Figure 4.11 (reproduced as E4.1) - Zoë's Optimal Altruistic Choice

An individual wins a prize of £200. They must decide how much of this money to keep for themselves (amount 'z') and how much to give to a friend (amount 'y'). The boundary of all possible choices is a straight line connecting the point where they keep everything (z=200, y=0) and the point where they give everything away (z=0, y=200). Considering the entire set of possible allocations (the feasible set), which of the following statements correctly analyzes a possible allocation?

Analyzing an Allocation Decision

An individual wins a prize of £200. They can decide how much to keep for themselves (amount 'z') and how much to give to a friend (amount 'y'). The total amount allocated cannot exceed £200. Match each allocation scenario with its correct description based on the set of all possible choices.

Evaluating an Allocation Choice

An individual has a fixed prize of £200 to divide between two options: keeping the money or giving it to a friend. The set of all possible allocation choices is represented by a feasible frontier (the boundary) and the entire area inside it. True or False: The choice to keep £120 for oneself and give £60 to the friend is a point that lies on the feasible frontier.

An individual receives a prize of £200. They can choose to keep a certain amount, represented by 'z', and give the rest to a friend, represented by 'y'. The equation that represents the boundary of all possible, maximum allocations (the feasible frontier) is y + z = ____.

An individual wins a prize of £200. They must decide how much of this money to keep for themselves (amount 'z') and how much to give to a friend (amount 'y'). The total amount allocated cannot exceed £200. Arrange the following allocation scenarios in order, starting with the one that is possible but does not use the full prize amount, followed by the one that uses the exact full prize amount, and ending with the one that is not possible.

Analyzing Changes to a Feasible Set

Evaluating an Allocation Strategy

An individual has a fixed prize of £200 to divide between keeping it for themselves (amount 'z') and giving it to a friend (amount 'y'). The boundary of all possible choices is defined by the combinations where the total amount allocated is exactly £200. If this individual is currently on this boundary and decides to increase the amount given to their friend by £1, what is the necessary change to the amount they keep for themselves?

Figure 4.10 (Left Panel) - Visualizing Zoë's Altruistic Preferences

Figure 4.10 (Right Panel) - Visualizing Self-Interested Preferences

Preferences Determine Optimal Choice in Zoë's Dilemma