Top

The European Journal of Health Economics

Published in:

01-05-2014 | Original Paper

Optimal choice on prevention and cure: a new economic analysis

Author: Mario Menegatti

Published in: The European Journal of Health Economics | Issue 4/2014

Abstract

This paper studies choices on prevention and cure in a context where an agent bears a health risk. In this framework we first analyze interdependence between the optimal levels of prevention and cure. Second, we study the effects on optimal choices of a change in the cost of one of the two instruments and we examine substitutability between them. Finally we present findings about the effects of a change either in the seriousness of the possible disease or in the efficiency of the medical treatment.

A wide literature studies various aspects of choice regarding lifestyle and bad habits. Two of the more recent contributions are Amador and Nicolás [1] and Sundmacher [33].

Prudence is a feature of the utility function related to its third derivative (see [25]). An agent is prudent if this derivative is positive and is imprudent if it is negative. Prudence is a relevant element for determining agent behavior in many economic problems. See also Menegatti [27].

Courbage and Rey show that an increase in the fear of sickness has ambiguous effects on prevention for health risks (as in Dionne and Eeckhoudt [12], an increase in risk aversion has an ambiguous effect on prevention for financial risks). They also show that an increase in prudence reduces prevention for health risks (as it does in Eeckhoudt and Gollier [14] for financial risks).

This parallelism is clear in the paper since Hennessy introduces the two variables into the maximization problem in exactly the same way.

See for instance the role of the sign of the cross-derivative of the utility function for many results below.

These papers respectively study the effect of background risk and contemporaneous different risks and substitutability between prevention and saving in a two-period model. A framework including “anticipated” prevention, as in Menegatti [28], studied together with “contemporaneous” prevention, is proposed by Hofmann and Peter [23].

Note that, in this work, uncertainty concerns the possibility of falling sick. Different sources of uncertainty, relevant for health decisions, have recently been discussed by Antonanzas et al. [2]. See the “Conclusions”.

For instance, by following a healthier lifestyle.

In particular, the assumption p′′(e) > 0, in addition to its plausibility, is useful in order to avoid the trivial case where the agent desires a potentially unlimited level of effort (which can occur when p′′(e) < 0).

This means that it is not possible to completely exclude the possibility of falling sick.

This is the case of diseases where cures merely reduce an agent’s pain.

Consider, for instance, a disease which requires a long and expensive rehabilitation. In this case the agent can choose to follow it until she gets a satisfying reduction in the pain and not until the complete removal of the disease.

As noted above, Hennessy [21] introduces a two-state framework (healthy or sick) and introduces cure as an instrument which increases the probability of moving from illness to health.

See, for instance, Courbage and Rey [8], Eeckhoudt and Gollier [14] and Menegatti [28].

Note that this independence has some similarities with the separation between insurance and prevention obtained by Dionne and Eekchoudt [11] and between insurance, prevention and saving obtained by Menegatti and Rebessi [30].

if we compute V _ec in Eq. (4), this is clear. If V _ec is computed in Eq. (3), we get a value which is nullified by using (4) (as in the proof of Proposition 1).

This is also shown by Eqs. (6) and (8). Equation (6) considers total differentiation of (3). However since V _ec is null, the effect of dc* in the equation disappears.

The reduction is “weak” in the sense that it is null when u ₁₂ = 0.

Uncertainty in this model is completely expressed by probabilities p(e) and 1 − p(e).

As noted in the “Introduction”, in Hennessy [21] the effect of an increase in prevention cost suggests that there is complementarity between prevention and cure.

For instance since health status has positive externalities in the economy,

The value of E[H ₁] is related to the whole population if the agent of our problem is representative of the whole economy.

Hennessy, however, argues that the effect is negative for a plausible calibration of parameters and functions.

Note that α is the ‘rate of return’ of the medical treatment in terms of health.

See “Introduction”.

In our framework, this would imply the assumption that α is a random variable.

In our framework, this would imply the assumption that d is a random variable,

Amador, L.B., Nicolás, A.L.: Self-control and support for anti-smoking policies among smokers, ex smokers, and never smokers. Eur. J. Health Econ. (2011, forthcoming)

Antoñanzas, F., Rodríguez-Ibeas, R., Juarér Castelló, C.A.: Coping with uncertainty on health decisions: assessing new solutions. Eur. J. Health Econ. 13, 375–378 (2012)PubMedCrossRef

Asheim, G.B., Wenche Emblem, A., Nilssen, T.: Health insurance: medical treatment vs disability payment. Res. Econ. 64, 137–145 (2010)CrossRef

Bleichrodt, H., Crainich, D., Eeckhoudt, L.: Comorbidities in cost benefit analysis of health care. J. Public Econ. 87, 2399–2406 (2003)CrossRef

Bleichrodt, H., Quiggin, J.: Life-cycle preferences over consumption and health: when is cost-effectiveness analysis equivalent to cost-benefit analysis? J. Health Econ. 18, 681–708 (1999)PubMedCrossRef

Briys, E., Schlesinger, H.: Risk aversion and the propensities for self-insurance and self-protection. South. Econ. J. 57, 458–467 (1990)CrossRef

Ehrlich, I., Becker, G.S.: Market insurance, self-insurance, and self-protection. J. Polit. Econ. 80, 623–648 (1972)CrossRef

Courbage, C., Rey, B.: Prudence and optimal prevention for health risks. Health Econ. 15, 1323–1327 (2006)PubMedCrossRef

Courbage, C., Rey, B.: Optimal prevention and other risks in a two-period model. Math. Soc. Sci. 63, 213–217 (2012)CrossRef

10.

Cuff, K., Hurley, J., Mestelman, S., Muller, A., Nuscheler, R.: Public and private health care financing with alternate public rationing rules. Health Econ. 21, 83–100 (2012)PubMedCrossRef

11.

Dionne, G., Eeckhoudt, L.: Insurance and saving: some further results. Insur. Math. Econ. 3, 101–110 (1984)CrossRef

12.

Dionne, G., Eeckhoudt, L.: Self-insurance, self-protection and increased risk aversion. Econ. Lett. 17, 39–42 (1985)CrossRef

13.

Dionne, G., Li, J.: The impact of prudence on optimal prevention revisited. Econ. Lett. 113, 147–149 (2011)CrossRef

14.

Eeckhoudt, L., Gollier, C.: The impact of prudence on optimal prevention. Econ. Theory 26, 989–994 (2005)CrossRef

15.

Eeckhoudt, L., Hammitt, J.K.: Background risks and the value of a statistical life. J. Risk Uncertain. 23, 261–279 (2001)CrossRef

16.

Eeckhoudt, L., Huang, R.J., Tzeng, L.Y.: Precautionary effort: a new look. J. Risk Insur. 79, 585–590 (2012). doi:10.1111/j.1539-6975.2011.01441.x CrossRef

17.

Evans, W.N., Viscusi, W.K.: Utility functions that depend on health status: estimates and economic implications. Am. Econ. Rev. 80, 353–374 (1990)

18.

Finkelstein, A., Luttmer, E.F.P., Notowidigdo, M.J.: What good is wealth without health? The effect of health on the marginal utility of consumption. Working paper 14089, National Bureau of Economic Research (2008)

19.

Friedman, M., Savage, L.J.: The utility analysis of choices involving risk. J. Polit. Econ. 56, 279–304 (1948)CrossRef

20.

Grossman, M.: On the concept of health capital and the demand for health. J. Polit. Econ. 80, 223–255 (1972)CrossRef

21.

Hennessy, D.A.: Prevention and cure efforts both substitute and complement. Health Econ. 17, 503–511 (2008)PubMedCrossRef

22.

Hoel, M.: What should (public) health insurance cover? J. Health Econ. 26, 251–262 (2007)PubMedCrossRef

23.

Hofmann, A., Peter, R. (2011) The impact of time-structure on optimal prevention. In: Paper presented at the 12th symposium of the German Economic Association of Business Administration, Zurich (2011, September)

24.

Julien, B., Salanié, B., Salanié, F.: Should more risk-averse agents exert more effort? Geneva Pap. Risk Insur. Theory 24, 19–28 (1999)CrossRef

25.

Kimball, M.S.: Precautionary savings in the small and in the large. Econometrica 58, 53–73 (1990)CrossRef

26.

Levaggi, L., Levaggi, R.: Welfare properties of restrictions to health care based on cost effectiveness. Health Econ. 20, 101–110 (2011)PubMedCrossRef

27.

Menegatti, M.: On the conditions for precautionary saving. J. Econ. Theory 98, 189–193 (2001)CrossRef

28.

Menegatti, M.: Optimal prevention and prudence in a two-period model. Math. Soc. Sci. 58, 393–397 (2009)CrossRef

29.

Menegatti, M.: New results on optimal prevention of risk averse agents. Econ. Bull. 32, 2166–2173 (2012)

30.

Menegatti, M., Rebessi, F.: On the substitution between prevention and saving. Math. Soc. Sci. 62, 176–182 (2011)CrossRef

31.

Rey, B., Rochet, J.C.: Health and Wealth: ow do they affect individual preferences? Geneva Pap. Risk Insur. Theory 29, 43–54 (2004)CrossRef

32.

Shapiro, C., Stiglitz, J.: Equilibrium unemployment as a worker discipline device. Am. Econ. Rev. 74, 433–444 (1984)

33.

Sundmacher, L.: The effect of health shocks on smoking and obesity. Eur. J. Health Econ. 13, 451–460 (2012)PubMedCrossRef

Title: Optimal choice on prevention and cure: a new economic analysis
Author: Mario Menegatti
Publication date: 01-05-2014
Publisher: Springer Berlin Heidelberg
Published in: The European Journal of Health Economics / Issue 4/2014
Print ISSN: 1618-7598
Electronic ISSN: 1618-7601
DOI: https://doi.org/10.1007/s10198-013-0479-y

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Optimal choice on prevention and cure: a new economic analysis

Abstract

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Abstract

Please log in to get access to this content

Other articles of this Issue 4/2014

Comparative cost-effectiveness analysis of oral triptan therapy for migraine in four European countries

Orphan drugs policies: a suitable case for treatment

Effects of health care decentralization in Spain from a citizens’ perspective

Announcement effects of health policy reforms: evidence from the abolition of Austria’s baby bonus

Distribution of health-related social surplus in pharmaceuticals: an estimation of consumer and producer surplus in the management of high blood lipids and COPD

Explaining differences in remuneration rates of nursing homes in Germany