Question

6. A decision maker has a vNM utility function over money of u(x) = x2. This decision maker is (a) risk-averse. (b) risk-neutral. (c) risk-loving. (d) none of the above.

7. Consider two lotteries: • Lottery 1: The gamble (0.1, 0.6, 0.3) over the final wealth levels ($1, $2, $3). (The expected value of this lottery equals $2.2) • Lottery 2: Get $2.2 for sure. a) Any risk-averse individual will choose the first lottery. b) Any risk-averse individual will choose the second lottery. c) Any risk-averse individual will be indifferent between these two lotteries. d) None of the above

Answer 1

U(X) = x2. For different devels of x we have uxlas marginal u tiut foom wealth X=100 u(x1= 200 2001 Constant 200 X=200 x=300 income - U(X) = 400 UCx1 = 600 marginal Utilin from The given decision maker is nisk-neutral (6) why? Because you visk heutral individual marginal Utilin from income remains constant ( DeJination ) (7) Expected For anisk Averse individual, Utility of expected value of wealth is greater than expected utility of weatth. So Expected wealth from Lottery - I 0.1(1) + 0.6(2) + 0-3(3) = 0.1 + 1.2 +0.9 = 2.2$ from Lottery 2.2 $ for sure.

Since, Expected and sure returns are equal So Risk Averse decision maker will (b) Choose Lottery-2 why? Because he want to minimize nsk for git Same Return of two options Available you to him.