In class we talked about how the Arrow-Pratt coefficient of absolute risk aversion can be thought of as proportional to the insurance premium that an expected utility maximizer would be willing to pay to completely avoid a small, mean zero risk. Mathematically, we could write this insight the following way: E[u(w + €)] = u(w − n) where u is the agent's Bernoulli utility function, w is their wealth level, □ is the insurance premium/willingness to pay to avoid è, and è is mean-zero risk (i.e. è is a random variable with E[è] = 0). Prove that for small è, r(w) = −u"(w)/u'(w) is proportional to . What is the constant of proportionality for this relationship? [Hint: start by taking the second- order Taylor expansion of the equation above].

In class we talked about how the Arrow-Pratt coefficient of absolute risk aversion can be thought of as proportional to the insurance premium that an expected utility maximizer would be willing to pay to completely avoid a small, mean zero risk. Mathematically, we could write this insight the following way: E[u(w + €)] = u(w − n) where u is the agent's Bernoulli utility function, w is their wealth level, □ is the insurance premium/willingness to pay to avoid è, and è is mean-zero risk (i.e. è is a random variable with E[è] = 0). Prove that for small è, r(w) = −u"(w)/u'(w) is proportional to . What is the constant of proportionality for this relationship? [Hint: start by taking the second- order Taylor expansion of the equation above].

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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