Contracting under unverifiable monetary costs

• Date: 01 October 2020
• Author: Antoine Soubeyran,Nicolas Quérou,Raphael Soubeyran
• DOI: http://doi.org/10.1111/jems.12389
• Published date: 01 October 2020

J Econ Manage Strat. 2020;29:892–909.wileyonlinelibrary.com/journal/jems892

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© 2020 Wiley Periodicals LLC

Received: 16 July 2019

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Revised: 9 June 2020

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Accepted: 10 June 2020

DOI: 10.1111/jems.12389

ORIGINAL ARTICLE

Contracting under unverifiable monetary costs

Nicolas Quérou

1

|Antoine Soubeyran

2

|Raphael Soubeyran

1

1

CEE‐M, Univ. Montpellier, CNRS,

INRAe, Institut Agro, Montpellier, France

2

CNRS and EHESS, Aix‐Marseille School

of Economics, Aix‐Marseille University,

Marseille, France

Correspondence

Nicolas Quérou, CEE‐M, Univ.

Montpellier, CNRS, INRAe, Institut Agro,

CEE‐M, 2 Place Viala, 34060 Montpellier,

France.

Email: nicolas.querou@supagro.fr

Funding information

Agence Nationale de la Recherche,

Grant/Award Number: ANR‐16‐

CE03‐0005

Abstract

We consider a contracting relationship where the agent's effort induces

monetary costs, and limits on the agent's resource restrict his capability to

exert effort. We show that the principal finds it best to offer a sharing contract

while providing the agent with an up‐front financial transfer only when the

monetary cost is neither too low nor too high. Thus, unlike in the limited

liability literature, the principal might find it optimal to fund the agent.

Moreover, both incentives and the amount of funding are nonmonotonic

functions of the monetary cost. These results suggest that an increase in the

interest rate may affect the form of contracts differently, depending on the

initial level of the former. Using the analysis, we provide and discuss several

predictions and policy implications.

1|INTRODUCTION

Most of the literature on contracts assumes that the agent's effort cost is nonmonetary, while there are many con-

tracting relationships where this cost is at least partially pecuniary. For instance, this is the case for issues related to

corporate social responsibility (Baron, 2007; Heyes & Martin, 2016), such as payment schemes for environmental

services (see Alix‐Garcia & Wolff, 2014). This is also consistent with cases where the agent is a profit‐seeking company,

and this agent's actions involve unverifiable monetary costs: Among other examples, subcontractors operating at arm's

length face this type of costs, as in the automobile industry (Kawasaki & McMillan, 1987) or for construction projects.

Even researchers working on a project funded by a public or private institution may declare spending more hours on

this project than they actually do. In all these cases, the agent's effort implies nonmonetary and monetary costs, which

are often unverifiable due to high costs of monitoring or lack of expert knowledge.

The existence of monetary costs raises a number of general questions regarding the optimal contract between a

principal and an agent. When is it in the principal's best interest to provide incentives or to fund an agent whose wealth

is limited? What is the best incentive/funding structure to manage such a relationship? What is the effect of the

magnitude of monetary costs on the specifics of the optimal contract? We attempt to answer these and related

questions.

1

In our environment the agent takes an unobserved costly action, which produces a stochastic output. The principal

provides incentives by paying the agent based on the observed output and by providing him with, or by requiring, an

up‐front payment. Unlike in standard models, we consider that the agent's effort induces monetary costs (as well as

nonmonetary costs, as in the standard setting). This cost can be covered by the agent's choice to undertake financial

investments, while the principal can indirectly cover it through financial transfers to the agent. In this context, the

agent's budget constraint (BC) restricts the set of feasible actions. Thus, the lower the level of wealth of the agent,

including transfer from or to the principal, the lower the maximum effort level that the agent can provide. The principal

and the agent are both risk neutral, so that the only distortion comes from the BC, which limits the agent's set of

feasible actions. When the BC binds, the up‐front payment and the effort become rivals. The agent cannot pay a large

up‐front payment and supply a high effort level.

We obtain several results that do not exist in the polar case of strictly nonmonetary costs, even under limited

liability, which is actually consistent with standard models used in Lewis and Sappington (2000a,b,2001). We first

show that funding is sometimes optimal, but that it prevents the principal to get the full returns of the project. Second,

the link between monetary costs and funding is not straightforward: Funding is optimal if and only if the agent's wealth

is sufficiently small and the monetary cost is neither too low nor too high. Indeed, when the monetary cost is small

enough the agent can cover the full monetary cost of the project and, when this cost is sufficiently large, the principal

has incentives to induce a decrease in the monetary costs through a decrease in the agent's share of profits, which

allows the agent to also cover the monetary costs of the project.

Third, the optimal contract exhibits interesting features: The incentive part decreases as the magnitude of the

monetary costs increases up to a threshold value, and it then increases for larger values of these costs. Fourth, up to a

threshold value of the monetary cost, the optimal bonus and the transfer both increase as the value of the project

increases. When the monetary cost moves above this threshold, the bonus paid to the agent increases, while the transfer

received from the agent decreases, as the project value increases. Fifth, we analyze welfare effects, and show that a

larger monetary cost has a negative effect on the surplus of both parties.

We then discuss several predictions and policy implications. Our model predicts that payment for environmental

services programs should not necessarily be more likely to fund projects when opportunity costs get larger. Moreover,

an increase in the interest rate may notably affect the optimal contract design: Depending on its initial level, an increase

in the interest rate may (a) lead to an increase or a decrease in the strength of incentives, (b) increase or decrease the

financial transfer, and (c) affect the qualitative nature of the transfer (funding to or payment from the agent). The model

also provides a rationale for the fact that outside financing and profit sharing be parts of the optimal contract when

monetary costs are partially unobservable.

2

Finally, we discuss several extensions. We prove that our setting differs from the classical notion of limited liability,

and we highlight the robustness of our results when the agent can borrow money from the principal, and when self‐

funding can be used as an outside option.

The present paper is related to the literature on moral hazard (Arrow, 1963; Pauly, 1968). The closest contributions

are Lewis and Sappington (2000a,b,2001), where the focus is on how constraints on the agent's wealth impede on the

efficient allocation of resources by limiting the optimal tailoring of the reward structure.

3

In these contributions, the

agent's effort does not induce any monetary cost, and we obtain novel results: We prove the optimality of funding, show

that funding occurs for intermediate values of the monetary cost, highlight the nonmonotonic effect of this cost on

incentives, and that funding and incentives may be complementary.

This study also highlights the optimal trade‐off between funding and incentives.

4

Unlike most of the literature on

financial contracts (see Bester, 1987; Innes, 1990), we consider that the investment level is endogenous. We thus

contribute to the important question of optimal contracting when both investment policy choices and effort are made

privately by the agent.

The effect of monetary costs induced by the agent's effort is conceptually different from the notion of limited liability

(see Macho‐Stadler & Pérez‐Castrillo, 2018; Sappington, 1983).

5

Limited liability might either bound the feasible

payments from the principal to the agent (which must lie above an exogenous threshold, see Jewitt, Kadan, &

Swinkels, 2008; Poblete & Spulber, 2012) or the agent's ex post payoff. We show this conceptual difference in Section 5.

6

The remainder of the paper proceeds as follows. The model is provided in Section 2, and the analysis in Section 3.

Policy implications are discussed in Section 4. Section 5discusses some of the assumptions. Finally, Section 6

concludes. All proofs are provided in the appendix.

2|THE MODEL

Consider a principal and an agent who may enter into a relationship to develop a project. The outcome of the project

can be either a success or a failure. If successful, the relationship yields returns

V

>0

, while failure results in zero

return. The agent's effort ∈ee,[0,1]

, determines the probability of success pe

e

()= of the relationship. The agent

incurs both a monetary cost

K

eθ()= e

2

2, with ≥θ0and a nonmonetary cost De ψ()= e

2

2with ≥

ψ

0when exerting

effort ≥e

0

. He has a limited budget

≥B0

. The principal is the residual claimant of the output.

QUÉROU ET AL.

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