As noted in Section 3, the form of Eqs. (5)-(7) is such that there is a maximum number of patients the purchaser wants treated by the hospital however large is 2. Call this number ~° when q = 0 and the corresponding cost reducing effort ~o. If .~ > .~°, the purchaser wants 2o treated (that is, x ° = ~°), whereas if < .~o the purchaser wants ~ treated (that is, x °= .~).