A banana costs $0.50 and a piece of candy costs $0.25 at the local cafeteria. You have $1.25 in your pocket and you value money. The money-equivalent value (payoff ) you get from eating your first banana is $1.20, and that of each additional banana is half the previous one (the second banana gives you a value of $0.60, the third $0.30, and so on). Similarly the payoff you get from eating your first piece of candy is $0.40, and that of each additional piece is half the previous one ($0.20, $0.10, and so on). Your value from eating bananas is not affected by how many pieces of candy you eat and vice versa.
Required:
a. What is the set of possible actions you can take given your budget of $1.25?
b. Draw the decision tree that is associated with this decision problem.
c. Should you spend all your money at the cafeteria? Justify your answer with a rational choice argument.

a. What is the set of possible actions you can take given your budget of $1.25?

bananas          candies        total utils

0                        5                    $0.78

1                         3                     $1.90

2                        1                     $2.20

b. Draw the decision tree that is associated with this decision problem.

I attached a decision tree on PDF

c. Should you spend all your money at the cafeteria? Justify your answer with a rational choice argument.

Yes, since you can obtain more benefits from purchasing 2 bananas and 1 candy than the money that you have (total benefits $2.20 vs $1.25 in cash).

Explanation:

utility obtained from first banana $1.20, payoff per $ spent = 2.4

utility obtained from second banana $0.60, payoff per $ spent = 1.2

utility obtained from third banana $0.30, payoff per $ spent = 0.6

utility obtained from first candy $0.40, payoff per $ spent = 1.6

utility obtained from second banana $0.20, payoff per $ spent = 0.8

utility obtained from third banana $0.10, payoff per $ spent = 0.4

answer; situational irony;