profits and of consumer surplus extracted given in the fourth row of Table 1, it is Ž
seen that 1 r ´
represents total profits both pecuniary and non-pecuniary, and
Pf
. as a proportion of revenue , whereas ´
r ´ represents the loss in consumer
Pd Pf
surplus due to market power, and at the same time the pecuniary profits of the Ž
. physician. It follows that 1
y ´ r ´
represents the physician’s non-pecuniary
Pd Pf
profits. Therefore, ´ provides a weight for the proportion of the physician’s
Pd
profits constituting of pecuniary profits. With ´ sy1, the inducing physician is
Pd
a pure profit maximizer, whereas with ´ s0, her profits only consist of
Pd
Ž non-pecuniary profits again, these are approximations neglecting the fact that
. marginal cost and altruistic marginal benefit could be non-constant .
Ž Importantly, ´
has a different magnitude in the neoclassical model see
Pd
. Section 3 . Correlation between P and d is spurious correlation there, as P and d
cannot be simultaneously changed without changing price. As lower prices both involves the physician having more patients P and each patient buying more
services d , this spurious correlation is positive. In the inducement model, on the contrary ´
is negative, reflecting the fact that the physician can set d for given
Pd
f and that it is optimal to her to set d such that additional d makes the number of patients decrease. The results for ´
are summarized in Table 2, and the
Pd
comparison between the inducement model and the neoclassical model leads us to Proposition 4.
Proposition 4. A negatiÕe correlation firm-leÕel patient-initiated and physician- initiated demand giÕes indication for SID. A positiÕe correlation giÕes indication
for the neoclassical model.
5. Caveats
We now state several caveats to the results presented in Section 4. First, the model ignores both time costs and insurance. If patients only co-pay a portion of
the fee that physicians receive, or if each d causes the patient a time cost, it can be checked that there will no longer be Pareto efficiency. In case of a coinsurance
Ž .
rate, there will be Pareto too much Farley, 1986 , and in case of a time cost, there will be Pareto too little. Second, in considering only one type of patients, the
model does not treat the issue of accessibility. Indeed, in the logic of the model capitation and fee-for-service remuneration of physicians leads to the same
outcomes. However, when there are several types of patients, the results apply only when physicians are able to third-degree price discriminate, i.e., charge
different prices to different patients. Third, our patients react to higher levels of utility provided by physicians. This implies that a raise in utility by a physician
will attract the same number of new patients no matter if it consists of high f and low d , or vice versa. However, it is likely that in the short run, differences in fees
Ž are more easily discernible to patients than differences in treatment intensity cf.,
. Dranove and Satterthwaite, 1992 . Fourth, the alternative SID models with
Bayesian patients shortly reviewed in Section 2.2 should not be rejected a priori. Rather, these models and Farley’s model could apply for different levels of
competition, and for different types of health care. For example, if the costs of switching to another physician are high, and if acquiring information about the
optimal level of treatment is relatively cheap, then a patient who finds out that a new physician in the market is providing her patients with more utility may use
this information to induce his current physician to provide him with more utility, rather than to switch to the new physician. Fifth, and importantly, both our
welfare implications and our empirical predictions hinge upon the physician’s ability to set prices. This reflects the reality in only very little countries. This
caveat is particularly important for the relevance of Proposition 1. Yet, our results are rescued if one assumes that f is implicit price, with f
sfrh, i.e., the implicit fee f equals real fee f divided by quality h, where the physician is then in fact
Ž .
setting quality cf., Bradford and Martin, 1995 , and if one additionally assumes that d
sdh, i.e., real quantity d and quality h are perfect substitutes to the patient. Sixth, individual consumers may make a trade-off between not initiating demand,
but running the risk of eventual high expenditures, and initiating demand, but running less risk of high expenditures. A negative ´
may then be explained by
Pd
some physicians facing relatively less risk-averse consumers, and other physicians facing relatively more risk-averse consumers, and it does not reject the neoclassi-
Ž .
cal model see Table 2 . SeÕenth, because of the costs involved with new patients, for constant Q, treating more patients less intensively may be more costly to the
Ž .
physician than treating less patients more intensively Hoerger, 1989 . The cost Ž
. Ž
. function should then be C P,d
instead of C Pd . In the SID model, margins Ž
. Ž
. 20 and 22 will then involve marginal costs C and C , respectively. Looking at
P d
Table 2 now, ´ ´
no longer rejects the pure inducement model. Eighth,
Pf df
the physician, rather than being an altruist, may be paternalistically valuing patient functioning instead of patient utility, or may be valuing applying her technical
expertise. Indeed, one may wonder how the physician can find out the patient’s preferences in the first place. For the physician as a technician, who derives utility
Ž .
from ‘‘doing a good job’’, one may imagine her utility function to be w Y,d . This completely reverses the results in the inducement case. It can be checked that
y1 y1
´ rather than ´
will now be the best approximation of physician
df Pf
y1
profits, as only the former involves non-pecuniary profits. Similarly, ´ is
df
now the approximation of the patient’s loss in consumer surplus. Furthermore,
16
there no longer is Pareto efficiency. Finally, it is ´
rather than ´ which
df Pf
16
Unless one wants to include the physician’s non-pecuniary benefit of providing each patient with an extra health service in the Pareto criterion.
can be smaller than one, and ´ must be smaller than minus one. It should be
Pd
stressed, however, that inducement in this case is only constrained by competition.
6. Conclusion
