Question

Suppose you have $30,000 in wealth and have the choice of two possible gambles:
Gamble 1: a single flip of a coin would pay you $16,000 if it is heads, cost you $16,000 if it is tails.
Gamble2: two coin flips, each payuing you $8,000 if it is head, each costing you $8,000 if it is tails.
Suppose you utility function for money is U=$1/2. How much less costly is the second gamble than the first.

Answer 1

I presume that U=($)^(1/2) = sqrt($).

Calculate the expected utility under both choices.
U1 = .50*sqrt(46000) + .50*sqrt(14000)
U2 = .25*sqrt(46000) + .50*sqrt(30000) + .25*sqrt(14000)

Take it from here. BTW, not playing at all gives the highest expected utility.