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Liverpool Merchants Versus Ohmi Merchants: How and Why They Dealt with Risk and Insurance Differently Read chapter Read first chapter

2021 | OriginalPaper | Chapter

8. Risk Aversion and Information Exchange: The Constant Absolute Risk Aversion Function and its Applications

Authors : Yasuhiro Sakai, Keisuke Sasaki

Published in: Information and Distribution

Publisher: Springer Singapore

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Abstract

The purpose of this paper is to carefully investigate the relationship between the concepts of risk aversion and expected utility, with a focus on the constant-risk-aversion function and its application to oligopoly theory. Whereas there is now a growing literature on risk, uncertainty, and the market, the operational theory of risk-averse oligopoly has been rather underdeveloped so far.One of the reasons for such underdevelopment is that the established concept of risk aversion remains too abstract rather than reasonably operational, whence very few economists have dared to study the economic consequences of a change of risk aversion by firms.
In this paper, we attempt to combine the constant absolute risk aversion function developed by K. J. Arrow and J. W. Pratt, two great economists of the 20th century, and the normal distribution function invented by K.F. Gauss, a mathematical genius of the 19th century: The resulting situation may be called the CARA-NORMAL case. We intend to invent a very useful mathematical theorem for this specific yet important case, and then apply it to the theory of risk-averse oligopoly. In particular, the impact of increasing risk aversion on the outputs of duopolies is carefully examined. It is shown among other things that the comparative static results depend on the degree of risk aversion and the state of product differentiation.

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previous chapter The Profit-Maximizing and Labor-Managed Firms: A Unified Approach to the Role of Information
next chapter Information Sharing of Private Cost Information: An Application of the Cardano Cubic Formula
Footnotes
1
In the light of the history of economic thought, the year of 1970 is regarded as the birth year of the modern economics of risk and uncertainty. It is in that year that K.J. Arrows’ outstanding essays in risk-bearing and G. Akerlof’s famous paper on the lemons market were both published. See Akerlof (1970), Sakai (1982, 1990, 2010, 2014, 2015), and Sinn (1983).
 
2
See Arrow (1965,70) and Pratt(1964).
 
3
There is now a vast literature on the working and performance of oligopoly under information. See Sakai (1990). Unfortunately, very few papers have ever discussed the CARA-NORMAL case, however. This paper intends to further develop this special yet important case.
 
4
The CARA-NORMAL case was first introduced to oligopoly theory by Sakai and Yoshizumi (1991a, b), and later developed in related areas by several papers including Sakai and Sasaki (1996). For a systematic discussion on statistics, see Mood, Graybill and Boes (1974).
 
5
For a detailed discussion on this point, see Sakai (1990).
 
6
When Sakai began graduate courses in the USA, his life was really guided by Professor Oka’s invaluable teachings: Hence he had due respect for mathematics, but had no fear for American culture whatever. We still remember the following inspiring words by Oka (1970): “When I [Oka] began my course work at the Department of Science, Kyoto University, I had too much fear for mathematics to specialize in it. I have never thought, however, that foreign cultures were fearsome and overwhelming. To my regret, the ordinary Japanese people tend to look at this matter from the opposite point of view: Although they do not show due respect for mathematics, they are so afraid of foreign cultures. I would like to emphasize that this is nothing but a terrible mistake.” As of 2020, our respect for Oka’s important teachings still remains, and is really growing larger.
 
Literature
Akerlof GA (1970) The market for lemons: qualitative uncertainty and the market mechanism. Quart J Econ 84:488–500CrossRef
Arrow KJ (1965) Aspects of the theory of risk-bearing. Yrjo Janssonin Saatio, Helsinki
Arrow KJ (1970) Essays in the theory of risk-bearing. North-Holland, Amsterdam
Foster S (1860) Old Black Joe. Firth, Pond & Co. Earhart W, Birge EB (eds.) Songs of Stephen foster. University of Pittsburgh Press, Pittsburgh, pp 61-62.
Hicks JR (1969) A theory of economic history. Oxford University Press, Oxford
Mood AM, Graybill FA, Boes DC (1974) Introduction to the theory of statistics, 3rd edn. McGraw-Hill, New York
Oka K (1970) Ten tales on spring evenings (in Japanese). Mainichi Shinbun Publishers, Tokyo
Pratt JW (1964) Risk aversion in the small and in the large. Econometrica 32:61–75CrossRef
Sakai Y (1982) The economics of uncertainty (in Japanese). Yuhikaku Publishers, Tokyo
Sakai Y (1990) The theory of oligopoly and information (in Japanese). Toyo Keizai Publishers, Tokyo
Sakai Y (2010) Economic thought of risk and uncertainty (in Japanese). Mineruva Publishers, Kyoto
Sakai Y (2014) Information and distribution: the role of merchants in the market economy with demand risk. The Hikone Ronso 399:66–81
Sakai Y (2015) Risk aversion and expected utility : the constant-absolute-risk aversion function and its application to oligopoly. The Hikone Ronso 402:172–187
Sakai Y, Sasaki K (1996) Demand uncertainty and distribution systems: information acquisition and transmission. Contained in Sato R, Ramachandran R, Hori H (eds.) Organization, performance, and equity: perspectives on the Japanese economy: 59-91. Kluwer Academic Publishers, Norwell, Massachusetts
Sakai Y, Yoshizumi A (1991a) Risk aversion and duopoly: is information exchange always beneficial to firms? Pure Math Appl 2:129–145
Sakai Y, Yoshizumi A (1991b) The impact of risk aversion on information transmission between firms. J Econ 53:51–73CrossRef
Sinn H-W (1983) Economic decisions under uncertainty. North-Holland, Amsterdam
Metadata
Title
Risk Aversion and Information Exchange: The Constant Absolute Risk Aversion Function and its Applications
Authors
Yasuhiro Sakai
Keisuke Sasaki
Copyright Year
2021
Publisher
Springer Singapore
Book
Information and Distribution

Print ISBN: 978-981-10-0100-0

Electronic ISBN: 978-981-10-0101-7

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-10-0101-7_8