Extension 1: Maintaining idle capacity

A feature present in countries with a National Health Service is the co-existence of a public and private sector. Often, the public payer contracts with private providers while holding idle capacity. This is one of the most striking features of some natio- nal health systems and it is often seen as inefficiency from the management of public facilities.¹⁶ We present here a different rationale for the existence of such idle capacity: the public sector may opt to use idle capacity as a way to gain bargaining power vis- à-vis the private provider, under the assumption of a more effi- cient private sector.

We consider a setting where a third party payer, say a National Health Service (NHS), has to negotiate prices for healthcare ser- vices with providers (Barros and Martínez-Giralt 2005b). We assu- me the presence of two providers. The public sector may or may not be capacity constrained. Both situations will be discussed below.

The NHS has a budget to pay providers. The NHS positively values free funds as it allows for its productive application elsew- here in the health sector. The gain to the NHS from negotiation is given by the difference in the net surplus under negotiation

16For a review of several countries, see Busse and Howorth (1999), Crainich and Closon (1999), Engelbert (1999) and Lancry and Sandier (1999).

and in the case of failure. Since a positive level of insurance cove- rage is always guaranteed to patients, that gain net of the fallback value will be the payment to be made by the NHS to ensure pro- vision in the private market, plus the value in monetary terms of the extra insurance level provided to patients (a copayment).¹⁷

Healthcare providers organize themselves as an association.

The association negotiates contractual conditions (price) with the NHS representative. The price agreed by the association with the NHS is common to all members of the association.¹⁸

We assume profits of both providers to be equally weighted in the objective function of the association. An alternative assump- tion would be that the more efficient provider has a greater influence over the association’s objectives. This would leave the qualitative results unchanged, as it would fall between the two extreme cases we discuss.

The setting we have in mind includes a first stage with the public sector deciding its capacity and a second stage where price bargaining occurs. The model is solved, as usual, by backward induction.

We also assume a less efficient public sector. Otherwise, in the absence of capacity constraints and equal efficiency in public and private facilities, the third party payer trivially would provide only public sector treatment.

The net surplus for agents (providers and NHS) is given by the difference between the surplus or profits earned from treating patients at the agreed price and the corresponding surplus or profits at the free market equilibrium price (in case of negotia- tion failure). Also, if negotiations fail, the fallback value for the NHS is defined as the budget left after reimbursing those patients exceeding the public sector capacity and paying the cost of the capacity installed.

In the capacity sub-game, decisions take into account the con- tinuation of the game and how they will affect the negotiated price.

17See subsection 2.2.4.

18Further details on the role of associations of healthcare providers are presented in the next section.

The objective function of the third party payer is the surplus generated. That is the budget left after paying for the patients treated in public and private facilities, and the cost of the capacity installed.

Under the stated conditions, it turns out that the optimal capa- city utilization is zero. On the other hand, depending on the para- meter values, there may be a positive equilibrium value for capa- city, which will be kept idle. The only reason to build capacity here is the strategic effect associated with the negotiation stage.

Increasing capacity reduces the fallback value of providers, valued at the margin by the price paid by patients that exceed public sec- tor capacity. This helps in obtaining a lower price during the negotiation stage. On the other hand, it may reduce or increase the fallback value of the third party payer, as it depends on whet- her using the extra capacity costs more than using the private market. In such circumstance, the third party payer would prefer to buy in the private market.¹⁹Each of these marginal changes in fallback values resulting from capacity decisions is weighted by the bargaining power of each side. Of course, if the cost diffe- rence between public and private treatment is high enough, the optimal capacity may well be zero in the public sector, and there will be a capacity constraint. However, the important point we want to convey is that the public sector may choose to have slack as a way to improve its negotiation terms. Naturally, this only has value if there is some gain from using the private sector vis-à-vis public facilities.

The argument is akin to the Dixit-Spence (Dixit 1979, 1980;

Spence 1977, 1979) excessive capacity result, where a firm builds extra capacity as a commitment to be aggressive in the market.

The idle capacity works as a commitment to extract more surplus from more efficient private providers that negotiate prices with the public payer. Therefore, empirical assessments of the role of idle capacity in the public sector must take into account whether negotiations with the private sector exist.

19We assume that in case of negotiations failure, the public sector will use all its capa- city. If this was not the case, the only equilibrium price would be the private market equi- librium price.