As in the case of a self-interested hospital, there are two simple ways to do that. One is to make the budget depend on 2, the lesser of the demand for treatment and the hospital capacity, but not on x, the number actually treated, so that in line with the efficient arrangement discussed above Bx(x, Yc,C )= 0. A second way is to have a payment per patient that depends on the number of patients treated but is zero for treatments beyond 2, the maximum number the purchaser wants treated however high the demand.