ZN)
• Zifi(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
7
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.

15
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 individuals 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 spouses 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
  recessionE(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.

31
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.

34
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.

35
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.

40
Child Support Enforcement Act

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