Becker “A Theory of the Allocation of Time”

Intro

“L” is home time “M” is market goods “H” is hours worked “V” is non-labor income “T” is endowment of time

Because the model involves “home production” we will introduce isoquants from the theory of the firm. Later, we will consider isoquants in more detail.

Production function from theory of the firm: Y = f(Land, Labor)

“Y” output: Land and labor are two inputs

Isoquants

“Iso”: same “Quant”: quantity

Diminishing Marginal Rate of Technical Substitution (MRTS) A and B both produce same quantity of wheat. A: Lots of labor not a lot of land: cultivate land very carefully, plant carefully, weed

water precisely. Need to give up a lot of labor to produce same quantity. B: Lots of land not a lot of labor: throw seeds wherever they fall, harvest only the wheat

that’s easy to get to. Don’t need to give up a lot of labor to produce the same quantity.

Now to Becker’s Model of Labor Supply and Time Allocation

Land

Labor

Y=10000 Bushels

Y=4000 Bushels

A

B

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There is no leisure in this model. We produce “commodities” with home time (L) and money (M) For instance going to a baseball game is not pure “leisure.” “L” includes the time spent at the game, plus the time going to the game and buying the ticket; and “M” is the financial cost, including ticket and transportation.

For instance: Thanksgiving Dinner. Than consider consume multiple commodities – some take more time vs $$

Thanksgiving Dinner for 10 people (try to keep quality constant)

Hours per person

$ Per person $/Hour

Caterers come to home, set up and clean up

3 $100 33.3

Go to restaurant 3.5 $60 17.14Pick up from Whole Foods 6 $40 6.7Cook using all prepared foods 7 $35 5Cook, but use some prepared pies, cranberry sauce, stuffing, etc.

10 $28 2.8

Cook, but from scratch 12 $20 1.7Raise turkey and vegetables and cook from scratch

20 $19 .95

List goes from market intensive to labor intensive: Plot Iso-Thanksgiving.

All options along the “Iso-Thanksgiving Curve” provide same utility.

Has diminishing MRTS, like an Isoquant.

At caterer’s: can give up a lot of money to add a little time and still have dinner At scratch: need to add a lot of time to save money

Z = Z(L, M)

“Z” is a Thanksgiving dinner L: Home time (hours) M: Market goods ($)

Next: Z is raising a kid. Various approaches to Raising a kids: Goods vs. Time intensive (let them do table)

Approach Hours/week $/week $/HourMaid, Full time nanny 10 $2000 200Part time maid, full time nanny 18 $1200 66.7

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Nanny 40 $600 15 Day Care 60 $400 6.7Part time sitter after school 80 $200 2.5Have relative help out, give them really nice birthday presents

120 $30 .25

Child Care Vegetarian 140 $20 .14

Again, do these provide the same utility? Has utility changed over time? Is it harder to stay home if other parents not staying home?

All in all we consume many, many Z goods. Becker’s model has utility from one aggregate Z good.

In aggregate we have U = U(L,M) By writing in terms of U, we allow preferences to matter, too.

Applying this Model

Interpret as:

“V” husband’s income is given“w” is wife’s wage rate“U” is families utility and husband and wife agree. Her market and home time, and

family consumption are chosen.

T = H+LC = wH + V = w(T-L) + V

= (V + wT) – wL

H L

M

Z1(L1,M1)Z2(L2,M2)Z3(L3,M3)Z4(L4,M4)

Z(L,M) U(L,M)

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We will call these curves “indifference curves”, but this is a little misleading because they incorporate productivity as well as preferences, and we can’t disentangle these with data.

Now: what shifts the budget constraint: same as before: w and V.

What causes the isoquants to differ?

Case A: stronger preferences for home produced goods.Case B: stronger preferences for market produced goods –

Case A: technology of home production – not good substitutes for timeCase B: good substitutes for time (Dishwasher, washing machine, Roomba,Electric kitty litter box cleaner)

“L” “H” T L

M

U = U(L,M)

U = U(L,M)

A

B

Case A L

M

Case B L

M

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Notice with A: same wage rate, choose point with higher L/M than with B

How have these changed over time?

Clearly technology has changed from A to B

What about preferences? Do people prefer market produced vs. home produced goods more now than before? Preferences for child care? Are women now less averse to leaving kids in child care? Is it less pleasant to be home with kids, given that other women aren’t home?

Now, we’ll look at the participation decision:

A: Does not participate w* is slope of isoquant at kink: wage at which she’d be indifferent between working and not working. W*>W. Would need w to increase more to pull her into the market

B: Participates: w>w*

NOW we want to explain increases in women’s labor force participation using this model. In terms of theory, what affects w* - i.e., the supply side?:

Preferences Technology of home production Where endowment point is: V

What affects w – ie. The demand side?: human capital, demand for labor – this is next section.W DOES NOT AFFECT W*

Effect of V on W*: Look at Right side: V↑ => w*↑, less likely to participate

Case A L

M

Case B L

M

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Decline in participation of prime-age men

Human Capital, Time Allocation, Home Production,& the Life Cycle

Our point of departure is Gary Becker's "Theory of the Allocation of Time" (1965), which unified earlier strands of analysis including human capital theory and Becker's 1960 "Economic Analysis of Fertility." We'll begin with a brief overview of these developments.

Case A L

M

Case B L

M

LS’

LS

LD

LS

LD

LD’

L L

To mid-70’s LS falling Since mid-70’s LD falling Due to increase in disability ben. Due to decline in manuf jobs.

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Modern human capital theory grew out of problems confronting economists engaged in growth accounting in the 1950s (cf., aggregate production function, quantity vs. quality of labor). Consideration of the role of improvements in the quality of the labor force (due primarily to education and on-the-job training) helped "explain" observed economic growth, and stimulated development of the concept and theory of human capital (in this context, human capital may be defined as skills and knowledge that enhance a worker's productivity in the labor market). Note, however, that the idea that human beings may be regarded as analogous to physical capital (where capital may be defined as a produced means of production) can be traced back to Adam Smith's Wealth of Nations (1776).

Human capital models (e.g., of optimal investment) were developed in the late 1950s and 1960s, and applied to analyses of investment in on-the-job training and in formal schooling. Particularly in applications focusing on post-secondary schooling, considerable emphasis was placed on the value of time.

That is, it was recognized that the forgone earnings associated with attending college constituted a major portion of an individual's (private) cost of attending college (cf., free tuition). While not a direct out-of-pocket cost, the opportunity cost of attending school (where the opportunity cost of any choice may be defined as the value of the next-best alternative forgone) was nonetheless substantial and real.

The importance of time costs (i.e., of the opportunity cost of time) was also mentioned by Becker in his seminal "Economic Analysis of Fertility" paper in 1960. As with schooling, the value of time was regarded as an important determinant of behavior -- fertility behavior, in this case. The opportunity cost of the mother's time spent in childbearing and child raising -- what she could have earned in the labor market if she'd been working instead of caring for children -- was implicitly recognized as a cost element in the decision to have children.

These two strands of analysis, human capital theory and the economics of fertility, along with several others were unified in a comprehensive framework by Becker's "Theory of the Allocation of Time." This theory will serve as the basic conceptual framework for the analyses of this first part of the course.

In brief, the approach entails applying economic analysis to household behavior. The household is no longer treated as a black box (cf., conventional circular-flow diagram). More specifically, the approach recognizes the importance of time in household production and consumption activities.

By providing a unifying framework for examining household fertility, migration, labor supply behavior, and resource allocation within the household, the theory of the allocation of time will be seen to be a microeconomic model of household choice. The resulting "economics of the family" came to be known as "the new home economics" as it began to be applied to various issues in the early 1970s.

At the heart of the theory is the view that households are producers as well as consumers (cf., Becker's home production in the circular flow). Each household is seen

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as seeking to maximize its utility (a household utility function), which is based on consumption of "commodities" (Zj) which are themselves produced by the household by combining inputs of market goods (Xj) and time (Tj). Note that these "commodities" (e.g., a steak dinner, good health, children) are not simply market goods -- they are produced with inputs of market goods but also with inputs of time.

Mathematically, the household seeks to maximize the utility function

1) U = U(Z1, ..., Zm) , subject to

2) Zj = fj (Xj, Tj) , the household production functions, where Xj and Tj are vectors of goods and time, respectively (cf., Tij).

Utility maximization is subject not only to the household production functions, but also to constraints on expenditures for market goods and "expenditures" of time:

3) "SUM" Pj*Xj = I = V + Tw*W , the market goods constraint, and

4) "SUM" Tj = Th = T - Tw , the time constraint.

The market goods constraint (equation 3) indicates that expenditures on market goods ("SUM" Pj*Xj, where Pj is a vector of unit prices of Xj) cannot exceed money income (I), which equals the sum of nonlabor income (V) plus earnings (time spent at market work, Tw, multiplied by the hourly wage, W).

The time constraint (equation 4) indicates that the sum of all time inputs to the production of commodities ("SUM" Tj), or total home production time (Th), is simply that portion of the total time available (T) which is not spent at work in the market.

Since time can be converted into goods (by using less time in home production and thereby earning more income in the labor market), it should be clear that the market goods and time constraints are interdependent. In particular, since (from eq. 4) Tw = T - "SUM" Tj, this can be substituted into equation 3 to give

"SUM" Pj*Xj = V + (T - "SUM" Tj)*W, or

5) "SUM" Pj*Xj + "SUM" Tj*W = V + T*W .

Equation 5 combines the market goods and time constraints into a single total resource constraint. The right-hand side of eq. 5 gives the household's "full income" -- nonlabor income plus the earnings available if all the household's time were devoted to earning income. The left-hand side of eq. 5 shows that full income is allocated to two components: expenditures on market goods ("SUM" Pj*Xj) to produce Zj and time expenditures ("SUM" Tj*W) in the production of Zj.

The full price of a unit of commodity Zj --"PI" j -- is the sum of the prices of the goods and of the time used to produce that unit. That is, the full price of consumption is the sum of direct and indirect components, in the same way that the full cost of investing in human capital is the sum of direct and indirect costs. These direct and indirect prices are symmetrical determinants of the total (i.e., full) price.

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In considering the commodity bundles (Zj), it should be evident that they may differ in the extent to which they are time intensive or market-goods intensive (i.e., in the relative importance of time inputs as compared to market goods inputs). For any given household, the relative importance of forgone earnings as a component of the full price of a commodity will depend on two factors: the amount of time used per dollar of goods (time intensity), and the opportunity cost per unit of time.

The existence of differences across households in the opportunity cost of time means that the full prices of various commodities will differ across households, even if the prices of the market goods used to produce the commodities are identical. The more time intensive are the commodities in question, the greater the interhousehold differences in full prices.

In the same vein, consider the process of economic development. As real wage rates rise, the opportunity cost of time rises correspondingly. Other things equal, then (i.e., if the real prices of market goods do not change, as might occur as a consequence of technological progress), the process of development implies that the full price of time-intensive commodities will rise relatively rapidly over time, while the full price of goods-intensive commodities will rise relatively slowly (see Fig. I.A.1; cf., "African time").

Becker traces out several implications of his theory, beginning with an analysis of hours of work. He notes that the traditional labor-leisure analysis of hours of work can be regarded as a special case of his more general analysis -- a case in which the cost of the commodity called "leisure" (i.e., nonmarket time) consists entirely of forgone earnings and the cost of other commodities consists entirely of market goods.

Consider the implications of an increase in the wage rate. This increase has two effects: it raises the opportunity cost of time spent outside the labor market, and it enables one to reach a higher level of utility, or real income.

The first effect, in and of itself, contributes to an increase in hours of market work (the substitution effect), while the second effect, in and of itself, results in a decrease in hours of market work, assuming that leisure is a normal good (the income effect). The overall response to the wage increase will depend on the strength of the substitution and income effects, and cannot be predicted a priori (see Fig. I.A.2).

The preceding discussion on income and substitution effects is not based on the theory of the allocation of time; rather, it is a standard conclusion of the traditional labor-leisure analysis of hours of work. Becker's theory leads to the same

conclusion, but provides somewhat richer insights and predictions, particularly with respect to substitution effects.

That is, consider an increase in nonlabor income (V): this produces a pure income effect. In Becker's model, this leaves the relative prices of commodities unchanged, so higher income results in increased consumption of (normal) commodities. This increased consumption requires more time (Th), which in turn means that less time will be

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available for work in the market (Tw). Hence, as in the traditional model, the income effect reduces hours of market work.

Now consider an increase in the market wage rate offset (compensated) by a lump-sum tax -- i.e., a pure substitution effect. The traditional labor-leisure analysis indicates that the higher wage raises the opportunity cost of leisure, thereby leading to an increase in hours worked.

Becker's approach, on the other hand, emphasizes that the (compensated) wage increase will alter the relative prices of different commodities. In particular, the full prices of relatively time-intensive commodities would rise more sharply than the full prices of goods-intensive commodities. Households in this situation would have a strong incentive to shift their consumption away from time-intensive commodities and towards goods-intensive commodities. This, in turn, would reduce total time spent in consumption, and hence increase time spent at work.

Thus, the theory of the allocation of time leads us to the traditional conclusion that the substitution effect of a wage increase will result in a reallocation of time toward market work. In addition, however, the theory also implies that there will be wage-induced changes in the allocation of time to various nonmarket activities. It is in this sense that the traditional analysis may be regarded as a special case of Becker's more general analysis.

In addition to extending economic theory to include a broad range of nonmarket activities in which time plays an important role, Becker's approach with its emphasis on home production also provides us with a richer theory of the demand for market goods. In microeconomic theory, we typically think of demand as reflecting prices, incomes, and tastes. However, none of these three factors can help us account for, say, seasonal fluctuations in the demand for heating oil, or the observed positive relationship between age and the demand for medical care.

However, if we think of households as having a demand for a warm home, the seasonal fluctuations in the production function for a warm home help explain the corresponding fluctuations in the demand for heating oil. Likewise, household production theory suggests that the consumer's ultimate demand is for good health, and medical care is the market service used to produce good health. Hence, biological changes with age alter the production function for good health so as to cause changes in the demand for medical care.

A related aspect here is the role of education in home production. In low-income developing countries, for example, there is evidence that greater mother's education contributes to higher survival rates and better health for children. In Becker's framework, this is equivalent to saying that education raises the productivity of mothers in the production of child health and survival.

To the extent that education improves productivity in nonmarket activities, this requires us to broaden our definition of human capital to include skills and knowledge that enhance productivity either in the market or in nonmarket activities. More

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generally, Becker's framework has applications not only to fertility and other demographic phenomena, as we shall see below, but also to areas such as health and development economics (e.g., farm output consumed by farmers and off-farm labor).

Once we allow for the possibility that a particular commodity may be produced with varying proportions of time and market goods (cf., production functions and isoquants), additional implications of home production theory are evident. We've already seen that an increase in the opportunity cost of time (i.e., an increase in the real wage rate) induces a substitution away from time-intensive commodities. In addition, there will also be a substitution away from time and towards market goods and services in the production of each commodity (cf., child care, meals).

For any commodity, the extent to which inputs of time and goods change in response to a change in their relative prices depends on the elasticity of substitution between time and goods in the commodity production process -- i.e., on how substitutable time and goods are for each other (cf., isoquant shapes). This elasticity of substitution will likely vary from commodity to commodity, and will change over time, with technological progress.

In general, then, it should be clear that as wages rise, time-intensive commodities become increasingly expensive; and commodities will increasingly be produced via goods-intensive technologies of production in order to economize on the use of time.

In addition to allocating time efficiently among commodities, multi-person households must also allocate the time of different members among various activities. Members who are relatively more efficient at market activities (those with access to higher wage rates) would be expected to engage in less home production than others. Those, like youth, who are relatively more efficient at investment activities like schooling (cf., life cycle) would be most likely to engage in human capital investment.

An increase in the relative market efficiency of any household member should lead to a reallocation of the time not only of that individual but also of other household members. That is, the allocation of the time of any household member is expected to be influenced by the opportunities open to other members.

The paper by Hersch and Stratton looking at housework and the division of housework time among employed spouses provides some relevant evidence on time allocation within the household. In the 1979-87 data that they look at, men spend an average of 42 hours per week at work in the labor market, while their (employed) wives average just over 30 hours per week of market work. Husbands report an average of just over 7 hours per week of housework, compared to nearly 20 hours per week of housework for their wives.

Reported housework of the husband decreases as his share of labor income increases, and wife's housework increases with higher husband's share of labor income. These findings are consistent with Becker's notion that higher relative market efficiency of the husband will increase the extent of his specialization in market activities and at the same time result in more housework being done by the wife.

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More directly, greater numbers of hours of market work by the husband are associated with significantly less male housework and significantly more female housework. The hours of market work of employed wives do not, however, help to explain husband's housework (cf., Joni Hersch's comment that "nothing explains husband's housework" and note adjusted R2 in Table 2), although they are negatively related to wife's housework hours.

Further, higher combined labor incomes of husband and wife are associated with significantly lower housework hours of both husband and wife. This is consistent with a substitution of market goods for time -- i.e., greater goods intensity -- in home production.

Finally, note the effects of the presence of children on housework. Preschool-age children significantly increase housework hours of both wives and husbands, although the impact is more than twice as large for wives. Elementary-school-age children also significantly increase both parents' housework hours, again much more so for mothers than for fathers; and the overall impact is somewhat smaller than for younger children. Teenagers have a smaller still positive impact on housework of mothers, and no effect on that of fathers. These results indicate that the presence of young children raises the demand for home production activities.

The results reported by Hersch and Stratton are thus, in several ways, quite consistent with Becker's approach. However, two major caveats are in order here. First, data on time allocation are often very imprecise and subjective, with work at home left to the respondent to define (cf., child care, shopping; desirability of detailed time diaries over simple recall, especially recall by one person for others, as in the H & S data set). This problem is exacerbated by the phenomenon of joint production -- producing multiple outputs simultaneously.

Second, it should be clear that noneconomic factors (e.g., culture or socialization) also play a role in time allocation decisions. The scarcity of house husbands (a phenomenon we'd expect to see in at least some cases where the wife's earning power in the labor market exceeds that of the husband) and the specialization of women in child care activities both support the view that noneconomic considerations also come into play.

Further, an alternative approach to time allocation, as noted not only by Hersch and Stratton as being consistent with some of their evidence but also discussed by Folbre, is that based on household bargaining models (sometimes called divorce-threat bargaining models). These models are pertinent to household formation and dissolution as well as to intrahousehold time and resource allocation decisions.

While the literature on household bargaining models tends to be very mathematical and theoretical, the basic ideas are fairly straightforward. Marjorie McElroy and Mary Jean Horney, in one of the early papers in this literature, proposed -- as an alternative to the single household utility function in Becker's neoclassical approach -- a cooperative Nash-bargained model of household behavior. Nash models permit and resolve conflicts among family members.

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Each household member has a utility function and a threat point. The threat point is the individual's maximum level of utility outside of the household, and hence represents the opportunity cost of being in the household.

The greater an individual's threat point, the more strongly will that person's relative valuations of goods be reflected in the household demands -- i.e., the more weight the individual will have in household resource allocation decisions. Individual-specific market wage rates, individual-specific nonwage incomes, and -- more broadly -- how well an individual can do outside the household all affect threat points.

Typically, bargaining model analyses focus on a case with two decision makers -- husband and wife. In this case, the husband and wife jointly allocate resources so as to maximize the product of their gains from marriage, where each person's gain from marriage equals the difference between utility within the marriage and the threat point.

In the bargaining approach, who has control over various income sources influences resource allocation within the household. This contrasts with Becker's neoclassical approach, in which only the pooled income of the household is relevant. The presence in many developing countries of separate household budgets (cf., a number of the papers in the Dwyer and Bruce book), where the husband has responsibility for certain types of expenditures (e.g., shelter) and the wife takes care of other expenses (food, children), is nicely concordant with the bargaining approach.

Further, the opportunity cost of family membership is important for intrahousehold distribution of resources in the bargaining models. A number of recent studies have found evidence that the intrafamily distribution of resources favors family members with better current or future ouside opportunities. McElroy has argued that in Becker's altruistic neoclassical model, outside opportunities do not influence internal allocation decisions (but cf., family approach to migration and resource allocation to children, to be discussed below).

In any case, the Nash model highlights a series of explanatory variables, called extra-household environmental parameters, or EEPs, that affect how well each family member could do in the next-best alternative outside of the family. These EEPs depend on the governmental and social setting, but can include:

1. indices of each member's control over resources outside the family (wages, nonwage income, and employability of each family member):

2. measures of how well each family member could do in the marriage or remarriage market (e.g., appropriate age-specific sex ratios; cf., Korea) or returning to the family of origin (cf., parental wealth);

3. measures of supporting social networks and social restrictions (e.g., religion, clan, caste);

4. parameters that describe the legal structure (e.g., rules for determining property settlements [cf., Lula Landa], alimony, and child support); and

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5. parameters that describe government and private taxes and transfers that are conditioned on marital and family status (e.g., AFDC payments, other payments to custodial parents, marginal tax rates).

A final note here concerns life cycle considerations. We've already mentioned biological changes with age, such as the capacity to bear children, the risks of mortality, and the ability to produce good health.

With respect to economic aspects tied to aging and the life cycle, as alluded to earlier models of optimal human capital accumulation emphasized the optimal timing of investment activity in relationship to labor force activity. These models concluded that net investment would be greatest for the young and negative for older workers.

Further, studies of income, saving, and asset ownership indicate that these variables change in predictable ways over the course of the life cycle (cf, age-earnings profiles, life-cycle saving behavior, and consumption, especially of durable goods). Indeed, these relationships underlie the common meaning of "demographics" as it is oriented toward marketing.

Hence, various aspects of the behavior of households may be seen as being related to the life-cycle stage of the household head or other household members. Throughout the semester we'll encounter occasions where life-cycle considerations are helpful in understanding certain behavior pattern

How to Find Out the Population Base of an Area

There are a couple ways to figure out the population base of an area. One is to do a site survey. Big chains and corporations routinely conduct some type of site survey before they begin building. Because a site survey can cost as much as $25,000 or more, it usually is not an option for a person starting an independent restaurant.

If you don’t have several thousand dollars sitting idyll in your bank account for a site survey, don’t despair! There are several ways to figure out the population of particular area, and most of the information is free. Take advantage of local government reports, speak with a representative from the Small Business Administration (SBA), or visit the nearest economic growth council for information on local employment and population data.

Population Census- Every ten years the US government publishes a population census. A census not only tells you exactly how many people live in a certain area, it gives you a median age and household income. These factors can influence your menu and restaurant style, as well as location. For example, if the median household income of an area is $40,000, it is a good idea to keep the menu prices on the inexpensive side. If the median household income is $200,000 a year, then you can offer a slightly more upscale menu.

Housing Value- Find out how much local houses are appraised at. If houses are going cheap, that is an indicator that incomes are lower. If every house in the area is selling for

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$500,000 or more, than it is a good indication that incomes are high and people have extra money to dine out.

Nearby Institutions and Attractions- Are there any big businesses or attractions that will bring lots of people into the area? For example, a sports stadium or major medical facility will attract hundreds, even thousands of visitors from outside the local area.

Unemployment Rate- You can find unemployment rates for towns, counties and states through local government websites. Currently the US unemployment rate is 4%. If an area is higher than this figure, you may want to think twice about locating your restaurant there.

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