This problem presents a new scenario based on the situation in Figure 4.11. After winning £200, but before she can share it with her flatmate Yvonne, Zoë receives a tax bill for £40 on her winnings. This effectively reduces the total amount of money available for allocation to £160. Assuming Zoë's altruistic preferences remain fixed, the challenge is to determine her new optimal choice for sharing the reduced prize.

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This diagram, identified as Figure 4.11 and reproduced as E4.1, illustrates how an altruistic Zoë chooses to distribute her £200 lottery winnings. It graphs 'money for Zoë' (horizontal axis) against 'money for Yvonne' (vertical axis). The feasible frontier, representing all possible splits, is a line from (200, 0) to (0, 200). Zoë's preferences are depicted by downward-sloping, convex indifference curves. Her optimal choice, which maximizes her utility, is at point A (140, 60), where the feasible frontier is tangent to the highest attainable indifference curve. This means she keeps £140 and gives £60 to Yvonne.

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

To cite the ebook, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/.

To cite a unit, use The CORE Econ Team 2023 The Economy 2.0: Microeconomics Open access e-text https://core-econ.org/the-economy/ Unit [unit number] (url).

CORE Econ - The Economy 2.0: Microeconomics

In the context of Zoë's altruistic choice, the points where her lowest reachable indifference curve intersects the feasible frontier represent outcomes that are possible but not optimal. While these combinations of her and Yvonne's payoffs are affordable, they do not yield the maximum possible utility. Zoë could improve her satisfaction by choosing a different point along the feasible frontier, specifically the point of tangency with a higher indifference curve. This demonstrates the principle that optimal choices are generally found where an indifference curve is tangent to the feasible frontier, not where it intersects it.

Intersection Points of an Indifference Curve and Feasible Frontier as Suboptimal Choices

Zoë's Allocation Decision After a £40 Tax on Lottery Winnings

In the context of Zoë's altruistic choice problem, the application of the first-order condition (MRS = MRT) leads to a specific behavioral conclusion. The model predicts that regardless of the total amount of the prize money to be split, Zoë will consistently choose to keep a larger share for herself than she gives to Yvonne.

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