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

Zoë's Utility Function for Altruistic Choice

An individual must decide how to allocate a fixed sum of money between themself and another person. The accompanying graph illustrates this choice. The straight diagonal line represents all possible allocations (the feasible frontier). The curved lines are the individual's indifference curves, where curves further from the origin represent higher levels of personal satisfaction. Which point represents the individual's optimal allocation, and why?

Analyzing an Altruistic Decision

Analysis of a Suboptimal Altruistic Choice

Consider a graphical model where an individual is deciding how to allocate a fixed sum of money between themself and another person. The straight line represents all possible allocations, and the curved lines represent the individual's levels of satisfaction (with curves further from the origin indicating higher satisfaction). If a specific allocation point lies on the straight line but is intersected by a satisfaction curve (rather than being just tangent to it), this point represents the best possible choice for the individual.

Interpreting Preferences in an Altruistic Choice Model

In a graphical model representing an individual's decision on how to allocate a fixed sum of money between themself and another person, match each graphical component to its correct interpretation.

In a graphical model of altruistic choice, the optimal allocation of a fixed sum of money between oneself and another person occurs at the point of tangency between the feasible frontier and an indifference curve. At this specific point, the individual's marginal rate of substitution (the rate at which they are willing to trade their own money for the other person's) is exactly ______ to the marginal rate of transformation (the rate at which they can trade their own money for the other person's).

You are tasked with creating a graphical model to determine the optimal way for an individual to allocate a fixed sum of money between themself and another person, based on their personal preferences. Arrange the following steps in the correct logical order to construct this model and find the solution.

The provided graph illustrates how an individual decides to split a £200 windfall between themself (horizontal axis) and a friend (vertical axis). The straight diagonal line shows all possible allocations. The curved lines represent the individual's satisfaction levels, with curves further from the origin representing higher satisfaction. Initially, the individual's optimal choice is at Point A (£140 for themself, £60 for their friend). Suppose the individual's attitude changes, and they become substantially more altruistic, valuing their friend's gain more than they did before. Which of the following points is the most plausible new optimal choice?

Impact of a Matching Grant on Altruistic Choice

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

Optimal Choice as Utility Maximization under Constraints

Principle of Constrained Utility Maximization

A graph is constructed to show the possible distributions of a sum of money between two people, Maria and Carlos. Maria's total money is plotted on the horizontal axis, and Carlos's total money is on the vertical axis. If Maria's indifference curves on this graph are perfect vertical lines, what can be inferred about her preferences?

Interpreting Social Preferences from Indifference Curves

Consider a scenario where an individual's payoff is plotted on the horizontal axis and another person's payoff is on the vertical axis. Match each description of the individual's preferences to the corresponding shape of their indifference curves on this graph.

Consider a graph where an individual's monetary payoff is on the horizontal axis and another person's payoff is on the vertical axis. If this individual's indifference curves are upward-sloping, it implies that for them to feel equally well-off, any increase in the other person's payoff must be offset by an increase in their own payoff.

Graphical Representation of Social Preferences

Explaining Altruistic Preferences via Indifference Curves

Consider a graph where Person A's payoff is on the horizontal axis and Person B's payoff is on the vertical axis. If Person A's satisfaction depends solely on the total combined payoff for both individuals (i.e., the sum of Person A's payoff and Person B's payoff), what will be the shape of Person A's indifference curves?

Predicting Choices Based on Social Preferences

Imagine a scenario where outcomes are represented on a graph, with your monetary payoff on the horizontal axis and another person's payoff on the vertical axis. You are currently at an allocation of ($10 for you, $10 for the other person). If you have altruistic preferences, meaning you derive satisfaction from both your own and the other person's well-being, which of the following alternative allocations would unambiguously place you on a higher indifference curve?

Consider a graph where your monetary payoff is plotted on the horizontal axis and another person's payoff is on the vertical axis. If your indifference curves are downward-sloping but very steep, what does this reveal about your preferences?

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

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