Traditional Procurement

Here, we study a typical traditional procurement mechanism, and derive the equilibrium to compare it with the equilibrium under a PPP. Let be the amount of transfer from G to C if B is greater than or equal to Bo. Equation (7) is the maximization problem of C to determine the amount of a and e:

By Assumption 1, the objective function of equation (7) is concave, so that we can derive the optimal level of C's effort by the first-order conditions. The conditions are:

Equation (8) shows how agent C decides the level of effort to decrease CC. As increases by one unit, C can save CC by one unit. Thus, C's marginal benefit of increasing a is one, which is the right side of the equation. The left side,

d'1(atp), implies C's marginal cost of increasing a. As a increases, OC increases by C'1(a) but C does not care about the changes in OC-that is the burden of operator O, which makes equation (8) different from (5). For maximizing social welfare, the marginal cost of C1 should be considered while C does not care about the cost in a traditional procurement contract, where OC is not covered by C. Therefore, the optimal level of a of C under traditional procurement, atp, is greater than the first best level, a*.

Proposition 1: The effort to lower construction costs under traditional procurement (atp) is greater than the first best level of the effort; that is, atp >a*.

Equation (9) shows how agent C decides the level of effort to increase the benefit of the infrastructure. By increasing e by one unit, the benefit of the infrastructure increases by one unit. However, C only gets the fixed amount of compensation, T, regardless of the amount of B if it is greater than Bo. Because C covers the cost of e, I(e) + d2(e), but does not get any benefit from it, C will choose zero effort, thus, etp = 0, which is obviously less than the socially optimal level, e*.

Proposition 2: The effort to increase the benefit of the infrastructure under traditional procurement is zero, which is less than the first best level of the effort; that is, etp = 0 < etp.

As shown in Proposition 2, C chooses a lesser level of effort under traditional procurement. Because C only cares about profit, which excludes operating costs and the benefit of infrastructure, C chooses different effort levels, atp and etp, from socially optimal levels a* and e* which means there is some inefficiency in a traditional procurement. In sum, the effort to lower construction costs is overachieved, while the effort to increase infrastructure quality is underachieved.