【正文】 t a consultation). For convenience of exposition we separate utility from treating GMS patients and from treating private patients. Utility from treating GMS patients is given by the revenue from visits initiated by the patient, GMSQp , and revenue initiated by induced visits, indGMSpQ . We assume that the number of visits initiated by the patient depends upon their underlying health, H, and a taste parameter, α. Thus we have: )(),(. i n dG M SG M Si n dG M SG M SG M SG M SG M SG M SG M S eQpHQpU ???? ?. Utility from treating private patients is likewise given by: )(),(. i n dp r i vp r i vi n dp r i vp r i vG M SG M Sp r i vp r i vp r i v eQpHQpU ???? ?. We make the crucial assumption that the marginal cost in terms of effort of inducing an extra visit from a private patient is at least as great as it is from a public patient . )()( in dG M Sin dp riv QeQe ??? . This is because the GMS patient will not have to meet the cost of the induced visit whereas the private patient will. Thus either the GP will have to spend extra effort in trying to persuade the private patient that a return visit is warranted, or the GP may have to charge a reduced fee. We also assume that the (.)e function is convex . 0(.)??e . This is necessary in order to obtain an internal solution. We also assume that the fee charged for a private patient is greater than that obtained for a GMS patient . privGMS pp ? . This is consistent with evidence presented in Tussing. Assume for the moment that the only choice variable open to the GP is the amount of induced visits – thus we are assuming that the GP cannot fix his fee. This is certainly true for GMS patients and may be a reasonable approximation for private patients. It seems reasonable to regard GPs as pricetakers and while there may be some degree of local monopoly power, the degree to which a GP can manipulate price may be quite limited. The first order conditions for the GP are thus: 0)( ????? ? i n dG M SG M Si n dG M S QepQ U 0)( ????? ? i n dp r ivp r ivi n dp r iv QepQ U The first order conditions can be represented diagrammatically below: Note that the marginal costs (of effort) curves are upward sloping – this is a consequence of the convexity of the e(.) function . (.)e? the marginal cost of effort is rising. Since fees are fixed, the marginal benefit curves are straight horizontal lines. The GP induces visits for both sets of patients – we cannot determine the precise quantity of private and GMS visits induced as this will depend upon the positions of the relative curves. In the diagram here an equal number of private and GMS visits are induced . *Q in dp rivin dG M S ?? . Now suppose that the reform introduced in Ireland in 1989 is incorporated into the model . payments for GMS patients switch from a feeforservice arrangement to a capitation system. The weighted capitation payment which GPs receive for their medical card patients will depend upon demographic factors s uch as the age and gender of the patients on their list. Crucially however, the absence of a feeperservice for these patients removes the financial incentives for GPs to induce return visits. The utility function for GMS patients now changes to )()( i n dG M SG M SG M SG M SG M S eDNU ??? where GMSN refers to the number of GMS patients on a GP’s list and GMSD refers to the underlying demographic factors influencing the weighted capitation payment. The utility function for private patients remains as before. The first order condition for GMS patients now bees 0)( ????? ? in dG M Sin dG M S QeQ U . This clearly indicates a corner solution and implies that GPs will induce zero visits from GMS patients. The diagram changes to below: MB, MC Induced visits MC Private Private fee GMS fee MC GMS *Q indprivindGMS ?? . The GMS fee schedule is now effectively the horizontal axis and hence the corner solution of 0?indGMSQ is obtained. It is possible that GPs will increase their private fees to offset this loss in ine and in turn they may induce extra visits by private patients. The effect on overall induced visits would then be ambiguous. What will be the overall effect on total utilisation by GMS and private patients before and after the reform? Before the reform total utilisation by GMS patients will be equal to induced and noninduced visits . in dG M SG M SG M S Q ,0,0,0 ?? where the “0” subscript refers to the period before the reform. Alternatively per capita utilisation can be expressed as in dG M SG M SG M S qqq ,0,0,0 ?? where lowercase refers to utilisation per head. Similarly total per capita utilisation for private patients will be