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 (amount y). Zoë's preferences for different divisions are represented by the utility function U(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 (amount y) are described by the utility function U(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 function U(z, y) = (z-100)^2 + (y-100)^2, where a lower utility value is preferred. Currently, the allocation is z=150 and y=50. Which of the following changes would this person prefer most?

An individual has £200 to divide between themself (amount z) and another person (amount y). Their preferences are described by the function U(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 (amount y) are represented by the function U(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 ____.