Fruit or Candy: 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.
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.
d. Now imagine that the price of a piece of candy increases to $0.30. How many possible actions do you have? Does your answer to (c) change?