Question

Lee Lin is an expected utility maximizer with u[y]=y^2, and a net worth of $50 million....

Lee Lin is an expected utility maximizer with u[y]=y^2, and a net worth of $50 million. Is Lee Lin risk-averse? He has an opportunity to pay $35 million to participate in a speculation that will yield him a $100 million profit with a probability he estimates to be .3, and otherwise will yield nothing. Will Lee Lin go for this deal? Explain.

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Answer #1

u(y) y^2

wealth = $50 million

cost of speculation = $35 million

profit = $100 million with prob 0.3 otherwise $0 with prob 0.7

Expected utility of gamble = 0.3 * u(50+100-35) + 0.7 * u(50 +0 -35)

= 0.3 * u(115) + 0.7 * u(15)

= 0.3 * 115^2 + 0.7 15^2 = 3967.5 + 157.5 = $4125

Expected utility of wealth = 50 ^2 = $2500

since EU of speculation is greater than EU of wealth , he will go for this deal.

- he is risk loving individual . as we know , that the utility function of a risk averse individual is concave over wealth whereas of risk loving is convex over wealth . and u(y) = y^2 is a convex function .

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