A functional approach to prove complementarity

Research output: Contribution to journalArticle

Abstract

Some complementarity among a firm's activities is an important source of its profits. In this paper, we focus on the way to prove complementarity. Though there are many studies on complementarity as supermodularity or the increasing differences of a function, we introduce the notion of self increasing differences with respect to a single activity, which is an essence of convexity from the viewpoint of complementarity, and investigate some interrelations among these three notions of complementarity. Mathematically, we give a sufficient condition for a composite function to have self increasing differences. This proposition is deeply related to Topkis' (1998) Lemma 2.6.4 on sufficient conditions for a composite function to be supermodular. Both propositions are combined and applied to yield and/or strengthen complementarity in an organization, which will also disclose the functional structure of an organization's activities.

Original languageEnglish
Pages (from-to)211-227
Number of pages17
JournalTaiwanese Journal of Mathematics
Volume15
Issue number1
Publication statusPublished - 2011 Feb

Fingerprint

Complementarity
Composite function
Proposition
Supermodularity
Sufficient Conditions
Profit
Convexity
Lemma

Keywords

  • Bandwagon effect
  • Complementarity
  • Economies of scale
  • Increasing differences
  • Supermodular

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A functional approach to prove complementarity. / Kido, Kazuo.

In: Taiwanese Journal of Mathematics, Vol. 15, No. 1, 02.2011, p. 211-227.

Research output: Contribution to journalArticle

@article{9c4df0b4a49942389c9cf6117410ef3d,
title = "A functional approach to prove complementarity",
abstract = "Some complementarity among a firm's activities is an important source of its profits. In this paper, we focus on the way to prove complementarity. Though there are many studies on complementarity as supermodularity or the increasing differences of a function, we introduce the notion of self increasing differences with respect to a single activity, which is an essence of convexity from the viewpoint of complementarity, and investigate some interrelations among these three notions of complementarity. Mathematically, we give a sufficient condition for a composite function to have self increasing differences. This proposition is deeply related to Topkis' (1998) Lemma 2.6.4 on sufficient conditions for a composite function to be supermodular. Both propositions are combined and applied to yield and/or strengthen complementarity in an organization, which will also disclose the functional structure of an organization's activities.",
keywords = "Bandwagon effect, Complementarity, Economies of scale, Increasing differences, Supermodular",
author = "Kazuo Kido",
year = "2011",
month = "2",
language = "English",
volume = "15",
pages = "211--227",
journal = "Taiwanese Journal of Mathematics",
issn = "1027-5487",
publisher = "Mathematical Society of the Rep. of China",
number = "1",

}

TY - JOUR

T1 - A functional approach to prove complementarity

AU - Kido, Kazuo

PY - 2011/2

Y1 - 2011/2

N2 - Some complementarity among a firm's activities is an important source of its profits. In this paper, we focus on the way to prove complementarity. Though there are many studies on complementarity as supermodularity or the increasing differences of a function, we introduce the notion of self increasing differences with respect to a single activity, which is an essence of convexity from the viewpoint of complementarity, and investigate some interrelations among these three notions of complementarity. Mathematically, we give a sufficient condition for a composite function to have self increasing differences. This proposition is deeply related to Topkis' (1998) Lemma 2.6.4 on sufficient conditions for a composite function to be supermodular. Both propositions are combined and applied to yield and/or strengthen complementarity in an organization, which will also disclose the functional structure of an organization's activities.

AB - Some complementarity among a firm's activities is an important source of its profits. In this paper, we focus on the way to prove complementarity. Though there are many studies on complementarity as supermodularity or the increasing differences of a function, we introduce the notion of self increasing differences with respect to a single activity, which is an essence of convexity from the viewpoint of complementarity, and investigate some interrelations among these three notions of complementarity. Mathematically, we give a sufficient condition for a composite function to have self increasing differences. This proposition is deeply related to Topkis' (1998) Lemma 2.6.4 on sufficient conditions for a composite function to be supermodular. Both propositions are combined and applied to yield and/or strengthen complementarity in an organization, which will also disclose the functional structure of an organization's activities.

KW - Bandwagon effect

KW - Complementarity

KW - Economies of scale

KW - Increasing differences

KW - Supermodular

UR - http://www.scopus.com/inward/record.url?scp=79251637008&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79251637008&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79251637008

VL - 15

SP - 211

EP - 227

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

SN - 1027-5487

IS - 1

ER -