9 FUNDING AND FINANCING INFRASTRUCTURE Comparative Statics. Simple comparative statics are immediately obtained from (2.4). As demand becomes more elastic, the optimal regulated price comes closer to the expected cost for the service. It is indeed harder to raise revenues from sales under those circumstances and public subsidies become a more attractive way of covering the upfront investment. When budgetary pressures are more stringent (i.e., for greater values of the cost of public funds _λ_ ), saving on public funds becomes more attractive. The wedge between price and (expected) cost thus also increases. Finally, when the expected cost itself increases, part of it is passed through to the regulated price.

Optimality of investment. Finally, the investment _I_ is socially valuable when: (2.5) _ω_ ( _p_<sup>_sf_</sup> ) _≥_ (1 + _λ_ ) _I._ Later, we shall be interested in how this condition becomes harder to satisfy when the firm has to rely on outside financiers and financial contracts are plagued with agency costs.

The complementarity between revenues and public subsidies. From the binding break-even constraint (2.2), we obtain the following expression of the optimal public subsidy _T_<sup>_sf_</sup> : Therefore the optimal price remains above expected cost, and: The reason the investment should not be entirely financed through public subsidies is that public funds are socially costly. Indeed, part of this investment can already be recouped by what consumers directly pay for the service, which is socially cheaper. There exists a complementarity between two modes of financing the investment, either through revenues from the service or through public subsidies.

# 2.2. _The Benefits of Outside Finance_

There are two main reasons why relying on outside financiers could _a priori_ be found attractive. First, the operator may not have retained enough earnings from previous operations elsewhere to bear the initial cost of investment by itself. From a previous remark, the model of Section 2.1 can nevertheless be also interpreted as picturing the case where the public authority directly pays for the investment. The fact that the firm has no cash to start with is thus not a real concern and public subsidies could be used to relieve such constraint anyway. However, nonlinearities in the cost of public funds<sup>9</sup> could render such solution difficult to implement, especially at times of raising budgetary discipline.<sup>10</sup>

> 9One _ad hoc_ modeling of such nonlinearity would consists in supposing that the cost of public funds is increasing and convex, say Λ( _T_ ) (with Λ<sup>_′_</sup> _≥_ 0 and Λ<sup>_′′_</sup> _≥_ 0). Section 3.6 below provides some modeling for such nonlinearities.

> 10Schmitz (2013) analyzes how budgetary pressures may affect the traditional theory of _PPP_ , which following Hart (2001), Bennet and Iossa (2006), Iossa and Martimort (2015) and Martimort and Pouyet (2008) suppose that task bundling under _PPP_ saves on various agency and transaction costs. Under such circumstances, while public subsidies might be preferred for investments of small size, relying on outside financiers might be a least costly solution to build the infrastructure if the upfront outlay is of significant magnitude.