A gamble is resolved by tossing an unbiased coin as many times as necessary to obtain heads. If it takes only one toss, the payoff is $2; if it takes two tosses, it is $4; if it takes three, it is $8; and so forth.

Gamble:

H $2

TH $4

TTH $8

a)What is the expected value of the gamble? (1 point)

b)If you are expected value maximizer, what price are you willing to pay for this gamble? (1 point)

c)Assume that the marginal utility of money is diminishing and the utility of given amount of money x might equal to the logarithm of x, so that . What is the expected utility of the gamble? (1 point)