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Consider the quadratic VNM utility function U(w) = a + bw + cw2. Consider the quadratic VNM utility function U(w) = a + bw + cw2. (a) What restrictions if any must be placed on parameters a, b, and c...

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Consider the quadratic VNM utility function U(w) = a + bw + cw2.

Consider the quadratic VNM utility function U(w) = a + bw + cw2.

(a) What restrictions if any must be placed on parameters a, b, and c for this function to display risk aversion?

(b) Over what domain of wealth can a quadratic VNM utility function be defined?

(c) Given the gamble

Show that CE < E(g) and that P > 0.

(d) Show that this function, satisfying the restrictions in part (a), cannot represent preferences that display decreasing absolute risk aversion.

Answered Same Day Dec 26, 2021

Solution

David answered on Dec 26 2021
120 Votes
Q.Consider the quadratic VNM utility function U(w) = a + bw + cw2.


(a) What restrictions if any must be placed on parameters a, b, and c for this function to display risk aversion?


Answer- Function to display risk aversion, should hold
Given,
Thus, for function to display risk aversion, c must be less than zero such that u"(w)<0
And if c<0 , then b must be greater...
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