Question

After losing few bucks on a roulette game at a casino company over the last weekend, Craig was about leaving for studying CFA exam. However, to retain customers in the store, the casino company was offering a promotion: a free cash of $140 or a chance to win the prize of a coin game. The coin game is described as follows:

The prize of the game depends on an unbiased coin you toss. If the heads appear, you get $200. If the tails appear, you get $100.

Assuming Craig was maximizing his utility function U(W)= W0.5 in making financial decisions. Would Craig stay and play this coin game? What was the lowest cash offer that Craig was willing to quit from playing the coin game and study CFA？

Answer 1

Given that Craig's utility function is U(W)= W*0.5

If the coin is heads, then he gets 200 and if it is tails, he gets 100. We know that probability of heads and tails are 0.5 each.

So, his utility from coin game= 0.5(200*0.5)+0.5(100*0.5)= 50+25= 75

His utility from getting free cash of 140= 140*0.5= 70

As his utility from coin game is more than utility from free cash, Craig will play coin game.

If craig cas to quit the coin game, lowest cash offer should be such that the utility from cash offer will be equal to utility from coun game. So, If the cash offer is 150, then utility from it will be 150*0.5= 75, which is equal fo utility from coin game.

So, Gor Craig to quit from playing coin game and to study CFA, the lowest cash offer should be $150.