Academic Articles Health Insurance

Optimal Health Insurance and Provider Payment

How does one design an optimal insurance policy where physicians and patients are compelled to tell the truth about the medical procedures that were completed?  This is the question of Ching-To Albert Ma and Thomas McGuire in their 1997 AER paper.  The paper is somewhat technical but I will briefly explain their setup and conclusions, along with my own analysis.


Individuals become sick with probability ‘p‘.  If this occurs and they can purchase health (medical care) which is a strictly concave function of the number of procedures done (‘t‘) and the physician effort level (‘e‘).  Thus:

  • Health=f(t,e)

The physicians can report any procedure level ‘T‘ to the insurance company that they wish regardless of the actual number of procedure (‘t‘) that they complete and which are recorded in the medical records.  Individuals get utility from income and health.  In this paper, health is measured in cash equivalent units.  Physicians are profit maximizers, but receive less utility the more effort they put forth.


  1. Truth Telling: In order to induce truth telling (T=t) physicians must receive a positive payment for their services (not strict capitation) and patients must have a positive co-payment.  This way, physicians will wish to increase T, but patients will not allow this since increasing T increases the co-pay.  The patient are able to reveal the true ‘t‘ to the insurer and thus truth telling is the Nash equilibrium.
  2. Effort: If the second derivative f_{t,e} is negative, effort and treatment are substitutes.  This means that more physician effort will reduce the demand for medical procedures since.  If this is the case, physicians will reduce ‘e‘ to the minimum level to maximize ‘t‘ (and thus their profits).  If the second derivative f_{t,e} is positive, effort and treatment are complements.  This means physicians can only increase ‘t’ when they increase their effort level.  In this case, physicians will put forth an high level of effort.
  3. Ethics:  What if physicians have ethical notion of a minimal level of care, so a necessary condition is that ‘f(t,e)>F‘?  In this case, e may increase from its lower bound (in the substitute case).  In a general equilibrium setting, capitation payments, however, may need to increase in order to induce individuals to enter/remain in the medical profession.  Overall, however, having an ethical minimal level of care is Pareto improving for society.


This paper is interesting theoretically, but greatly simplifies the market.  Competition within insurance plans as well as the variety of plans available does not appear in this paper.  Further, there is likely no explicit function f(t,e) in which medical procedures translate into health; there is a significant stochastic element to health even in the face of known treatment quantities.  The paper also abstracts from many of the informational problems (such as the fact that patients may not know/understand the procedure they undergo) and assumes that supplier induced demand is limited by the patients’ medical knowledge. 

Ma and McGuire (1997), “Optimal health insurance and provider payment,” American Economic Review, Vol. 87(4), pp. 685-704.