Long‐Term Contracts, Irreversibility, and Uncertainty

• Author: MALIN ARVE
• DOI: http://doi.org/10.1111/jpet.12148
• Published date: 01 October 2016
• Date: 01 October 2016

LONG-TERM CONTRACTS,IRREVERSIBILITY,AND UNCERTAINTY

MALIN ARVE

NHH Norwegian School of Economics

Abstract

Long-term contracting implies contracting based on expected future

demand. In this paper, I develop a multiperiod procurement model

where, once the actual level of demand is realized, the irreversible ini-

tial provision level may be supplemented by additional provisions. This

paper shows that, with the possibility of additional upward adjustments,

the first-period provision level will be lower than when no additional

adjustments are possible. This reduction in first-period provision level

is higher under complete contracting than under incomplete contract-

ing, and because of the reduction in information rents it yields a higher

expected utility to the principal but lower total welfare.

1. Introduction

When a firm hires a computer specialist to provide a customized computer service, it

needs to decide upon the specifications of the service before it hires the specialist and

without knowing exactly how the new service will fit into the everyday tasks of its em-

ployees. When the service is ready and the employees start using it, the firm may realize

that further details can be added to improve its performance. If these improvements

are important enough, the firm may ask the computer specialist to further improve the

already existing service without waiting for the expiration date of the initial contract.

This paper explores the idea that, because of ex ante uncertainty, initial decisions can be

improved upon.1

This paper presents a setup where the initial gain from an irreversible project is

subject to uncertainty. Over time this uncertainty disappears and the realized value of

the project becomes known. The legal entity taking the provision decision (hereafter

1However in the short run reducing the initial service may also turn out to be infeasible. The agent (IT

firm) might be unwilling to reduce the scope of the contract because costs related to the technician

cannot be reduced in the short run. For instance a wage still needs to be paid regardless of whether the

technician provides the service or not.

Malin Arve, Department of Business and Management Science, NHH Norwegian School of Economics,

Bergen, Norway (malin.arve@nhh.no).

I particularly thank David Martimort for his kind help and comments. Special thanks also go to

Ingela Alger, Olga Gorelkina, Elisabetta Iossa, Yassine Lefouili, Humberto Moreira, Franc¸ois Salani´

e,

St´

ephane Saussier, Giancarlo Spagnolo, Wilfried Sand-Zantman, and Chengsi Wang. I thank seminar

participants at the Toulouse School of Economics and various conferences for useful comments and

suggestions. I gratefully acknowledge financial support from the DFG (German Science Foundation)

under SFB/TR-15.

Received November 7, 2014; Accepted November 15, 2014.

C2015 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (5), 2016, pp. 764–785.

764

Long-Term Contracts 765

the principal) can exploit the fact that a second-period service provision can be added

to the initial provision and she can avoid unnecessary high costs in the first period. In

this framework, I show that this trade-off leads to lower initial service levels than when

no adjustment can be made. This is because there is a trade-off between service provi-

sion under uncertainty (and obtaining full benefit earlier) and waiting until the true

value of the project is observed (and avoiding unnecessary spending on an irreversible

service provision). When positive adjustments are available, the principal can be more

flexible and only pay the cost of a high service level if this is indeed required. Without

adjustments such flexibility is not possible.

I study the levels of service provision, when the cost of the service is the agent’s

private information, both when the initial contract can be contingent on the realization

of the realized benefit (complete contracting) and when the initial contract cannot be

contingent on its realization (incomplete contracting). I show that initial service levels

are higher under incomplete contracting. This is because distortions from asymmetric

information are lower under incomplete contracting where full separation of different

types of agents is not possible and distortions that are justified by reducing information

rents are less effective. Finally, I compare the outcome and service levels in the two

setting and I argue that if nature or the agent can make it costly to write a complete

contract then we are likely to see more incomplete contracts which lead to higher levels

of information rent. This would for instance be the case when the agent can choose to

adopt a very technical and detailed language that is unfamiliar to the principal.

In the paper, I focus on the case of an information technology (IT) service. But of

course the model remains valid for other goods and services such as cleaning services

or the maintenance of infrastructure or other durable goods. In the latter example,

it is clear that the required maintenance, for instance a network for water supply or

a road, will depend on the level of usage and the degree of deterioration. Presumably,

the estimated maintenance is based on forecasts of future demand for the durable good.

However, the actual level of maintenance may need to be adjusted according to realized

demand and this is exactly the kind of environment studied in this paper.

This paper is related to the (real) option value literature in that a decision is irre-

versible and the investors can get more information about the cost or value of a project

by postponing the investment decision. When agents have to take irreversible invest-

ment decisions, they have to consider the trade-off between the extra return from an

early investment and the benefit from learning more information when postponing

the investment (see Dixit and Pindyck (1994) for an introduction to this literature).

This paper is different in that an early provision generates a benefit not only in the

final stage but also in the early stage and that this provision can be complemented by

an additional adjustment once more information on the benefit of the project becomes

available. Thus the benefit can be adjusted upward once there is more information avail-

able. This is also studied in a series of papers pioneered by Arrow and Fisher (1974) and

Henry (1974a, 1974b).2They showed that when additional investments or decisions can

be made over time, but that these decisions are constrained by earlier decision, more

flexible initial decisions are always favored. This result is known as the irreversibility ef-

fect. This paper illustrates the irreversibility effect in a service provision setting and shows

how asymmetric information further reduces the incentives to contract for high initial

investments or service levels. In a recent paper Martimort and Straub (2012) also study

uncertainty and irreversibility in a contractual setting, but they focus on moral hazard

issues and not on adverse selection.

2See also Epstein (1980), Demers (1991), Ulph and Ulph (1997), Gollier, Jullien, and Treich (2000),

and Salani´

e and Treich (2009).