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Consider the quadratic VNM utility function . (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...

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Consider the quadratic VNM utility function .

(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

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

Answered 105 days After Nov 20, 2021

Solution

Komalavalli answered on Mar 05 2022
119 Votes
Quadratic VNM utility function u (w) = a+bw+cw2 --------- (1)
a)
Condition for risk aversion
u’(w)>0
u’’(w)<0
Finding u’(w) = ∂u/∂u and u’’(w)= ∂2u/∂u2
u’(w) = b+2cw        -------------(2)
u’’(w)=2c        -------------(3)
Applying risk aversion condition for (2) and (3), we get
b+2cw>0, 2c<0
From above we can say that the parameters c should be <0 and
2|c|w.we consider absolute value of c in order to make 2cw positive.
)
By utilizing the restriction of b in above...
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