A person has an expected utility function of the form U(w)=w^1/2.He has an initi

Question

A person has an expected utility function of the form U(w)=w^1/2.He has an initial wealth of $25.He also has a lottery ticket that will be worth $75 with probability 1/2 and will be worth $0 with probability 1/2.
a)What is the person's expected utility?
b)What is the lowest price p at which the individual would be willing to sell (or part with) the ticket?
c)Suppose the individual's initial wealth is$50.Repeat parts (a) and (b).
d)compare the value of p between (b) and (c)and explain the difference in economics terms.

Explanation / Answer

for part a we can take the derivative and his expected utility will be 1/2w^(1/2)=1/(2sqrtw) we now plg in w 1/(2sqrt(25))= 1/(2*5) 1/10 For B the lowest price to sell the ticket is (75*1/2)+(0*1/2)=37.5 For c, a. we use our same derivative and plug in 50 1/(2sqrt(50))= 1/(2sqrt(25*2))= 1/(2*5sqrt())= 1/(10sqrt(2))= For C part b the lowest price to sell the ticket is (50*1/2)+(0*1/2)=25 For D, we compare our probability of a ticket at 75 and 50. The reason we sell the one at 75 for more is because our expected rate of return is higher. The probability is the same therefore, this is not a factor. In addition, our opportunity cost of selling is the same as well. To sum it up, the only difference is our expected level of return which in the end, the 75 will give us a higher utility than the 50.

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