Lisa's optimal basket cannot be to the South West of her budget line

Question

BlackTom AI · Accepted Answer

Question restatement: The prompt asks whether Lisa's optimal basket cannot be to the South West of her budget line, and provides an assertion that True: she would afford consuming to the South West of her budget line, but would prefer a basket on her budget line.

First, recall the core idea: the budget line represents all combinations of goods that exhaust Lisa's income (assuming prices and income are given). A location southwest (to the lower-left) of the budget line is affordable but implies spending less than her income. An optimal basket, given typical consumer preferences, depends on the shape of those preferences.

If Lisa has monotone (more is better) preferences, she strictly prefers more of at least one good without giving up the other, so any bundle that lies strictly inside (southwest of) the budget line is Pareto-dominated by moving to a bundle on the budget line that uses all income. In other words, with monotonic preferences, the optimal choice lies on the budget line, not inside it. Therefore, being southwest of the budget line would not be optimal because you could increase consumption and reach a higher (better) indifference curve while staying within the budget.

Even in cases with non-monotone or corner solutions (e.g., if one good is undesirable or if there are satiation points), the interior of the budget set southwest of the line is generally not preferred to a bundle on or inside the boundary that aligns with the budget constraint, but the typical benchmark assumption is monotone preferences leading to an on-budget-line optimum.

Why the statement could still be considered true under standard assumptions: the assertion says the optimal basket cannot be southwest of the budget line and would be on the line instead. This aligns with the common result that, when more of goods is preferred, consumers choose bundles on the budget line to maximize utility given limited income.

Why this statement might be misleading if taken without assumptions: if Lisa had non-monotone preferences (e.g., a dislike for a lot of one good, or satiation), it could change where the optimum lies, potentially interior to the budget set or at a corner not on the line. In those atypical cases, the optimal basket could theoretically be southwest of the budget line or elsewhere, depending on the exact preferences.

Summary interpretation: Under standard monotone preferences, the assertion that the optimal basket cannot lie southwest of the budget line and should lie on the line is correct. The Southwest region is affordable but not utility-maximizing when more is preferred, hence the move to a bundle on the budget line.

SIPAIA6400_001-002_2025_3 - Microeconomic Analysis for International and Public Affairs Problem Set 4, Individual Portion

Lisa's optimal basket cannot be to the South West of her budget line

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