Optimal Choices for Altruistic vs. Self-Interested Preferences in Zoë's Dilemma

Zoë's Constrained Optimization Problem

An individual wins £200 and is deciding how much, if any, to share with a friend. The winner's personal satisfaction increases with both the amount of money they keep and the amount their friend receives. Suppose that just before the decision is made, the winner learns that their friend has unexpectedly received a separate £50 gift from another source. How would this new information most likely alter the winner's sharing decision regarding the £200 prize?

Analyzing Preferences in a Sharing Scenario

An individual with purely self-interested preferences wins a £200 prize. This individual would be indifferent between the outcome where they keep all £200 for themselves and an alternative outcome where they keep £150 and give £50 to a friend.

An individual with altruistic preferences wins a £200 prize and is deciding how to split it with a friend. The individual's happiness increases with both the amount of money they keep and the amount their friend receives. Given this, which of the following statements most accurately describes their likely decision-making process?

Inferring Preferences from Choices

An individual wins a £200 prize and is deciding how to allocate it between themself and a friend. The individual's preferences are altruistic, meaning their personal satisfaction is positively affected by both the amount they keep and the amount their friend receives. Given four potential scenarios, which outcome would result in the lowest level of satisfaction for this individual?

Evaluating Altruism from Observed Choices

An individual wins a £200 prize and must decide how to allocate it between themself and a friend. Match each of the following preference types to the allocation choice that an individual holding those preferences would most likely make.

Deconstructing an Altruistic Choice

Zoë's Feasible Set and Budget Constraint in the Lottery Dilemma

Altruistic Choice as a Decision Problem, Not a Game

Modeling Altruistic Choice as a Budget Allocation Problem

Social Preferences Determine Indifference Curve Shape (Figure 4.10)

Yvonne's Allocation Decision After Winning the Lottery

Yvonne's Allocation Decision After Winning the Lottery

A large technology firm, which holds a dominant position in the operating system market, invests billions in developing a next-generation artificial intelligence. In contrast, a small-scale wheat farmer, operating in a market with thousands of other farmers selling identical crops, does not invest in developing a new, revolutionary irrigation system. Which statement best analyzes the economic incentive behind these different investment decisions?

A researcher models an individual's social preferences using the utility function u(y,z) = y^2 * z^(-1), where 'y' is the individual's own income and 'z' is a colleague's income. If both the individual and the colleague currently have the same income, which of the following scenarios would result in the greatest increase in the individual's utility?

Interpreting Social Preferences in a Utility Function

An individual's social preferences can be modeled with the utility function u(y,z) = y^a * z^b, where 'y' is their own wealth, 'z' is another person's wealth, and the parameter 'a' is assumed to be positive (a > 0). Match each description of a social preference to the parameter conditions that best represent it.

Yvonne's Donation Decision

Consider an individual's preferences modeled by the utility function u(y,z) = y^a * z^b, where 'y' is their own wealth, 'z' is another person's wealth, and both 'a' and 'b' are positive constants.

True or False: If both the individual's wealth and the other person's wealth were to double, the individual's resulting utility would also exactly double, regardless of the specific positive values of 'a' and 'b'.

Social Welfare Policy Evaluation

Critique of a Social Preference Model

In a social preference model represented by the utility function u(y,z) = y^a * z^b, where 'y' is an individual's own wealth and 'z' is another person's wealth, a negative value for the parameter 'b' (i.e., b < 0) indicates a preference that can be described as ____.

An individual's social preferences are modeled by the utility function u(y,z) = y^0.5 * z^0.5, where 'y' is the amount of money they possess, and 'z' is the amount of money a friend possesses. Initially, both the individual and their friend have $100 each. If the individual's money decreases to $64, how much must the friend's money increase for the individual's utility to return to its original level?

An individual's social preferences can be modeled with the utility function u(y,z) = y^a * z^b, where 'y' is their own wealth, 'z' is another person's wealth, and the parameter 'a' is assumed to be positive (a > 0). Match each description of a social preference to the parameter conditions that best represent it.