Question

I need step by step solution to the following this question asap .I have limited time so please do it quickly with detailed explanation

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Question 4 Mr Magoo owns and drives a car which he will wreck with probability it (and does not wreck with probability (1-1)). If Mr Magoo wrecks the car his wealth is reduced from 10 to 3 SEK. Mr Magoo's utility from wealth in each state of the world i E {1, 2} is u(ci) = c;? where ci is the wealth in state i. In state 1 Mr Magoo wrecks the car and in state 2 he does not. a) Write down Mr Magoo's expected utility function. (2 points) b) Is Mr Magoo risk averse, risk neutral or a risk lover? Explain your answer. (3 points) c) Mr Magoo can choose to buy car insurance which would pay out K in the case of a car wreck. For this insurance contract he would have to pay yK. Assume also that i = y. Write down Mr Magoo’s new expected utility function (including the insurance). What is this particular price level called? (5 points) d) How much insurance would Mr Magoo buy? Explain your answer! (5 points) Questions

Answer 1

o a) ucc) = Co² wi=10 Poby= (1-2), - W.= 3, Pa = π (3 EU = (1-4) 4(10) + T U (3) otw, = (1-A) (10)2 + Ã (3) 2 EU= 100 (1-7) + 9 = 100-look +9 h a EU = 100ted 100-91 ñ Ang as utility funch is convex, 80 Risk Lover as au = 26, 224 = 230 Cconuex) 202 : T=Y, New Eu funch on Good State (NO wreck) jous & wealth = 10-YK In Bad state Wg= 10-7-YK tk = 3tk (1-2) 80 FU' = (1-) 4 (10-YK) + U( 37 BCM) Eu' (1-1) (10-76) + ( 3+ * (17)] This price is called . Insurance Premium put =, EU = (IA) (10-18)2 + ( 3 + B(1-)]?

d) Now Insusance will be boughts 80 that d Ey=0 OK as Y=t, so DEU! - (+) 2(10-ñk) (-1) + 7 2 [ 3 + KC1-)] CEP) (1-A) dk -20 CHA) [ 3+ KC-r)] = -A ) & (10-TK) 3+k- KK = 10-Tyk. - K=7 full Insurance is bought An