To investigate which shadow prices are set high relative to other shadow prices, we use (10′) to construct a ratio of qs to qs. where s’ is some other service. We simplify by abstracting from individual differences in enrollment response by assuming that O’j = Ф\ This amounts to saying that an increase in the value of plan i increases the likelihood of joining for all individuals equally. Equation (10′) can now be used to write the ratio of two shadow prices, q and q\ Note that the Ф’ term cancels out of this expression:
There is no particular reason to expect (10″) to be equal for all service pairs unless the risk adjustment system is so good as to equalize the relative incentives to supply each service.
The Effect of Individuals’ Information
Information plays an important role in creating distortions of adverse selection. We are now ready to study how individuals’ information (beliefs) about their future health care needs affect the plan’s profit maximizing shadow prices. Let
The effect of an individual’s information on the choice of qs enters through as. Suppose, initially, that all individuals are identical in their beliefs about their health care needs of all services for the coming period. In such a case, a = 0 for all s and qs =-— for all s. Thus, in this case all shadow prices are the same and no distortion is obtained. This result is independent of the risk adjustment system and of correlation of predicted spending for different illnesses.
Suppose, now, that individuals have some information that makes them differ from each other with respect to their beliefs about their need of some service s. In such a case, as > 0. Suppose that there is no risk adjustment, so rs = r. We can see that the more heterogeneous are individuals with respect to their mis, the larger will be cts and the higher will be the shadow price qs. This is the standard adverse selection result. The better the information that individuals have about their future needs, the bigger will be the distortion created by the plan in order to attract the profitable individuals.
The effect of correlation among spending on different services on the shadow price can also be observed in (11). If needs are not at all correlated, then ps s. =0 and the only effect on the shadow price comes from individuals’ information a s. If, however, needs are correlated, pss. >0 and the larger ps s. the higher will be the shadow price of services s and s’. Risk adjustment can counter these forces. The larger is the correlation between predicted spending on service s and risk adjustment payment, pr s, the higher will be the denominator of (11), and the lower the shadow price.