Distorted Input Ratios in Vertical Relationships*

• Date: 01 October 2020
• Author: Martin Peitz,Dongsoo Shin
• DOI: http://doi.org/10.1111/sjoe.12382
• Published date: 01 October 2020

Scand. J. of Economics 122(4), 1480–1509, 2020

DOI: 10.1111/sjoe.12382

Distorted Input Ratios in Vertical

Relationships*

Martin Peitz†

University of Mannheim, DE-68131 Mannheim, Germany

martin.peitz@googlemail.com

Dongsoo Shin

Santa Clara University,Santa Clara, CA 95053, USA

dshin@scu.edu

Abstract

A project leader sources an input from a supporter and combines it with an input produced in-

house. The leader has private information about the project’s cost environment. We show that

if the leader can commit to the in-house input level, the input ratio is distorted upward when

the in-house input is not too costly – the in-house input is produced in excess and thus partly

wasted. By contrast, without the leader’s commitment to the in-house input level, the input ratio

is distorted downward when the in-house input is sufficiently costly – the outsourced input is

produced in excess and thus partly wasted.

Keywords: Agency; commitment; input ratio

JEL classification:D82; D86; L23

I. Introduction

In many industries, individual firms do not have the capacity to produce

complex final products alone. Often they rely not solely on their own input

but on the complementary input of external suppliers. In many instances,

as part of a supply chain or a joint venture, the firm assembling the inputs

assumes the role of “project leader”, specifying the project and proposing

the terms and conditions to obtain a contribution by a “project supporter”.

For example, in a contractual joint venture, firms do not pool their

productive capacities but instead agree on a contractual solution for how

to implement the project. In such a situation, coordinating the production

of multiple complementary inputs is a defining feature of the project.

As reported by practitioners, inputs are wasted in operations even by the

most successful manufacturers (see Badurdeen, 2007). A firm may produce

*A previous version of this paper was circulated under the title “Capital–Labor Distortions in

Project Financing”. We received helpful comments from three anonymous reviewers. M. Peitz

gratefully acknowledges financial support from the Deutsche Forschungsgemeinschaft (DFG)

through PE 813/2-2 and CRC TR 224 (project B05).

†Also affiliated with CEPR, CESifo, and ZEW.

C

The editors of The Scandinavian Journal of Economics 2019.

M. Peitz and D. Shin 1481

in-house inputs in excess, or its supplier may produce outsourced inputs in

excess (i.e., the ratio between in-house and outsourced inputs is distorted

upward or downward). This raises the question of whether such distortions

can be optimal under some circumstances. As will be shown, when the

project leader obtains some private information on the cost environment,

she might want to distort the input ratio.1

We study the optimal contract that a project leader (e.g., a manufacturer)

offers to a project supporter (e.g., a parts supplier). The project leader

combines the component sourced from the supporter (the outsourced input)

with another component produced in-house (the in-house input) to yield the

final output. She offers a contract that specifies the project supporter’s input

level and a transfer payment from the leader to the supporter. If the project

leader can commit to the in-house input level (full commitment), then

that input level is specified in the contract as well. If only the outsourced

input level can be contracted (limited commitment), then the project leader

chooses the in-house input level according to her ex post interest. For

example, contractual joint ventures often agree on a complete plan of action

with all input levels from all parties, whereas in supply-chain management it

is common that only the outsourced inputs from the suppliers are contracted

(see Kirshner, 2017).

After contracting, the project leader obtains private information about

the project’s cost environment. The contract offered by the leader is

contingent on her subsequent report about the cost environment, which,

in our model, is either good (low-cost for the in-house and the outsourced

input) or bad (high-cost for the in-house and the outsourced input).

We show that the optimal input ratio for carrying out a project can be

distorted in either direction from the efficient ratio that prevails under full

information. As the project leader is privately informed about the project

environment, she might have an incentive to misrepresent her information to

the project supporter. In addition, a further incentive problem arises under

limited commitment (i.e., when the project leader cannot commit to the

in-house input level). In such a case, the project leader’s contract offer has

to account for not only her private information but also her hidden action.

Our main results are as follows. Under full commitment, the project

leader either employs inputs at their efficient ratio or distorts the input ratio

upward (i.e., she produces the in-house input in excess of the outsourced

input). Her choice is the latter in a good project environment where

the marginal cost of the in-house input is sufficiently low. The reason

for this is as follows. The project leader is tempted to misrepresent the

project environment as good when it is bad. This manipulating incentive

is anticipated by the project supporter. In order to convince the project

1Throughout this paper,the project leader is refer red to as “she” and the project supporter as “he”.

C

The editors of The Scandinavian Journal of Economics 2019.