Taiwanese Journal of Mathematics

A Functional Approach to Prove Complementarity

Kazuo Kido

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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.

Article information

Source
Taiwanese J. Math., Volume 15, Number 1 (2011), 211-227.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406171

Digital Object Identifier
doi:10.11650/twjm/1500406171

Mathematical Reviews number (MathSciNet)
MR2780281

Zentralblatt MATH identifier
05943149

Subjects
Primary: 62P20: Applications to economics [See also 91Bxx] 90B99: None of the above, but in this section 91B99: None of the above, but in this section

Keywords
supermodular increasing differences complementarity bandwagon effect economies of scale

Citation

Kido, Kazuo. A Functional Approach to Prove Complementarity. Taiwanese J. Math. 15 (2011), no. 1, 211--227. doi:10.11650/twjm/1500406171. https://projecteuclid.org/euclid.twjm/1500406171


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