Zoë's Utility Function for Altruistic Choice
Zoë's altruistic preferences are mathematically defined by the utility function . In this equation, represents the amount of money Zoë keeps for herself, and represents the amount she gives to Yvonne. This specific function is used to generate the indifference curves depicted in Figure E4.1, which illustrate her choices.
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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
Learn After
Figure 4.11 (reproduced as E4.1) - Zoë's Optimal Altruistic Choice
A person named Zoë has £200 to divide between herself (amount
z) and another person, Yvonne (amounty). Zoë's preferences for different divisions are represented by the utility functionU(z, y) = (z-100)^2 + (y-100)^2. A higher utility value indicates a more preferred outcome. Based on this function, which of the following divisions would provide Zoë with the highest level of satisfaction?Firm Viability in a Market Economy
Interpreting a Preference Function
A person's preferences for an allocation of money between themselves (amount
z) and another person (amounty) are described by the utility functionU(z, y) = (z-100)^2 + (y-100)^2. This function implies that the person is indifferent between the allocation (z=200, y=0) and the allocation (z=100, y=100).Analyzing Preferences from a Utility Function
Optimal Altruistic Choice Under a Constraint
A person's preferences for dividing money between themself (z) and another person (y) are represented by the function U(z, y) = (z-100)^2 + (y-100)^2, where a lower value of U is preferred. Match each feature of this preference model to its correct description.
A person's preferences for dividing money between themself (
z) and another person (y) are given by the utility functionU(z, y) = (z-100)^2 + (y-100)^2, where a lower utility value is preferred. Currently, the allocation isz=150andy=50. Which of the following changes would this person prefer most?An individual has £200 to divide between themself (amount
z) and another person (amounty). Their preferences are described by the functionU(z, y) = (z-100)^2 + (y-100)^2, where a lower value indicates a more preferred outcome. To find their optimal choice, one must combine their preferences with their constraint. Arrange the following steps into the correct logical sequence for solving this problem.A person's preferences for dividing a sum of money between themself (amount
z) and another person (amounty) are represented by the functionU(z, y) = (z-100)^2 + (y-100)^2. Lower values of this function correspond to more preferred outcomes. The person's most preferred outcome, regardless of any budget limitations, occurs when the amount they keep (z) is ____.