The O‐ring theory of the firm

• DOI: http://doi.org/10.1111/jems.12216
• Date: 01 March 2018
• Author: Michael T. Rauh
• Published date: 01 March 2018

DOI: 10.1111/jems.12216

ORIGINAL ARTICLE

The O-ring theory of the firm

Michael T. Rauh

Indiana University,Bloomington, IN, USA

(Email: mtrauh@indiana.edu) Abstract

We develop an O-ring production function characterized by specialization and divi-

sion of labor and where shirking or negative shocks can have major adverse conse-

quences. We show that when the principal can monitor individual output, the firm

tends be large (potentially larger than first best), with a high degree of specialization

and division of labor, weak incentives, and low pay as in traditional nonunion manu-

facturing. Moral hazard can only limit the size of the firm relative to the first best when

the principal can only monitor team output, in which case the firm has the opposite

characteristics.

One man draws out the wire, another straights it, a third cuts it, a fourth points it, a fifth grinds it at the top for

receiving the head; to make the head requires two or three distinct operations; to put it on, is a peculiar business,

to whiten the pins is another; it is even a trade by itself to put them into the paper; and the important business of

making a pin is, in this manner, divided into about eighteen distinct operations, which, in some manufactories, are

all performed by distinct hands, though in others the same man will sometimes perform two or three of them. I have

seen a small manufactory of this kind where ten men only were employed, and where some of them consequently

performed two or three distinct operations.

Smith (1904, Book I, Chapter I)

1INTRODUCTION

The above production process described by Smith has several features in common with many modern production technologies,

particularly in manufacturing. The first is that production can be divided into a number of distinct tasks: drawing the wire,

straightening it, etc. It is this aspect of the production process that allows for a division of labor (an allocation of tasks across

agents) and specialization (investments in task-specific human capital). Beckerand Mur phy (1992) develop a model along these

lines where an increase in employment leads to a more extensive division of labor (fewer tasks per agent), greater specialization,

and therefore higher productivity.

A second feature is that a breakdown at one stage of production due to shirking,poor decision-making, or a negative shock can

have serious adverse consequences. A batch of bent pins or an automobile with defective brakes is at best useless. Automobile

recalls can be extremely costly in terms of damage to the firm’s reputation evenwhen the cor rectivefix is relatively inexpensive.

This feature is the central element in Kremer’s (1993) O-ring theory of the firm coined after the source of the space shuttle

Challenger disaster.

Finally, the O-ring nature of the production technology implies something about the nature of the moral hazard problem.

If the principal can directly monitor individual effort (the first best case) or individual output (the second best), then shirkers

I thank Editor Casadesus-Masanell and an anonymous Co-Editor and referee for comments that substantially improved the paper. I also thank conference

participants at the International Industrial Organization Conference (IIOC) in 2015 and 2016, especially Dongsoo Shin. This paper was supported by a Kelley

School of Business summer grant. It is a revised and retitled version of the previous working paper “Moral hazard, firm size, and the size-wage differential.”

82 © 2017 Wiley Periodicals, Inc. J Econ Manage Strat. 2018;27:82–101.wileyonlinelibrary.com/journal/jems

RAUH 83

will be discovered and punished with probability 1. In the second best case, agents who experience negative shocks will also

be punished. For example, if pins lack sharp points, then under a clear division of labor, the principal will presumably know

which agent is responsible. In other settings, such as restaurants, things may not be so clear. Was it the food? The service? The

principal may not know unless the customer can communicate the source of the dissatisfaction. If the principal can only monitor

team output (the third best), the entire team will be punished for sure if any worker shirks. In each of these cases, there is no

free-rider problem because shirkers cannot hide behind the efforts of other workers.

In this paper, we develop an O-ring theory of the firm that combines the main elements in Becker and Murphy (1992) and

Kremer (1993) and extends those two papers to the case of moral hazard. In the contract theory literature, the production function

is usually nondescript and generic. In contrast, we show that the O-ring production technology developed here has powerful

implications for the nature of the moral hazard problem, incentive contracting, the size of the firm in terms of employment, and

the extent of specialization and division of labor.

We consider a production process where the set of tasks is the unit interval. The number of agents is endogenous and chosen

by the principal, who divides the set of tasks equally across all employed agents. Each agent chooses his production effort and

investment in task-specific human capital for each of his assigned tasks. A unit of output requires one unit of output in each

task (e.g., one automobile requires one headlight assembly, one steering column, etc.), so output is zero if any agent shirks or

experiences a negative shock in any of his assigned tasks. As in Becker and Murphy (1992), an increase in employment implies

fewer tasks per agent, which allows each agent to make greater investments in human capital for each of his smaller set of

assigned tasks. The result is an increase in productivity, which leads to increasing returns to employment.

We motivate the stochastic component of the production technology as follows. In addition to production effort and invest-

ments in human capital, each agent monitors his assigned tasks and makes decisions about whether or not a problem has arisen,

whether or not to halt production to fix it, whether he can fix it himself, and which potential solution is appropriate. When

there is only one agent, there is a high probability that at least some of these decisions will be faulty because he has limited

cognitive resources and performs all the tasks himself. When there are two agents, the probability that either one will make a

mistake should be lower because each performs only half the set of tasks and can therefore devote more care and attention to

each of them. On the other hand, we now have two probabilities instead of one, so the effect of an increase in employment is

ambiguous.1

Formally, we assume that the probability that the agent experiences a negative shockin at least one of his assigned tasks is an

increasing function of the proportion of tasks he performs. Assuming independence, the probability of a product defect is the

product of the individual probabilities. An increase in the number of agents therefore has two effects: it reduces the probability

that each individual will experience a negative shock but it also increases the number of stages of production where a negative

shock can occur. We say that the production process exhibits the O-ring property if eventuallyt he probability of a product defect

is increasing in the number of agents and converges to one as the number of agents increases without bound.2

A central question of the paper is: what limits the size of the firm? The seminal answer, due to Coase (1937), is that there

exist certain transaction costs associated with conducting economic activity within firms. In this paper, we focus on the trans-

action costs associated with moral hazard; that is, agency costs. In our model, there is a one-to-one correspondence between

employment and the extent of the division of labor, so the same question can also be posed as: what limits the extent of the

division of labor? Becker and Murphy (1992, p. 1138) take issue with Smith’s contention that the division of labor is lim-

ited by the extent of the market and argue that “a variable of great importance is the cost of combining specialized work-

ers.” But in their model, the relevant cost function is exogenous and only loosely justified in terms of “principal-agent con-

flicts, free-riding, and the difficulties of communication.” In contrast, in this paper, the cost function is constructed from the

optimization problem of the principal whose objective is to implement effort and investments in human capital at minimum

cost.

To determine the effect of moral hazard on the size of the firm and the extent of the division of labor, we start with the

first best benchmark where the principal can directly monitor effort so there is no moral hazard. Regardless of the moni-

toring technology, the optimal employment level balances the following considerations: (i) the increasing returns to employ-

ment due to specialization and division of labor, (ii) the O-ring property of the production technology, where the prob-

ability of team failure increases with the size of the team, and (iii) the marginal cost of employment (the cost of hiring

another agent). We obtain the standard result that the first best contract provides zero incentives and full insurance. Since

each agent receives a constant transfer, the first best cost of employment (the number of agents times the expected transfer

to each agent) is linear in employment and the marginal cost of hiring another worker is constant. But a linear cost function

cannot contain the increasing returns to employment due to specialization and division of labor so that the size of the first

best firm can only be limited either by the extent of the labor market (the total number of available workers) or the O-ring

property.