Hjalmer Ingqvist's son-in-law, Earl, has not worked out very well. It turns out that Earl likes to gamble. His preferences over contingent commodity bundles are represented by the expected utility function

u(c₁,c₂,p₁,p₂) = p₁c₁²+ p₂c₂².

(a) Just the other day, some of the boys were down at Skoog's tavern when Earl stopped in. They got to talking about just how bad a bet they could get him to take. At the time, Earl had $100. Kenny Olson shuffled a deck of cards and offered to bet Earl $20 that Earl would not cut a spade from the deck. Assuming that Earl believed that Kenny wouldn't cheat, the probability that Earl would win the bet was 1/4 and the probability that Earl would lose the bet was 3/4. If he won the bet, Earl would have ____________ dollars and if he lost the bet, he would have ____________ dollars. Earl's expected utility if he took the bet would be ____________, and his expected utility if he did not take the bet would be ____________. Therefore he (accepted, refused) ____________ the bet.

(b) Just when they started to think Earl might have changed his ways, Kenny offered to make the same bet with Earl except that they would bet $100 instead of $20. What is Earl's expected utility if he takes that bet? Would Earl be willing to take this bet?