Question

Question 2 Suppose that your friend has a limited budget of $20 and offers you the St. Petersburg paradox bet. Therefore, if the first five or more flips are tails, then you win $20 automatically (have a look at the table below). For each of the utility functions, calculate the expected utility and the certainty equivalent. Payoff S2 $4 $8 Draws T II

Answer 1

the St. petersburg paradox bet deals with the flipping of the coin, that is the number of time tails comes up, the total number of flips(n), detrmine the prize suppose $2n.the probability of P(n)flips is 1,is divided by 2n and expected payoffs is the price times probability. the expected value is the sum of expected paayoff of all consquences.

a):
u(x)= (x)^2

=EU= (20)^2= 4.57

CE= -(20)* In(1-4.5)

=25.05

b) :
u(x)= (x)1/3

Eu= 2.68

CE= -(20)* In (1-2.68)

=10.37

c):
u(x)= x2

EU= 400

CE= -(20) * In(1-400)

=119.7