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Optimal choice on prevention and cure: a new economic analysis

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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.

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Notes

  1. 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].

  2. 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].

  3. 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).

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

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

  6. 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].

  7. 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”.

  8. For instance, by following a healthier lifestyle.

  9. 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).

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

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

  12. 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.

  13. 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.

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

  15. 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].

  16. 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).

  17. 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.

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

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

  20. 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.

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

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

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

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

  25. See “Introduction”.

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

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

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  1. Dipartimento di Economia, Universitá degli Studi di Parma, via Kennedy 6, 43125, Parma, Italy

    Mario Menegatti

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Menegatti, M. Optimal choice on prevention and cure: a new economic analysis. Eur J Health Econ 15, 363–372 (2014). https://doi.org/10.1007/s10198-013-0479-y

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