WeekofFeb16_solns

WeekofFeb16_solns - (d Since Joe is risk-averse U z...

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Solutions to Recitation: Week of Feb 16 Anukriti Sharma February 16, 2009 Question 1 . Since γ > 0, the given utility function is a strictly increasing transformation of V ( x,y ) = ( αx + βy ). So, the demand functions for x and y would be the same as in the case of V(x,y). Since α β > 1, the demand functions are x = w and y = 0. Question 2 . U(w) = ( αw ) γ . U ”( w ) = α 2 γ ( γ - 1)( αw ) γ - 2 < 0; Risk-averse. Question 3 . Let z be the probability that the widget is a success. EV(Contract 2) = z.50,000 + 0. This is equal to \$10,000 if z = 0.2. Question 4 . (a) EU(Contract 1) = U(10,000) (b) EU(Contract 2) = z.U(50,000) (c) Indiﬀerent if U(10,000) = z.U(50,000)
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Unformatted text preview: (d) Since Joe is risk-averse, U ( z * 50 + (1-z * )0) > z * U (50) + (1-z * )0 = z * U (50) = U (10). ⇒ U ( z * 50) > U (10). Since U(.) is strictly increasing in wealth, z * 50 > 10 ⇒ EV ( Contract 2) > EV ( Contract 1). Question 5 . Let K be the Certainty Equivalent of Contract 2. ⇒ U(K) = 0.5 U(50,000) ⇒ √ K = 0 . 5 √ 50 , 000 ⇒ K = 12,500. Question 7 . Y is the same as K. Question 8 . (a) K (b) 15,000 - K = 2500 (c) 0.5 U(50,000 - X) + 0.5 U(1000 - X) = EU(Contract 2) ⇒ √ 50 , 000-X + √ 1000-X = √ 50 , 000 1...
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