Non‐linear revenue evaluation
| Published date | 01 November 2022 |
| Author | Alex Dickson,Ian A. MacKenzie,Petros G. Sekeris |
| Date | 01 November 2022 |
| DOI | http://doi.org/10.1111/sjpe.12303 |
Scott J Polit Econ . 2022;69:487–505. wileyonlinelibrary.com/journal/sjpe
|
487
© 2021 Scottish Ec onomic Society
1 | INTRODUCTION
The traditio nal approach in industr ial organization is to view fi rms as profit- maximizing entities. Even thou gh this
seems to be a reason able assumptio n from the shareho lders' or owner's perspect ive, the critic al strategic de ci-
sions that determ ine a firm's performance are mo re often than not in the hands of CEOs or man agers who may
pursue diffe rent objectives. T his feature has been recog nized early on and integra ted into the development of t he
theory of the f irm and organization e conomics (e.g., Baumol, 19 58; Williamson, 196 3). Under this a lternative par-
adigm, the fir m is still seen as maximizi ng profits, but the agen ts contracted for ful filling this goal can be en dowed
with compleme ntary objecti ves such as sales (i.e., tot al revenue) or market share ma ximization, or produ ction cost
minimization. This, admittedly more realistic, modeling strategy alters the predictions relating to the degree of
competition b etween firms, as well as th e effect of policy meas ures, or changes in market con ditions.
A manager maximi zing a combination of profit s and some other per formance can be just ified by the manager's
need to increase their power, status, or prestige, which can be symptomatic of a desire for empire- building con-
siderations (B aker et al., 1988; Baum ol, 1959; Hope & Thomas, 20 08; Jensen, 1986; Williamson, 19 63), to reduce
Accepted: 21 September 2021
DOI: 10 .1111/sjpe.1 2303
ORIGINAL ARTICLE
Non- linear revenue evaluation
Alex Dickson1 | Ian A. MacKenzie2 | Petros G. Sekeris3
1Departme nt of Economics, Str athclyde
Business Sch ool, Universit y of Strathclyde,
Glasgow, UK
2School of Econo mics, Universit y of
Queensland, Brisbane, Qld, Australia
3Montpellier Business School, Montpellier,
France
Correspondence
Alex Dickson, Department of Economics,
Strathclyd e Business School , 199 Cathedral
Street, Gla sgow G4 0QU, UK.
Email: alex.dickson@strath.ac .uk
Abstract
In this article, we inve stigate different m arket structure s
where decision makers a re incentivized by both prof it and
revenue. Our innovatio n is that we consider managers t hat
evaluate revenue in a non- linear way, exhibit ing diminish-
ing marginal utilit y. This implies that increme ntal changes
in revenue— for example, due to demand shocks— generate
production choices that depend on the existing revenue
base of the firm. We show that t his intuitively appealing ex-
tension reverses some co nventional results: de cision mak-
ers may increase outp ut in the presence of negative dema nd
shocks, which dep ends on the concavity of thei r utility func-
tion with respec t to revenue.
KEYWORDS
delegation, non- profit maximization, oligopoly
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DICKSON et al.
their unemploy ment risk (Amihud & Lev, 1981) , or to enhance promotion objec tives (Cao et al., 2018) bec ause of
internal scrut iny on these measures of firm ‘succe ss.’ While the original contribu tions conceived of firm decisio n
makers having gene ral preference s over multiple obje ctives, exis ting approach es that account for s trategic be-
havior among fir ms have assumed linear evaluat ion of these alternative obj ectives (e.g., Fershtma n & Judd, 1987;
Sklivas, 1987 ), essentiall y assuming decision makers care a bout a weighted average of profit and al ternative ob-
jectives. Su ch an assumption, however, is neith er innocuous nor necess arily realistic.
There is no a prior i justification, other tha n perhaps the conve nience of modelin g, for restric ting analysis to
linear evaluati ons and, indeed, it is very r easonable in such circumst ances to consider the manager 's utility to be
more general in a lternative objective(s), as o riginally proposed wit hin Williamson (1963) (bu t where his focus was
not on the alterna tive objective of sales). The rea son for considering that manage rs are motivated by alternati ve
objectives as w ell as profit is that t here is scrutiny on t hese objectives, either to d etermine remun eration, or in
terms of the manage r's internal or external r eputation. In a model wh ere managers care about a we ighted combi-
nation of profit an d revenue, we see it as highly pla usible that managers' evalu ation of revenue is concave, exhi b-
iting diminishi ng marginal payoffs so tha t changes in revenue have a greate r impact when revenues a re small than
when they are lar ge. From an external scruti ny, empire- buildin g, perspective, a key asse ssment metric will be the
manager's abili ty to make the firm grow (oft en judged by sales) in relative terms; so, a gi ven increase in revenue wil l
have more gravita s when revenue is small than when i t is already large.1 Likewise, for inte rnal kudos of the man-
ager among the or ganization's employees. An add itional justification com es from recognizing that manager s are
often remuner ated by stock options: empirica l studies have uncovered a robust ‘f irm- s ize effect,’ that is at p lay
above and beyond fi rms' profitabi lity measures , whereby the sto cks of small firms t end to produce high er (but
more volatile) exp ected returns (e.g., A sness et al., 2018; Reing anum, 1981). This, i n turn, implies that th e marginal
return to manager s is decreasing in the fir m size, which is determined by th e magnitude of revenues. Th e findings
of Nourayi (2006) and C anarella and N ourayi (2008) fur ther support these obser vations since they empiricall y
find that, whi le managers' comp ensation is convex in t he firm's profit s, it is concave in the r eturns of the fir ms'
stocks. This e stablishes a concave mapp ing from performance into re muneration itself, consis tent with the man-
ager's evaluatio n of revenue being concave.
Baumol (1958) considere d that managers are mot ivated by sales maxim ization subject to a mi nimum profit con-
straint, me aning the manager's payof f is linear in sales. Whe n managers value sale s non- li nearly, negative demand
shocks may gener ate highly counter- i ntuitive results since we d emonstrate that produ ction may increase in som e
circumstan ces both under monopol y and oligopolistic ma rket structures. T he intuition for this res ult is clear. If the
sole objecti ve of a decision maker is either to ma ximize profits or sales, a n egative demand shock wil l always lead
to lower product ion. Indeed, a n egative demand s hock reduces mar ginal sales, a nd, thus, incent ivizes both the
profit- maximizing and the r evenue- maximizing decision m akers to reduce their pro duction. If, however, a manager
values sales n on- linearly, a neg ative demand shock may reduce t he marginal profits while increasing the m arginal
utility of sale s (since sales have re duced). When the l atter effec t is stronger than t he former, the manage r will
opt for higher product ion. Interestingly, this result sur vives in oligopolistic set tings where the decision var iables
(quantities) are st rategic substi tutes. The sam e result, however, cann ot be obtained in e xisting linear v aluation
models of altern ative objectives beca use the marginal utilit y of sales would always trac k the change in demand.
2 | RELATED LITER ATURE
Our main focus in this article is investigating how managers— with multiple objectives, including profit
maximization— adjust their o utput decisions in the event of dema nd shocks. While we show that out put choices
1Asplund (2002) considers r isk- averse firms in u ncertain env ironments, t hus also diverg ing from tradit ional modeli ng assumptions . In contrast to t he
literature c onsidering al ternative obje ctives to prof its, risk- aversion in profits ten ds to make firms le ss aggressive .
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