## Calculate the elasticity of the premium, Econometrics

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You are a property insurer and one of your potential clients, whose current wealth is \$450,000, wants to insure her \$250,000 house.  The chances of the house burning down in any given year are one in one thousand.  There are no other risks.  Will she buy insurance from you if you set the premium at \$300?  Assume that her utility function is u(W) = ln(W) .  How sensitive is the maximum premium she is willing to pay to her current wealth?  Calculate the elasticity of the premium to wealth to ?nd out.  (Hint: In class we refer to the Markowitz risk premium as the difference between expected wealth and the certainty equivalent,  E (W) - CE , which is valid only for fair gambles.  In this case, the gamble is not fair, so you should compute the insurance premium as the cost of the gamble, namely, W0 - CE .)

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