Question

1. Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a loss of 20 Hollars. The probability of loss ik 0.2. It is also possible that someone breaks in Tom's home. In this case, he runs a risk of a loss of (80 dollars. The probability of loss is 0.1, These two probabilities (events) are independent. It is possible, however, for Tom to buy insurance. One unit of car insurance costs r dollars and pays 1 dollar if the loss occurs. On the the other hand, one unit of home insurance costs dollars and pays 1 dollar if the loss occurs. Thus if a units of car insurance are bought and a units of home insurance are bought, the wealth of Tom will be 100- Tra -r'a if there is no loss. In the case that only his car is stolen, his wealth is 100-ra- 1-20to when only his home is broken in, his wealth is 100 ra-r'a'-80+ a'. In the worst

Answer 1

U(x) ln x since two events are independent so of both occurring together = P(A) P(B) = 2 times 1 = 0.2 thus prof of Good state p_G = 1 - 0.2 = 9.8 P_B = 0.2 thus E4 = pG u(Wg) + PA u(WA) + p_B (W B) + PA P_B u (AB) = 98 ln (100 r alpha - r alpha^1) + 24 (100 - rd - r^1 -20 + alpha) + 1.4 (100 r alpha alpha alpha - 80 + alpha) + 0.2 ln (100 -rd - r alpha - 20 - 80 + alpha + alpha) e4 = 98 ln (100 - r d r' alpha) + 2ln (80 - r alpha 61 + alpha (1 - r)] + 1 ln [20 - rd + alpha (1 - r^1) + 0.2 ln [alpha (1 - r) + alpha (1 - r^1] Now FOC partial differential u/ partial differential alpha = 98 (- r)/100 - rd - r alpha) + 2 times (1 -r)/80 - r^1 alpha^1 (1- r) + 1 (-r)/[20 - rd + alpha^1 (1- r^1)]