Question

Find A's wealth for each possible case and calculate A's expected utility under this risk pooling arrangement. Is A better off under this risk pooling agreement compared to the no insurance case? How about compared to the full-coverage, fair-price insurance case? 3. An individual purchases a dozen eggs and must take them home. Making trips home is costless, but there is a 50% chance that all the eggs carried on one trip will be broken during the trip. The individual considers two strategies: (1) take all 12 eggs in one trip, or (2) take two trips with 6 eggs in each trip. (a) Calculate the expected number of eggs remaining under strategy 1 and strategy 2. (b) Suppose the utility over the final number of eggs is u(2) = Vr. Calculate expected utility under strategy 1 and strategy 2. Which strategy is preferable? (c) Would expected utility be further increased by taking more trips? (d) Now suppose the utility over the final number of eggs is u:) = r?. Calculate expected utility under strategy 1 and strategy 2. Which strategy is preferable? (e) Now suppose the utility over the final number of eggs is uar) = 2. Calculate expected utility under strategy 1 and strategy 2. Which strategy is preferable?

Answer 1

STRATEGIES (A): Take all 12 eras in no tio Tave two trips with 6 Eggs in each trip I. Expected Value = èpidi pizprobrebility a; = number of eggs. Expected value for Strategy I = 0.50*12+ 0.500 = 6 to II. Expected value for Stoutegy I I - 2nd trip ist the =co.so x6 +0.50x0) +0.50x6 +0.58xo) +(3+0) =(3+0) = 3+3 732 (B): RISK AVERSE CU(R) = a) Expected Utility = È piu(x) Here, pi= probability UG) = utility function STRATEGY Expected Utility (EUR)) = 0.50 x√12+0.50x to = 11.732 ] STRATEGY I Expected Utility (EU (x) asoxta = (6.50 56to.soxro +(0.50x86 +0.50 xro- and Trip 2nd - U 1st Trip = 2.449]

(b) Strategy II will be more preferable

(c) The statement is TRUE ,because yes by taking more trips the expected utility will increase because there will be less variation ( variation to reduce). Here the increase in utility will be at a diminishing rate.

(D) uca)= x² this means RISK SEEKING STRATEGY I EU(x) = 0.50X122 to.soxco =0.50 X 144 to.soxo = 72 to STRATEGY II = 172 Expected Utility EU (n)= =co.sox(6)² +0.50 x(0)² + (oso x (6)² +0.50 x (02) = (0.50x 36 to soxo) + (o.sox36+0.50 xo) = (18 +o) + (18+o) = 136

(d)Strategy I will be more preferable because of higher utility

- (E) u (a) =n STRATEGY Expected Utility EU (n) = 0.50x 12 to.soxo = 6 to STRATEGY I Expeted Utility EU (R) = (0.50x6 to.soxo) + (o.so*6 + 0.50xo) = ( 3+0) +(3+0) = 3+3 = 6 . Here we can see that both Strategies are neutral