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On the Optimal Timing of Research ExpendituresAuthor(s): A. G. HoltmannSource: Inquiry, Vol. 10, No. 1 (March 1973), pp. 47-49Published by: Excellus Health Plan, Inc.Stable URL: http://www.jstor.org/stable/29770761 .

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A. G. Holtmann Research Report On the Optimal Timing of Research Expenditures

In a recent paper, Professor Burton Weis brod showed that the research expendi? tures that were started in 1930 to develop a vaccine against poliomyelitis resulted in a rate of return of approximately 8 to 12

percent on the investment.1 Such evidence is important because it suggests that, at least in the case of polio, the research ex?

penditures to eliminate a disease represent a "good" investment. While it is clear that the results from one study cannot be gen? eralized to all medical research, the results are encouraging. Current expenditures on research to eliminate other diseases sug? gest that we believe these investments will be worthwhile; however, we should also be concerned with how fast a disease is eliminated.

It may not always be apparent that an intensified effort would lead to an earlier elimination or control of a disease, but one would think that there is sometimes a stage at which a meaningful estimate can be made concerning the marginal productivity of resources devoted to in?

creasing the speed at which research pro? gresses. Surely, for example, James Wat? son, in his book The Double Helix, suggests that additional efforts by his group may have led to the discovery being made be? fore Linus Pauling could solve the prob? lem involved.2 In this same vein, some

writers have suggested that research proj? ects associated with defense might be car?

ried out at a faster pace, but at a higher cost.3 The relationship between the speed of a research project and its cost is, of

course, an empirical matter about which we have little evidence. Part of the pur? pose of this paper is to stimulate such research.

The fastest time at which research can

proceed may sometimes be optimal. On the other hand, it may be that the total cost of a research project is always greater than the total benefits and no research is

justified. In any case, the optimal speed at which to eliminate a disease seems worth exploring.

Using data from the earlier study, the

optimization rules for the completion of a medical research project are related, and the level and time pattern of expenditures

made in the case of polio are examined. Problems of optimal timing are, of course, familiar to economists. The optimal ma?

turity of fine wine is a common example of the optimal termination of an invest? ment project; and the introduction of

weapons systems provides an example of a problem of the optimal introduction time.4 However, this framework has not been applied to medical research, where it could be an important tool of analysis.

In this case, assume that a technology to develop a polio vaccine at an earlier date would have been more expensive than the technology used.5 This suggests that the optimal technology would be one where the additional costs of a faster research

design is just equal to the additional bene

A. G. Holtmann, Ph.D. is Professor of Economics, State University of New York at Binghamton (New York 13901).

This research was supported by Health Services Contract #HSM 110-70-355, Department of Health, Education and Welfare. The author ap? preciates the earlier comments of Burton Weis brod.

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Inquiry/Volume X, March 1973

fits from having the vaccine earlier. Ad?

ditional costs, in this case, include the

marginal cost of adopting the faster tech?

nology, the loss of interest from the initial

application costs, and the cost of one ad? ditional period of operating costs. Addi? tional benefits include the reduction in the number of polio victims and the possible reduction in research costs associated with a shorter research period. Of course, at some point the gains from a shorter re?

search period must be less than the addi? tional cost of adopting a faster research

technology, or it would pay to complete the

project in the shortest possible time. Without information concerning the

technology available to the polio research?

ers, one is not able to specify the optimal time that the polio vaccine should have been developed. The formulation of the

optimal program for the introduction of a

vaccine, however, does focus our attention on the cost and benefit factors that are

important in this decision. Using data re?

ported in the earlier paper on polio, cer? tain plausible situations for finishing the polio research earlier can be simulated. Such a simulation effort allows us to gain some idea of the increase in research costs that might possibly be justified to finish earlier. In addition, the results will show the influence of certain types of costs and benefits on the possible optimal decision.

Hopefully, this procedure will provide a model for setting limits on the speed at which health research might proceed.

Benefits and Costs

The gains from finishing the polio re? search project earlier are illustrated by assuming that the decision-maker in 1930 could have elected a more expensive tech?

nology to complete polio research one year earlier. According to earlier estimates, this

implies that approximately 36,000 addi? tional cases might have been prevented. Each case prevented would have resulted in a saving to society of approximately $1,350 in 1957.6 Using a 5 percent dis? count rate, a dollar in 1956 is worth about 28 cents in 1930. As shown in Table 1,

Table 1. Benefits and costs of eliminating polio one year earlier

Nature of benefits and costs

Present value in 1930 at a discount rate of:

5 percent 10 percent

Additional cases

prevented

Elimination of 1956 research costs

Total benefits

Interest lost on

initial applica? tion costs

Additional year's operating costs

Total estimated costs

Maximum justified expenditure to

increase speed

$13,656,600

582,232

14,238,832

4,917,500

2,412,000

7,329,500

6,909,332

$4,082,400

174,048

4,256,448

2,940,000

684,000

3,624,000

632,448

Source: Text.

this implies a gain in benefits of about $14-million from eliminating polio a year earlier.

While a faster technology would be more expensive, finishing the research a

year earlier saves some of the costs asso?

ciated with the slower technology. In this

case, the last year's research expenditures under the technology actually employed is

an estimate of this saving. These expen? ditures amounted to about $2-million in

1956, or about $580,000 when discounted back to 1930.7

Turning to the additional cost of finish? ing earlier, we see that the present value

in 1930 of a year's interest on the initial application costs is part of the marginal cost. Initial application efforts, in the case of polio, amounted to the vaccination

for everyone under 50 years of age. Based on this assumption, the start-up costs have

been estimated at $350-million in 1957.8

These costs imply a loss of interest of

about $4.9-million discounted back to 1930. The interest costs reflect the opportunity cost of using resources to get the vaccina?

tion program under way a year earlier. It is interesting to note that these costs are

substantial and amount to about one-third

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Research Reports

the gain from preventing those cases of

polio that occurred in 1956. Obviously, the costs associated with applying research

findings are an important component in the decision of how fast the research should proceed.

Assuming a constant terminal year for

calculating returns to the vaccination pro? gram, introducing the vaccine a year ear? lier would mean an additional year of

operating costs. These costs would now start in 1957 rather than 1958. The ear? lier analysis determined these costs to be about $9-million.9 As shown in Table 1, using a 5 percent rate of discount, these costs would be valued at about $2.4-mil lion in 1930.

Maximum Justified Expenditure

We have estimated all the costs and bene? fits of an accelerated research program, except those costs associated with speed? ing up the research program. However, by subtracting the estimated marginal costs from the estimated marginal bene?

fits, we can determine the maximum ex?

penditure that would have been justified to apply a faster technology. Given our

assumptions, an additional cumulative ex?

penditure with a present value of $7-mil lion in 1930 would have been justified. As in most investment decisions, the discount rate is important. If we use a 10 percent rate of discount, as shown in Table 1, the maximum justified cumulative expenditure would have a present value of about $632, 000 in 1930.

Although these estimates are consistent with the earlier estimates of a rate of re? turn to research investments with an in? itial period of 1930, it is likely that little

was known of the possible speed at which research might proceed. Nevertheless, the

procedure outlined here is useful in simu?

lating the possible justifiable expenditure for speeding up research at any given date. Like the rate of return estimates

presented earlier, these estimates do not show that we have been able to select op? timal strategies in health research. How?

ever, it does remind us that extra research funds may be justified on the basis of faster results. Perhaps research scientists can make crude approximations of the in? creased speed at which research can pro? ceed with additional funds.

References and Notes

1 Weisbrod, Burton. "Costs and Benefits of Medi? cal Research: A Case Study of Poliomyelitis," Journal of Political Economy 79:527-544 (May/ June 1971).

2 Watson, James D. The Double Helix (New York:

Signet Books, 1969) pp. 107-109. 3 Scherer, Frederic. "Government Research and

Development Programs." In: Dorf man, R. (ed.) Measuring Benefits of Government Investments

(Washington, D.C.: The Brookings Institute, 1965).

4 For detailed discussions of the issue of timing in investment decisions, see: Marglin, Stephen.

Public Investment Criteria: Benefit-Cost Analysis for Planned Economic Growth (Cambridge, Mass.: The M.I.T. Press, 1967) pp. 74-79.

5 The formal model implied in the text is as fol? lows. We should maximize the profit function

H T

b (t) e-*t dt - J* T o H

/ g e-rt dt - S e-rT T + l

where b(t) are the benefits that will result from the completion of research at time T until the conclusion of all benefits at time H; c(T,t) are the research costs from the beginning of the

project until time T; g reflects the constant op? erating costs after the positive research results; S represents the initial start-up costs; and r is the discount rate. The first order condition for a

maximum development time is

? = -b(T)e? _

T j - e-rt dt + c(T, T) e-rT

o 3T

+ ge-rt(T + l) + s r e-rT = o

We assume the second order conditions are sat? isfied.

6 Weisbrod, op. tit., p. 535.

7 Ibid., p. 530.

8 Ibid., p. 536.

9 Ibid.

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