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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.
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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(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
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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 FC i = full cost of Z i :
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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 Z i 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.
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