Simple Cost-Sharing Contracts

Economic guidance can be of substantial value to policymakers in principle. However, guidance delivered in the form of complex formulae and detailed mathematical characterizations of optimal policies may not be fully appreciated or warmly embraced. Consequently, insights like those of William Rogerson (2003) are particularly important. Rogerson demonstrates in a plausible setting that a pair of simple procurement contracts can secure a surprisingly large fraction (at least three-fourths) of the surplus that a fully optimal contract can secure. The two simple contracts are a fixedprice (FP) contract and a cost-reimbursement (CR) contract. Under an FP contract, the supplier is paid a fixed price for delivering the good in question, regardless of the supplier’s realized production costs. Under a CR contract, the supplier is reimbursed exactly for all realized costs. Rogerson assumes the supplier’s innate production cost is the realization of a uniformly distributed random variable. While this is a natural and plausible case to analyze, it is important to determine whether Rogerson’s powerful conclusion persists in other plausible settings. In addition, if there are plausible settings in which a combination of an FP contract and CR contract (i.e., an FPCR contract) is unable to secure a large fraction of the surplus that a fully optimal contract captures, it is important to determine whether alternative simple contracts can outperform an FPCR contract. We provide two primary observations in this regard. First, we demonstrate that although an FPCR contract can sometimes secure substantially more than three-fourths of the expected surplus secured by a fully optimal contract, the FPCR contract may secure much less than three-fourths of this surplus when the information asymmetry regarding the supplier’s innate production cost is particularly pronounced and the higher cost realizations are relatively likely. Second, we demonstrate that another relatively simple contract can always secure a substantial portion (at least 2/e 73 percent) of the expected surplus secured by a fully optimal contract in the class of settings we consider. The contract in question consists of two options: a CR option and a linear cost sharing (LCS) option. The LCS option specifies a lump-sum payment and a single fraction, [0, 1], of realized costs for which the supplier will be reimbursed. Although the optimal design of the LCS option may be somewhat more complex than the corresponding design of the FP option, the LCS option can secure substantial gains relative to the FP option, particularly in settings of pronounced information asymmetry where the higher cost realizations are quite likely.