Household production of health investment: analysis and applications.

• Author: Goodman, Allen C.

1. Introduction

   Grossman (1972a, b) demonstrated how the economic valuation of time could be extended into a powerful examination of the allocation of tame and money to the production of health. By building on Becker's (1965, 1971) seminal contributions on human capital, Grossman recognized that the consumer demands health rather than medical care per se. Thus, medical care is a derived demand from health investment. Furthermore, health is not purchased passively in medical markets. Instead, in the Becker tradition, consumers actively produce health by combining medical inputs with time spent on health-improving activities. Similarly, unlike standard demand theory, the consumer does not derive utility directly from purchases of other market goods. Consumers combine nonmedical market inputs with leisure time to produce consumption goods and activities or home goods (e.g., baking bread).(1)

   Although Grossman's work remains a standard in healthcare analysis, the richness of its implications tends to be overlooked (Cutler and Richardson 1998). Originally formulated with calculus, Grossman's model and various theoretical extensions (e.g., Muurinen 1982; Zweifel and Breyer 1997) have been inaccessible to a wide range of professional economists and students alike. Alternatively, many graphic interpretations have been so simplified that they hide some of the more important conclusions. For example, Rapoport, Robertson, and Stuart (1982) derive the demand for health services but do not consider either the labor-leisure trade-oft or the allocation of time to the production of health care. Olsen (1993) extends a model previously developed by Wagstaff (1986) that distinguishes between health and health care, but the new model does not recognize the time inputs that are needed to produce both health and nonhealth goods.

   In this article, we develop a geometric model that retains Grossman's central features and applies it to a wide range of analyses in which the allocation of time is important. Although Grossman emphasized the intertemporal nature of health investment, many aspects of the demand for health and/or healthcare services are appropriately treated in a single-period model. After we develop our model, we show how income effects for health services and health investment depend on whether the production of health is relatively resource or time intensive. We continue with applications to other variables, placing special emphasis on the effects of alternative insurance arrangements, including managed care.

2. Model

   The single-period presentation requires consumers to trade leisure time for income to be spent on market inputs consisting of medical inputs (from hospital stays to over-the-counter products) and home inputs (all nonmedical inputs in a two-good model). Market inputs together with time are needed to produce health investment and home goods. By assuming that the consumer's utility is a function of the amounts of health investment and home goods that are produced in the period, consumers must make the following simultaneous decisions: (i) allocation of time to labor (and by implication, income) and leisure; (ii) production of health capital through health investment, and production of other goods (i.e., home goods); (iii) purchases of market health inputs (to be used in the production of health capital) and other market inputs (to be used in the production of home goods); and (iv) determination of health investment that will address long-term individual needs regarding health capital.

   A Two-Quadrant Framework

   Our geometry describes the optimization process through a two-quadrant approach shown in Figure 1. Solution values are indicated with asterisks.

   The consumer optimizes between health investment I on the x axis and home good C on the y axis. Given a well-behaved utility function in quadrant I, he or she chooses a labor-leisure combination allowing the purchase of medical inputs M and home inputs B, and allocating time to health activities [T.sub.b], home activities [T.sub.b], and work = 24 - [T.sub.h] - [T.sub.b]. We will show how the production possibilities are derived to provide a unique quadrant I equilibrium.

   Resource constraints and production are derived in quadrant II and indicate a standard labor-leisure trade-off with respect to the allocation of time to wage-earning activities. The x axis reflects time constraints, and the y axis reflects market inputs, either medical or home inputs, that can be purchased through the income earned from market work. Unearned income or transfer payments, reflecting pure income effects, can be indicated as upward shifts, at the maximum level of time (e.g., 365 days per year or 24 hours per day). Assuming no days are lost to illness, in equilibrium the consumer chooses how many hours to work and how much income [G.sup.*] to earn for spending on either medical or home inputs.

   Quadrant II also indicates how health is produced. The consumer's resource constraints can be modeled as an Edgeworth box. The box width indicates the amount of leisure remaining after the allocation of time between work and leisure. The box height indicates the dollars [G.sup.*] of income that were earned. Amount [G.sup.*] is divided between medical inputs M and home inputs B = ([G.sup.*] - M). The amount of money spent on medical inputs is measured downward from [G.sup.*]; the remainder is spent on expenditures for home inputs.(2)

   The isoquants in the Edgeworth box are mapped in opposite directions (with health investment = 0 in the northwest corner and home good production = 0 in the southeast corner). The contract curve indicates that any change in the allocation of time and market inputs to the production of the two goods must decrease the production of one of the goods.(3)

   We show below that the outcomes of qualitative analyses depend on the relative intensities of the two processes. Unless otherwise noted, we will assume that the relative market prices of health market inputs and home inputs, as well as wage rates, are constant. Without loss of generality, we will begin by assuming that health investment is more market intensive (less time intensive) than is the home good. Differential factor intensities with either constant or decreasing returns to scale are sufficient to provide a production trade-off that is bowed outward from the y axis. Although this is obvious with decreasing returns to scale, note that under constant returns to scale, if the two goods have the same factor intensities at any two points, they must have them everywhere (only then yielding a linear production trade-off). We assume constant returns unless otherwise noted, and Appendix 1 outlines a more formal proof that the production possibilities curve (PPC) is always bowed outward under constant returns.

   We recognize that time and market goods are complements for some health investment activities and substitutes for others. Niacin tablets, which reduce low-density lipoprotein cholesterol levels, substitute for time-consuming exercise. In contrast, cholesterol tests require time-consuming visits to the clinic. However, in a two-dimensional framework, it is essential only that the factor intensity of health investment differs from the factor intensity of home production (otherwise, there is no distinction between the two goods).

   Equilibrium

   Assume that the consumer has chosen a large amount of leisure and thus has little earned income, as shown by the horizontal Edgeworth box (dashed lines) in quadrant II. Because health investment I is market intensive, the consumer would be able to produce only a small amount of it, although considerable amounts of home good C. It is likely that more I (and less C) would increase utility so that the consumer, as in Figure 1, will move northeast up the income-leisure trade-off. Each point on the leisure-income line provides a box and a corresponding PPC. In quadrant I, we show only the PPC corresponding to the box determined by A and the production possibilities frontier (PPF) (i.e., the outer envelope of these PPCs). The utility-maximizing consumer chooses optimal levels of [I.sup.*] and [C.sup.*] at point A.(4)

   Quadrant II indicates how [I.sup.*] and [C.sup.*] are produced. From the derivation above, point A (quadrant I) implies a unique Edgeworth box in quadrant II with dimensions [G.sup.*] and [T.sup.*]. Moving down the y axis from [G.sup.*] shows the amount of medical inputs [M.sup.*] to be combined with leisure [[T.sub.h].sup.*] to produce health investment [I.sup.*]. The remainder of time, [[T.sub.b].sup.*] = [T.sup.*] - [[T.sub.h].sup.*], and the remainder of expenditures, [B.sup.*] = [G.sup.*] - [M.sup.*], are combined to produce home good [C.sup.*].

   This analysis shows clearly that the optimal amounts of health investment and home goods depend on both production and preferences. Suppose that the consumer had preference function [U.sup.**], valuing the home good relative to health investment. Point A would not be efficient. Because by assumption health investment is relatively market intensive, the consumer could choose more leisure (and less income), producing less investment, with the resulting equilibria at points [A.sub.1] and [A.sub.1][prime], respectively.

   The construction of the production trade-off is logically separable from the individual's utility function. Thus, one may be able to produce health investment efficiently yet not value it very much or vice versa. This implies that the demands for leisure and medical inputs depend jointly on the ability to produce and the utility derived from consumption.

   Although this presentation does not explicitly address the intertemporal aspects of the Grossman model, it can be used to consider them. Health investments are reflected through successive snapshots of this model...