Pairing provision price and default remedy: optimal two‐stage procurement with private R&D efficiency

• Author: Jingfeng Lu,Bin Liu
• Date: 01 September 2018
• DOI: http://doi.org/10.1111/1756-2171.12247
• Published date: 01 September 2018

RAND Journal of Economics

Vol.49, No. 3, Fall 2018

pp. 619–655

Pairing provision price and default remedy:

optimal two-stage procurement with private

R&D efficiency

Bin Liu∗

and

Jingfeng Lu∗∗

This article studies cost-minimizing two-stage procurement with Research and Development

(R&D). The principal wishes to procure a product from an agent. At the first stage, the agent can

conduct R&D to discover a more cost-efficient productiontechnology. First-stage R&D efficiency

and effort and the realized second-stage production cost are the agent’s private information. The

optimal two-stage mechanism is implemented by a menu of single-stagecontracts, each specifying

a fixed provision price and remedy paid by a defaulting agent. A higher delivery price is paired

with a higher default remedy, and a moreefficient type opts for a higher price and higher remedy.

1. Introduction

Procurement is ubiquitously employed as a cost-efficient way to acquire goods, services,

or work from an external source. On average, around 15% of yearly global domestic product

is spent on public procurement alone, with military acquisitions as a significant component.1It

has long been recognized that procurement of new goods/services often involves and stimulates

private research and development (R&D) and/or innovation before production and delivery (see

∗The Chinese University of Hong Kong, Shenzhen; binliu@cuhk.edu.cn.

∗∗National University of Singapore; ecsljf@nus.edu.sg.

We are grateful to the Editor in charge, David Martimort, and two anonymous reviewers for insightful comments and

suggestions, which significantly improved the quality of the article. We thank Masaki Aoyagi, Tilman B¨

orgers, Jimmy

Chan, Yi-ChunChen, Jeffrey Ely, Robert Evans, Daniel Garrett, YingniGuo, Chiu-Yu Ko, Daniel Kr¨

ahmer,Laurent Lamy,

Hao Li, Meng-YuLiang, Hitoshi Matsushima, Vai-Lam Mui, Martin Osborne, Alessandro Pavan, Carolyn Pitchik, John

Quah, Xianwen Shi, Roland Strausz, Bal´

azs Szentes, Satoru Takahashi, Rakesh Vohra, John Wooders,Okan Yilankaya,

Lixin Ye, Jun Yu, and participants in the 15th SAET Conference on Current Trends in Economics and the 11th World

Congress of the Econometric Society for helpful comments and suggestions. Liu gratefully acknowledges financial

support from National Natural Science Foundation of China (71703138). Lu gratefully acknowledges financial support

from MOE, Singapore (R122000252115). Any remaining errors are our own.

1Refer to p. 1 in “Supplement to the 2013 Annual Statistical Report on United Nations Procurement: Pro-

curement and Innovation,”www.unops.org/SiteCollectionDocuments/ASR/ASR_Supplement_2013_WEB.pdf(accessed

October 6, 2015).

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Rob, 1986; Hendricks, Porter, and Boudreau, 1987; Lichtenberg, 1988; Rogerson, 1989; and

Tan, 1992; among others).2More recently, Nyiri et al. (2007) emphasize the role of public

procurement in promoting R&D investment and innovation in information and communication

technology (ICT) in European Union (EU) member states. The United Nations Office for Project

Services (UNOPS), in its 2013 report,3also stresses the role of public procurement in fostering

investment in new technology and research in both developed and developing countries.

Cost effectiveness has long been the central issue in procurement design.4An established

literature has been devotedto designing cost-minimizing acquisitions in a variety of environments.

It is clear that contractors’ predelivery R&D incentive for cost reduction should be used fully

by procurers to lower their acquisition costs. To achieve the most cost reduction, an optimal

procurement policy must appropriately balance extracting surplus ex post and providing the right

R&D incentive ex ante.5

Typically, both R&D effort and the efficiency of goods/services delivery (i.e., production

cost) are a contractor’s private information. Moreover, situations abound in which a contractor’s

R&D efficiency (e.g., the marginal cost of R&D effort) is also his private information. R&D

activities require both technical facilities and researchers with different expertise and specialties.

The contractor’s competence in organizing, coordinating, and carrying out a specific R&D task

(e.g., the quality of its technical facilities, the abilities and experience of its researchers, and

its efficiency in project management) is usually not observable by the procurer. An immediate

implication is that the contractor’s R&D incentive must respond to his R&D efficiency. Several

interesting issues thus arise for procurement design. How does this additional dimension of the

agent’s private information affect his R&D incentive and, consequently, the optimal design for

procurement? In particular, how should the optimal design incorporate this new element in the

information flow into the natural dynamics of the procurement process? Which form does the

optimal contract take?

The fixed-price contract is among the most widelyadopted procurement contracts. According

to the “Performance of the Defense Acquisition System, 2014 Annual Report,”6fixed-price

contracts constitute about half of all Department of Defense (DoD) obligated contracts. They are

most common in production contracts and are often used for goods and services acquisitions.

According to the “DoD SBIR Desk Reference,”7fixed-price contracts are almost alwaysused for

Phase I awards.The National Aeronautics and Space Administration (NASA)awarded fixed-price

contracts worth $6.8 billion to Boeing and SpaceX in 2014 to ferry astronauts to the International

Space Station. More recently, the National Defense Authorization Act for Fiscal Year 2017

establishes a preference for the DoD to use fixed-price contracts.

A fixed-price contract has several apparent advantages from the procurer’s perspective,

which could explain its popularity. It shifts most or all the risk to the contractor and is easier to

design and implement, as it imposes a minimal regulatory and administrative burden, and fewer

financial/cost reports are required. Although these advantages are well understood, it would be

2Hendricks, Porter, and Boudreau (1987) observe that in federal auctions for leases on the outer continental shelf,

bidders make private investments to acquire more information before bidding. Abundant empirical evidence in defense

procurement demonstrates that bidders make significant privateinvestments in R&D prior to bidding. Tan (1992) provides

an example of jet-fighter procurement by the US Air Force.Lichtenberg (1988) provides more examples of private R&D

investment in public defense procurements.

3“Supplement to the 2013 Annual Statistical Report on United Nations Procurement: Procurement and Innovation,”

2014, www.unops.org.

4Rob (1986) points out that “the importance of the cost effectiveness in the acquisition process cannot be overem-

phasized.”

5Notably,contractors’ predelivery R&D incentive has been incorporated into the analysis in many pioneer studies,

including Rob (1986), Dasgupta (1990), Tan (1992), Piccione and Tan (1996), and Arozamena and Cantillon (2004),

among others.

6www.defense.gov/Portals/1/Documents/pubs/Performance-of-Defense-Acquisition-System-2014.pdf (accessed

September 29, 2015).

7www.acq.osd.mil/osbp/sbir/sb/resources/deskreference/deskreference.pdf (accessed September 29, 2015).

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interesting to investigate whetherthere are deeper and subtler economic justifications for the wide

adoption of fixed-price contracts. In this article, we address this issue and provide a plausible

justification from a dynamic mechanism design perspective by establishing fixed-price contracts

as the cost-minimizing procurement design in a two-stage environment.

We consider a two-stage contract between a procurer (she, the principal) and a supplier (he,

the agent) in the following environment. The principal wishes to procure a product from the

agent that she can acquire from an alternative source at cost c0. The agent can invest in R&D that

improves his endowed production technology and generates a production cost potentially lower

than c0. The agent’s ability to conduct R&D is his private information; higher (lower)R&D ability

is referred to as a more (less) efficient type. At the first stage, the agent is offered the contract. If

he accepts, then he exerts an unobservable effort in R&D.Each effort level leads to a distribution

of production cost. Higher effort generates better distribution, in the sense of first-order stochastic

dominance. However, higher effort also costs more, given the type of the agent. In the second

stage, the production cost is realized, and it is again the agent’s private information. The contract

has to sequentially elicit the agent’s private information and provide the right incentive for the

agent to exert effort in R&D at the same time. The principal’s goal is to design the optimal contract

to minimize her expected procurement cost.

We focus on deterministic mechanisms in searching for the optimal design and provide

a set of sufficient conditions for the optimality of deterministic mechanisms. A necessary and

sufficient condition for a deterministic mechanism to be incentive compatible is provided, which

greatly facilitates the analysis. We find that the optimal two-stage mechanism is implemented by

a menu of single-stage contracts, each specifying a fixed provision price and remedy paid by a

defaulting agent. That is, each contract specifies the (fixed) provision price for the product if the

agent delivers it and the default remedy the agent has to pay to the procurer if the agent fails to

deliver the product because of his realized high delivery cost. The contract with higher provision

price is paired with a higher default remedy. At equilibrium, a more efficient type (i.e., higher

R&D ability) chooses the contract with higher price and higher default remedy.This feature of the

optimal contract is largely consistent with the commonly observed practice in reality, by which

a more reliable supplier (who is reputed to have better capacity) usually demands a higher price

but offers a higher default remedy.

In practice, a default clause is often inserted into fixed-price procurement contracts, which

states what will happen if one of the parties fails to live up to the agreement. In our procurement

scenario, the agent defaults if he fails (is not willing) to provide the product because his delivery

cost is too high. By law, the procurer (the principal) has the right to claim a remedy from the

supplier (the agent) with the amount of (up to) the difference between the market price (i.e., c0)

and the contract price (i.e., the provision price) if the supplier defaults.8Another important feature

of the optimal contract is that the sum of the contract price and remedy is always smaller than or

equal to the market price c0. This feature notably coincides with widelyobser vedpractice—which

is regulated, for example, bythe Unifor m Commercial Code and Federal Acquisition Regulation.

In addition to the aforementioned advantages of fixed-price contracts, the established optimality

of the fixed-price plus default-remedy contract in our setting provides an in-depth economic

rationale for the use of a fixed-price plus default-remedy contract in reality: it is indeed optimal

from the procurer’s perspective. Given that procurement often involves a natural dynamic flow

of information, unobservable R&D investment, and private R&D efficiency and delivery cost,

it is reassuring to know that this convenient contract form is optimal in these quite common

environments.

Before discussing other features of the optimal contract, it is helpful to introduce two

benchmark scenarios: the first-best environment and the pure adverse selection setting. In the

8For example, the Uniform Commercial Code (U.C.C)Ar ticle 2-712 and Article 2-713. The FederalAcquisition

Regulation (FAR) is another example; see, for example, FAR Article 52.249-8 on Default (Fixed-Price Supply and

Service) and FAR 52.249-9 Default (Fixed-PriceResearch and Development).

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The RAND Corporation 2018.