Capítulo 3 Marco Metodológico
3.5 Variables o categorías de análisis
The setup of the model will be exactly like the previous two-sector models. For a project that can generate a stable flow of revenues in the operation stage, the government lacks the construction technology and tries to find out what the best concession contract is. The general model is static and with only one principal. The government as the principal opti- mally chooses three instruments: the authorized phasetijand the participation probability Pij and the monetary transfersTij and the contractor reports its type(Fi;cj)
In this section, we will first present the government’s program and then report several important observations of the first order conditions of our choice variables. The specific conditions will be provided at the appendix.
max (P,t,T) i∈{
∑
H,L}αji[(n−t j)s−T ji]Pji s.t. ∀i, ,j,m,l ∈ {H,L} [tji(R−cj) +Tji−Fi]Pji ≥[tml(R−cj)−Tml−Fi]Pml (IC) [tji(R−cj) +Tji−Fi]≥0 (IR) 0≤Pji ≤1A few important observations of the first order conditions can offer us some hints about the optimal contracts. Each type’s effect for the government is up to its prior, therefore when considering extracting efficiency and paying rents, prior speculation is especially important for the government to achieve optimality. Namely exclusion of types will be part of the optimal contract, and this is closely associated with the previous attributes of the best choice of the instruments.
Proposition 8. The construction decision is not random in the optimal contract.
First of all, the optimal authorized phase can optimally extract the contractor’s relative operational efficiency. The optimal construction decision will consider both dimensions of private information. Since both optimal allocation decisions are linear in the government’s utility, instead of randomization, exclusion of certain type will be optimal. Exclusion of types depends on the prior of type distribution and the information rents paying on both dimensions. If the net surplus a certain type can generate is lower than the information rent paid to other type by inclusion of such type, this type should be excluded from the contract.
Second, different from the two-sector model, the construction cost is not sunk cost in this scenario. Therefore we see an extended proposition 6. If the information rent is higher on the construction dimension and the prior probability of(cL,FL)is very low, the
government will exclude(cL,FL)type and treat the rest types as if they were all(cH,FL). In that case,(cH,FH)only get information rent on construction dimension, the(cH,FL)type get the first best contract and the(cL,FH)type uses information rent on the construction dimension to compensate the inefficiency on the operation dimension.
Proposition 9. Under the condition all types can create positive utility for the government and relatively operational efficient. BOT contract can be used to reduce the rent paying by pooling and partial pooling (pooling after exclusion) for types according to the prior distribution and depending on rent paying on different dimensions, pooling conditions will differ:
• ∆F >n∆c – αLL < ndnH∆−cF L: PLL=0, PHH = PHL =PLH =1. – αLL > ndnH∆−cF L: Pij =1. • ∆F <n∆c – αLL < ndL∆−FF H: PLL=0, PHH = PHL =PLH =1. – αLL > ndL∆−FF H: Pij =1.
Since the contractor’s actual utility will come from rent if any there. That means the high type would always have the incentive to mimic the low type. In other words, inclusion of the low type would mean a rent must be paid to the high type. When the prior that there is low possibility for(cL,FL)type, exclusion of such type would be optimal. Because the government only has to pay one-dimensional information rent to (cH,FH) type. When the prior of(cL,FL)is relatively high, the optimal thing to do is full pooling: treat everyone as if they were(cL,FL)L.
When the operational dimension information rent is high and exlucsion is proper. The optimal contract says every one except(cL,FL) is doing BOT contract: they build, they operate and they get the same contract as if they were all(cL,FH)type. In this case,(cH,FH) type gets the operational information rent; the(cL,FH)type’s participation condition binds
and for the (cH,FL) type is using his information rent on the operation dimension to compensate its inefficiency on the construction dimension. If the information rent on the construction dimension is higher, the government is partially pooling(cH,FH),(cL,FH) and(cH,FL)as if they were all(cH,FL)and the logic is similar.
When the(cL,FL)type is excluded, the intermediate type ((cH,FL)or(cL,FH)) would have to use rent owned on one dimension to compensate its inefficiency on the other dimension if both intermediate types are participating in the contracts. Because the govern- ment is only paying information rent on one dimension, and depending on different cases, such rent can cover the inefficiency on other(which is the other dimensioal information rent), both intermediate types would have the incentives to participate and truth telling (because of the pulling contract).
As long as a low type on both dimensions are included. The(cH,FH)type can choose the one with higher information rent to mimic. The logic is just as we analyzed before. One can infer that if the prior of the (cH,FH) type is sufficiently high, the government would exclude all types but the(cH,FH)type. So what we present here is just a part of the optimal contract, which gives an idea of how the optimal contract should be written:
Based on the prior distribution and information rent comparison on each dimension, the optimal contract is function of both.
Different from the two sector model, where the government would treat construction cost as a sunk cost, in the single regulator model, if the probability that the types being low construction is low and the construction information rent exceeds the relative operational efficiency, the government would let the types with high construction efficiency to do BOT. Even though here the government here is more capable of operation, the government is using partial ownership offered by BOT contract to reduce the rent paying.