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Relative Risk Aversion as an Arc Elasticity

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Abstract

Risk aversion is the central reason why individuals purchase insurance and undertake other forms of risk management. But deriving the Pratt–Arrow coefficient of relative risk aversion from a utility function requires familiarity with differential calculus—a level of mathematics beyond the prerequisites for most introductory risk management courses. Thus, students are not exposed to one of the most important and fundamental concepts in the field unless and until they take more advanced courses. The present article demonstrates that relative risk aversion can be obtained as an arc elasticity using only elementary mathematics. This approach highlights the relationship between risk aversion and the demand for insurance, and integrates concepts from the principles of economics course, helping to unify the business curriculum. Numerical examples are easily computed and graphed using electronic spreadsheets, providing students with a hands-on learning experience. For sufficiently small risks, the arc elasticity measure reduces to the Pratt–Arrow coefficient, providing a platform for discussing the difference between large-scale and small-scale risk aversion in upper-level courses.
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Document Type: Research Article

Publication date: 2010-03-01

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