History specific reception

This describes additional numerical simulations detailing how the consumption of reactive care and time spent on preventive care change as an individual ages. The parameter values used as a standard are the same as in Appendix C.1. I modify my assumptions on how the productivity of preventive and reactive care change over age years. I assume that the productivity of preventive care decreases at an increasing rate as an individual ages. This means that, to use preventive care to maintain good health, it will take more and more preventive care to accomplish this.¹⁵⁴

I assume that the productivity of reactive care initially increases at an increasing rate, then starts to increase at a decreasing rate. Eventually, at some age, reactive care is as productive as it will ever be. After this age, the productivity of reactive care falls at a constant rate. This means that, while young, reactive care as a curative measure is highly effective and, as medical technology advances, will continue to be more and more effective. Eventually, at a certain age, the aging process overcomes any additional productivity found as reactive medical technology improves.¹⁵⁵ Figure E.1 highlights the paths in the productivity of preventive and reactive care as an individual ages. This matches a result in Hall and Jones (2007), as to how the marginal productivity of health care spending changes as an individual ages.

E.1.1 Assumption 1 - Numerical Illustration 1

Figure E.2 shows an intuitive pattern as to how the consumption of reactive care and time spent on preventive care change as an individual ages. As an individual ages, he will spend more time working to build up income during the peak-earning years and so time spent on preventive care will fall at an increasing rate. Eventually, because of the age of the individual, the time needed to maintain one’s health using preventive care is so high that the individual chooses to spend even less

154This assumption means that the productivity of exercise is many times more productive at age 18 than at age 50;

the same holds true between ages 50 and 75. This seems to be a reasonable assumption for most individuals.

155This assumption means that the use of reactive care may actually harm the individual, even if it is better technology; this is because, at a certain age, the body does become frail and cannot take advantage of the more productive reactive care.

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time on it. This means that time spent on preventive care will rapidly decrease for an individual at later ages.

Consumption of reactive care shows a different pattern. During his peak-earning years, the individual will choose to consume reactive care at an increasing rate, choosing to offset illnesses after they occur rather than preventing them before they occur; he values his time for work rather than for preventive care, knowing he can offset the health impacts of this decision through more productive reactive care. At a certain age, the benefits of using reactive care in increasing quantities ends; as an individual ages, his ability to ’bounce back’ from illness diminishes. The consumption of reactive care starts to decline; the depreciation of the existing stock of health (φ) makes it not worth it to invest as much in the stock of health.¹⁵⁶ These are the years near retirement age, when the individual does not have to spend as much time in good health to maintain earnings power. As the individual reaches advanced ages, consumption of reactive care and time spent on preventive care both decrease. This signals an individual nearing the end of his life; consumption of non-medical care goods and increased leisure time are worth more, on the margin, to the high age individual.

This decline signals that, in this model, an individual will not choose to live forever. The depreciation of the health stock increases the costs of maintaining an extra year of life. It is more valuable to the individual to consume non-medical goods and leisure, foregoing increased life spans.

E.1.2 Assumption 2 - Numerical Illustration 2

Figure E.3 shows how the consumption of reactive care and time spent on preventive care change as an individual ages. Again, this yields the same trends as in all previous sections. The decrease in time spent on preventive care and the consumption of reactive care at later ages is very large, similar to that found in the first numerical simulation. This occurs because the nominal wage grows slowly. The benefits of living longer, in terms of higher wages, are muted. Similarly, the costs of extending life based on the use of reactive care are reduced as individuals face higher and higher reactive care prices as they age. Note, however, the continued use of reactive care; even as its price increases at a faster rate than the price of time spent on preventive care, the wage, individuals will still choose to consume relatively large amounts of it. At advanced ages, it is still the best action an

156For instance, getting cancer at age 88 and then aggressively treating it with chemotherapy is not a choice most individuals will make.

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individual can take to live longer.

E.1.3 Assumption 3 - Numerical Illustration 3

Figure E.4 shows how the consumption of reactive care and time spent on preventive care change as an individual ages. As before, time spent on preventive care decreases uniformly while consumption of reactive care initially declines, then follows the similar trends found earlier; high over what is assumed to be the peak earnings years for an individual, then decreases steadily as the individual reaches an advanced age. The figure is less ’smooth’ than those found in the other four numerical simulations, but this is due to the rapid changes that are assumed for the inflation rate of reactive medical care.

E.1.4 Assumption 4 - Numerical Illustration 4

Figure E.5 shows how the consumption of reactive care and time spent on preventive care change as an individual ages. Again, this yields the same trends as in previous sections. The decrease in time spent on preventive care and the consumption of reactive care at later ages, however, is very small. This occurs because, as the wage continues to increase, the benefits of living longer include very high potential earnings. Individuals will choose to work longer and live longer simply because they will earn higher and higher income levels over time.

E.1.5 Assumption 5 - Numerical Illustration 5

Figure E.6 shows how the consumption of reactive care and time spent on preventive care change as an individual ages. Note that this yields the same conclusions as in the previous section, but the changes in the consumption of reactive care and time spent on preventive care are muted.¹⁵⁷

157In other words, the increase in the consumption of reactive care at early ages is less, while the decrease in time spent on preventive care over the whole lifespan is less pronounced.

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