the real world, all interesting optimization problems are constrained, .... One type of non-economic family resource management research which might ... Economic theory has more obvious applications to business management, because the.
OPTIMIZATION FOR FAMILY RESOURCE MANAGEMENT Sherman Hanna The thesis of this paper is that management is optimization, but that the field of family resource management has not adequately used the methodology of optimization available from mathematics and economics. Use of optimization techniques may be important in development of computer based expert systems and in advancement of the rigor of the field of family resource management. The field of family resource management has its roots in domestic science, whose theme of "The Art of Right Living" was the title of a book by Ellen H. Richards in 1904. However, the field has become an applied social science with the apparent purpose of describing household behavior and identifying and analyzing public policy issues. There are few attempts to analyze what is "right living" in a way analogous to attempts to define good diets. This is in contrast to the field of agricultural economics and to the work of economists in management and finance departments, where explicit attempts are made to define "right" behavior. The thesis of this paper is the field of family resource management does not adequately use the methodology of optimization available from mathematics and economics. Use of optimization techniques may be important in development of computer based expert systems (Hanna, 1988a) and in advancement of the rigor of the field of family resource management. Optimization means obtaining the best result, in terms of some goal such as profit maximization for a business, or maximizing satisfaction for a household. Often a narrow goal will be chosen to make the analysis feasible -- for instance, minimization of inventory costs of a business might be a reasonable optimization task for a business. Mathematically, optimization can be thought of as "getting to the top of the hill." Intriligator (1971) has characterized deterministic optimization problems in terms of time (static or dynamic), nature of constraints (none, equalities, inequalities) and number of decision- makers (one or many). An optimization problem can be described in terms of : 1. an objective function (e.g., a utility function), 2. instruments (e.g., consumption levels of different goods),
3. constraints (e.g., budget constraints), and 4. normative rules derived for the optimization problems (e.g., allocate income among goods so that the ratio of marginal utility to price is the same for all goods.) (Intriligator 1971, 4.)
Unconstrained optimization problems are relatively simple to analyze, with the only mathematical problem being to find the global maximum rather than a local maximum. In the real world, all interesting optimization problems are constrained, although for some, the constraints can be incorporated into the objective function to yield a simple optimization problem. The best solution for an optimization problem can be obtained by: -- trial and error, -- graphical techniques, or
-- mathematical analysis. Intriligator's (1971, xiii) schema of optimization techniques is: Treatment of Time Static
Dynamic
Classical Programming
Calculus of Variations
Linear Programming
Maximum Principle
Nonlinear Programming
Dynamic Programming
Game Theory
Differential Games
One Decision Maker Equality constraints Inequality Constraints 2 or More Decision Makers Game Theory
The economic theory of the household is developed with classical programming methods, which are basically an extension of the two-good budget constraint problem to n goods. Classical programming techniques can also be used for more limited technical optimization problems, such as inventory questions. Differential calculus is used to derive the basic results, although many of the intuitive results can be illustrated with simple two dimensional graphs. Numerical solutions are easy now with simple optimization programs available for microcomputers, such as the Eureka program. Linear programming techniques have been used for finding least cost diets (Stigler 1945). Game theory has some potential for analysis of interaction within a household, although the limited application to oligopoly in markets suggests that game theory will yield few insights. Dynamic optimization has theoretical applications to the household, although it is probably not worth the effort at present, as static optimization can provide many useful insights. For instance, lifetime utility maximization can be approached as a problem of static optimization, with consumption of a good in different time periods considered as merely different goods.
Herbert Simon(1977; 1983) criticized assumptions that economic agents optimize, and has even questioned the extent to which it is possible to find mathematical solutions to most interesting management problems. Simon(1977, p. 48) proposed the following scheme of decision-making techniques for business: Types of Decisions
Decision-Making Techniques Traditional
Programmed: Routine, repetitive
Nonprogrammed: One-shot, ill-structured
1. Habit 2. Clerical routines 3. Organizational structure
1. Judgment 2. Rules of thumb 3. Selection and training of executives
Modern 1. Operations Research 2. Mathematical analysis 3. Computer simulation; models 4. Electronic data processing Heuristic problem-solving techniques applied to novel policy decisions a. Training decision-makers b. Constructing heuristic decision-makers
The modern techniques listed by Simon for routine decisions under the term "operations research" include a variety of mathematical optimization methods. Simon suggested that many problems are not structured enough for mathematical optimization and criticizes the economists' vision of utility maximization as a description of the people act (Simon 1983.) However, attempting to analyze selected family resource management problems as optimization problems may produce useful insights. Family Resource Management as a Field Historically, "Home Management" had the purpose of helping people manage their homes better. Going back to 1900 and earlier (Gross, Crandall and Knoll 1973, 660-668), the field of home management focused on prescriptions for more efficient use of resources. Throughout history, management has been more important when technology and/or society have changed. During stable periods of time, cultural norms usually develop which tend to be relatively efficient in terms of a culture's values and goals. Social sanctions and rewards exist to encourage people to adhere to the norms. Management was taught within the family and other societal institutions, but was not a field of study, because there is only one way of doing things. The evolutionary process tended to lead to relatively optimal practices. The interest in home management within the field of home economics coincided with rapid changes in society around the year 1900 -- massive foreign immigration, massive migration from rural to urban areas of the United States, rapid technological changes. The old ways of doing things were no longer optimal. Much of the study of home management consisted of scientific research of efficiency similar to research in business management. Management of narrow technical goals was feasible, but perhaps ultimately boring. Just as obtaining the maximum efficiency on an assembly line is only part of the management of a
manufacturing firm, ascertaining the most efficient kitchen layout is but a small part of family resource management. Research today in family resource management tends to be descriptive rather than oriented toward prescription. Some of the descriptive research has a policy focus -- if things are bad, the implications for government policy or consumer education are X, Y, and Z. There is little explicit emphasis on prescriptions applicable for individual households. However, given the widespread interest in government policy, ignoring analysis of optimality for individual households may be wrong. For instance, if a descriptive analysis of energy conserving measures taken by households finds that certain types of households do not take all possible conservation measures, the usual recommendation made is that a vigorous consumer education campaign should be undertaken, or perhaps conservation measures should be required by the government. The possibility that households may already be acting optimally is often ignored1. One type of non-economic family resource management research which might be useful for prescriptive results is satisfaction research, which is similar to business management research on profitable firms. If it is assumed that similar households have similar tastes and standards, and if resources are statistically controlled, then households that tend to have higher satisfaction levels may be doing something right. The problem with this type of quasi-experimental statistical analysis is that it is very difficult to control for all relevant factors. For instance, if households which save a high proportion of their incomes have a higher level of satisfaction with their financial status than do households which save less, should we advise households to save more money? Perhaps so, but with much less confidence than the agronomist who concludes that adding Y pounds of fertilizer X will increase yields by Z percent. The Problem with Economic Theory Economic theory has not seemed appealing as a source of insight about family resource management because the economic theory of the household has not really focused on normative implications for individual households, but rather on constructing a consistent theory to be used for explaining and predicting market demand for particular goods and services. Consider the usual budget constraints and indifference curves. If we assumed that all consumers shared the same preferences (identical sets of indifference curves), then it might be possible to derive optimal consumption patterns for goods A and B for different price and income levels. However, for many goods, tastes obviously vary, and it is perfectly reasonable for two individuals with the same income and wealth to consume different levels of goods. This could be illustrated merely by drawing a different set of indifference curves. The usual assumption that consumers are behaving optimally is also hard to accept in a field concerned with helping consumers do better. Economic theory has more obvious applications to business management, because the objective function of a firm is usually assumed to involve the maximization of profit. If 1
. The simple economics of optimal investment in energy conserving devices (Hanna, 1975; 1978) suggests that the aftertax real interest rate faced by a household plays an important role in determining the optimal action by a household. Households face very different aftertax real interest rates, yet this simple fact has been ignored in a large number of empirical studies.
profit maximization is considered as a static, one period process, and if information on marginal revenue and marginal cost is available, economics can provide clear guidance for business management. In the real world, this is not always possible, and many successful businesses have no guidance from economists. Businesses have been slow to adopt some optimization methods developed by economists (Faulhaber and Baumol 1988). There are some technical problems of optimization amenable to quantitative analysis, such as inventory control problems, while there are other optimization problems, such as whether to introduce a new product, which are less quantifiable. There is a vast literature on optimal financial management. Agricultural economists have produced many recommendations for increasing farm profits. Beyond these technical considerations, much of business management consists of looking for techniques that worked elsewhere. Applying the Economic Model to Family Resource Management The most obvious application of economic theory to family resource management is in terms of the maximization of satisfaction or utility subject to resource constraints. The potential application of the economic framework is very wide, extending to all consumer purchases of products and services, and also including labor force, fertility, and even marriage decisions. With a normative approach, if we can identify a person's goals (ideally, his or her utility or preference function) and resources, we can specify the optimal situation. Example: if you want to buy term life insurance, you should buy the XYZ policy rather than the ABC policy, because they have equal quality and XYZ has a lower price. In this example, with simplifying assumptions it is easy to identify the optimal decision -namely, minimize expenditures for a given quality of product. It is often useful to go a step further with empirical analysis. We observe behavior and compare to what seems to the optimal behavior. Then we infer appropriate policy for government regulation or consumer education. Example: we observe that most people do not buy the lowest cost term life insurance policies. We can infer that many consumers are not making optimal decisions in terms of what would be optimal if they had full information. Unfortunately, even when the full information optimum is identified, there is not always a simple definition of optimal behavior for all consumers. For instance, the optimal amount of searching for information depends on the value of time for the consumer, as well as the psychic costs and benefits of shopping. With more complex goals, it is even more difficult to be sure that we have correctly identified optimal behavior. As Roger Swagler(1979) has noted: "There is an unfortunate tendency for people to think of any pattern of behavior that is different from their own as irrational. Irrationality comes to be equated with different, strange, or unusual. From the economist's point of view, such contentions are totally unjustified, since they overlook the fact that utility is highly individual." (Swagler 1979, 29.) Nevertheless, it is useful to attempt to identify "right" and "wrong" decisions, because people desire advice, whether from "Dear Abby", the Cooperative Extension Service, financial planners, or Consumer Reports magazine. Decisions may be "wrong" from several different causes, including: 1. Lack of information.
2. Inability to process information. 3. Lack of time to gather or process information. An appropriate priority for formal and informal consumer education should be helping consumers with complex, important decisions, by providing information and/or instructing in decision-making techniques. Yet consumer educators need to realize that many consumers will be unable or unwilling to use such information, especially if there is too much. Simple rules of thumb -- if they are appropriate for most people -- are a common solution to the "information overload" problem. Unfortunately, many rules of thumb are not very valid. For example: "You should have life insurance equal to five times your annual income." Computer software ("Expert Systems") should provide more valid, yet "user-friendly" help for harried consumers. If we consider the range of decisions that are discussed under the umbrella of "Family Resource Management", clearly only some are amenable to quantitative normative analysis in an economic framework. For instance, I might ignore a quantitative model of optimal life insurance decisions because I prefer to purchase it from my brother. However, that type of consideration does not make quantitative prescriptions inappropriate -- it just means that there must be implicit and explicit contingencies and qualifications. The role of attitudes and some nonfinancial objectives does make empirical analysis of consumer decisions more difficult (Ferber 1973). Financial Decisions. The key to application of quantitative normative analysis is making reasonable assumptions to narrow the possible range of objectives, and ignore most attitudinal considerations. For instance, many financial decisions (asset management, saving behavior, money management, credit, insurance) can be modeled in terms of maximization of expected utility, with utility a function only of total wealth. A rich set of implications can be derived, many of which depend largely on one's level of wealth, and depend little on the exact nature of one's utility function (Hanna, 1988c). It is possible to design computer software that could enable educated consumers to use utility analysis without mathematical skills or detailed knowledge of economics (Hanna, 1988a.) Spending Decisions. Spending behavior includes allocation between spending and saving, allocation among categories of spending, and choices of particular brands and models. Common advice is to save a constant proportion of income. The simple lifecycle model (Ando and Modligliani, 1963) implies constant real savings when working if real earnings are constant, in order to have equal consumption over the life cycle. If real earnings increase, the model implies initially low or negative savings and then increasing real savings as retirement approaches. More sophisticated modeling of optimal saving can provide better insight into empirical patterns. Ultimately spending decisions are a matter of taste, although certainly some technical decisions (such as purchases of financial products or "utilitarian" products) can be subjected to quantitative normative analysis. If quality does not vary, it is possible to analyze how much more consumers are spending than necessary. If there are a limited number of characteristics in a product, it is possible to identify inefficient models (Lancaster 1966; Eastwood 1985) and it may be possible to derive an overall quality measure valid for most consumers ( Maynes 1976). Geistfeld
(1977) described a technical efficiency approach to consumer decision-making, and Kamakura, et al. (1988) describe a methodology of estimating the degree of inefficiency inherent in purchasing a particular brand. If quality can validly be reduced to one dimension, the bewildering array of choices faced by a consumer can sometimes be reduced to a few efficient choices. Ultimately, a consumer has to consider whether an additional amount of quality from a product will yield as much additional utility as alternate uses of the extra money would yield, which is a matter of taste and income or wealth. Even if all consumers had identical tastes, the optimal level of quality for a product would depend on the consumer's wealth. The optimal level of energy efficiency or durability can be modeled and shown to depend on the real interest rate faced by the consumer(Hanna, 1975; 1978). The optimal level of safety can also be modeled and shown to depend on the consumer's wealth and level of risk aversion (Hanna, 1985). Although the assumptions necessary to construct manageable models may seem to be exceedingly unrealistic, at least such efforts can provide a starting point for analysis. The alternative is arbitrary assumptions about what is optimal. Fertility. Although economists have analyzed fertility decisions extensively, it is difficult to derive general prescriptions about optimal fertility decisions, including the number and timing of children. However, it is not so difficult to derive technical results, such as for a given money income, having an additional child will lower one's level of living in terms of food, housing, savings, etc. Empirical research on teen pregnancy can be used to derive probabilistic information, such as having a child before age X will lower one the average lower one's education by y years. There are problems in interpretation of causality in such research (e.g., were all other factors controlled for, or were teenagers who became pregnant likely to achieve less education anyway?) but provision of such information may be useful. It is not clear whether such information will change behavior. It is possible that teenagers who become pregnant had information and were behaving rationally, or could not incorporate information rationally into their behavior. More rigorous modeling of optimal behavior could provide more insight into fertility behavior. Time Use Decisions regarding time use, including paid work versus home production, may seem to depend only on tastes. However, reduction of everything to money terms can be useful for management prescriptions, especially for advice to "harried perfectionists" (Maynes 1976, 301): ... Reduce the number of activities to be undertaken, ... Make less important choices on the basis of less information, ..., Try to hire substitutes to carry out less important tasks. In general, advice to consider alternate ways of doing things can be useful because it is possible that higher utility can be obtained. In the business world, firms that do not adopt more efficient ways of doing things will not survive in the long run, but households can just muddle along using inefficient techniques. Consider the manufacture of pins. According to Adam Smith (1776) an untrained workman working alone could perhaps make one pin a day, but in a factory with
specialized equipment and specialization of labor, daily production averaged 4,800 pins per day. At one factory in the United Kingdom in the 1970s, daily production of pins per worker averaged 800,000 using machines (Pratten 1980). Clearly home production has not had similar increases in productivity, although the decline in home sewing may be considered a shift to greater productivity, as the average worker in textile and clothing factories can produce much more than the average home sewer working alone. The important efficiency issue for household production is the judicious purchase of substitutes for one's own time. Values other than efficiency are important for many people, including satisfaction derived from the process rather than the end-product, and creation of unique products not available from the market. Nevertheless, useful advice can be generated by making simple assumptions about the monetary value of time, combined with technical data or empirical surveys of the marketplace (Crowell and Bowers, 1977; Dunkelberg and Stephenson, 1973; Hawkins and McCain, 1979). Consideration of the economics of information can lead to advice concerning optimal information search (Jung, 1979). Safety and Health. It is possible to model safety and health decision in terms of maximization of expected utility, with utility a function only of total wealth. A rich set of implications may be drawn, although dependent on the individual's degree of risk aversion. For a tradeoff of money versus safety, quantitative models might help consumers make better decisions. Cost-benefit models using available probabilities of risks can provide insight into optimal behavior for risks which can be prevented or for which the probability can be reduced by some sacrifice. Consider seat belt usage, which Dardis (1983) analyzed based on probabilities of accidents of various types. Although the preventative act (fastening one's seat belt) does not have direct monetary cost, Dardis assumed that the act had a opportunity cost in terms of the value of the time involved. She then showed that it was rational to fasten one's seat belt for small cars, but perhaps not for large cars. Hanna (1985) showed that with moderate risk aversion, it would be rational to fasten one's seat belt even with large cars. With the somewhat analogous problem of AIDS prevention there are psychological considerations, but it could be modeled in a similar fashion in terms of the monetary and time costs. For both problems, the many psychological issues are fruitful to explore, but economic analysis can provide insights into optimal behavior so that there can be a rational basis for public policy and consumer education. Conclusions The field of family resource management can benefit from more application of the methodology of optimization in order to help consumers and families better manage their resources. The relatively few attempts to ascertain optimal behavior have been focused on very narrow optimization issues and used extremely simplified assumptions, yet have produced important insights. Future emphasis on computer expert systems will require greater focus on mathematical optimization analysis. References Crowell, P. M. & Bowers, J. S. (1977). Impacts of time and transportation costs on food shopping. Journal of Consumer Affairs, 11(1), 102-109.
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