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(1.1) An individual has the following utility function: u(w) = w1/2.Her initial wealth is 10...

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(1.1) An individual has the following utility function: u(w) = w1/2.Her initial wealth is 10 and she faces the lottery X : (-6, 1/2; +6,1/2). (a) Compute the exact value of the certainty equivalent and of the risk premium.(b) Apply Pratt^?s formula 10 obtain an approximation of the risk premium(e) Show that with such a utility function absolute risk aversion is decreasing in wealth while relative risk aversion is constant. (d) If the utility function becomesv(w) = w^1/4,answer again part (a). Are you surprised by the changes in the certainty equivalent and in the risk premium? Relate this change to the notion of ^'more risk averse^' (i.e. express v(w) as a concave transformation of u (w)).(e) lf the risk becomes Y : (-3 , 1/2; +3, 1/2 ), compute the new risk premium as approximated by Pratt^'s formula. Why is the approximated risk premium four times smaller than the risk premium for X

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