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# We now have $5,000 in assets and are given a choice between investment 1 and investment 2. With investment 1, 80% of the time weincrease our asset position by$295,000, and 20% of the time we increase our asset position by $95,000. With investment 2, 50% of the time we increase our asset position by$595,000, and 50% of the time we increase our asset position by \$5,000. Our utility function for final asset position x is u(x). We are given the following values for u(x): u(0) = 0, u(640,000) = .80, u(810,000) = .90, u(0) = 0, u(90,000) = .30, u(1,000,000) = 1, u(490,000) = .7. a. Are we risk-averse, risk-seeking, or risk-neutral? Explain. b. Will we prefer investment 1 or investment 2?

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(a) To see how risky a person is, we need to look at the utility function values and determine if the function is convex or concave(or neither). Let's map out the points that were given to us by the task and we get the following:

The points are marked as $\text{\textcolor{#4257b2}{blue}}$ and the graph is colored $\text{\textcolor{#c34632}{red}}$. The graph is approximated with

$u(x) = \frac{\sqrt{x}}{1000}$

and we know that that function is $\textbf{concave}$ on its domain.

From that, we can say that this decision-maker is $\textbf{risk-averse}$.

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