chapter7

# chapter7 - Theallocationoftime (Zi)in U=U(Z1,Z2,ZN...

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Household Production Model I: The allocation of time

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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 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.)

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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.
Assumptions U=U(Z 1 , Z 2 ,…, Z N ) Z i =f i (t i ,x i ) Where: t i  = amount of time devoted to producing  and consuming commodity  i . x i  = 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
Goods constraint

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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.

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Full-income constraint (cont.) The full-income constraint may also be  expressed as: Where FC i  = full cost of Z i :
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.
Indifference curves / isoquants An isoquant is  also an  indifference  curve since Z i  is  held constant.

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Points on an isoquant At point A, an  individual may  prepare meals using  basic ingredients
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chapter7 - Theallocationoftime (Zi)in U=U(Z1,Z2,ZN...

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