Answer Happy

This is all the information offered on the question. I
cannot elaborate more as this is the complete questions
set.
4. 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 + ē)] = u(w – T) where u is the agent's Bernoulli utility function, w is their wealth level, 7 is the insurance premium/willingness to pay to avoid ē, and ē is mean-zero risk (i.e. ē is a random variable with Ele) = 0). Prove that for small ē, r(w) -u"(W)/U'(w) is proportional to 7. What is the constant of proportionality for this relationship? [Hint: start by taking the second- order Taylor expansion of the equation above).