The authors assume that the quantity of medical services is produced by the following production function:
- qi = f(hi, ti, ki, ei, θi)
- h: physician hours, t: non-physician hours, k: capital, e: effort level, θ: other factors.
- ui = yi – vi(ei, hi)
- yi = α(P-C)qi + n-1(1-α)(P-C)Σ(1 to n) qi
- The variable α represents the percentage of work that physicians receive 100% of the net profit they generate and (1-α) represents the net profit generated shared among the n physicians in the group.
- ∂ui/∂ei = [α + n-1(1-α)](P-C)(∂fi/∂ei) – ∂vi/∂ei) = 0
So know we’ve done some math. Who cares? What do we get out of all these equations? The first order equation, ∂ui/∂ei, shows that when physicians optimize their effort level, they trade off the benefit from extra effort (more money) versus the cost of more effort (they’d rather be golfing). The authors can also use comparative statics to to predict how they will affect physician effort.
- α: An increase in the percentage of work where the physician receives 100% of the profit generated will increase effort.
- P: An increase in the price of a medical service will increase physician effort.
- C: An increase in the cost of a medical service will decrease physician effort
- n: As the number of physicians increase, effort decreases. This is because physicians will have to share more of their income with other doctors. This results falls in line with the finding of Newhouse (1973). This paper found evidence of “behavioral diseconomies of scale” whereby physicians shirk more as the number of physicians in the group increases.
- Martin Gaynor and Mark V. Pauly (1990) “Compensation and Productive Efficiency in Partnerships: Evidence from Medical Groups Practice” Journal of Political Economy, 1990, vol. 98, no. 3, p. 544-573.
- Newhouse JP (1973) “The Economics of Group Practice” Journal of Human Resources, Vol. 8, No. 1, pp. 37-56.