[Continuation of question 14]
Given that the original optimal basket (x = 50, y = 50) is just affordable on the new budget line, will the original optimal basket remain the optimal basket at the new income and prices?

Question

BlackTom AI · Accepted Answer

The prompt provided has the question but does not supply any answer options to analyze, only a single proposed answer string. Because options are missing, I cannot perform a standard option-by-option evaluation as requested.

To engage with the core concept, consider what it means for the original optimal basket (x = 50, y = 50) to be just affordable on a new budget line. In consumer theory, the optimal bundle is the point where the highest attainable indifference curve is tangent to the budget constraint. If the new budget line just allows (50, 50), several key things could occur depending on how prices and income have changed:
- If the new budget line is such that it is tangent to the same indifference curve at (50, 50), and the slope (marginal rate of substitution) matches the slope of the budget line at that point, then (50, 50) could remain optimal.
- If the new budget line is not tangent but merely touches the indifference curve at (50, 50), the optimal point could still be (50, 50) provided the consumer cannot reach any higher indifference curve given the new constraint. However, any shift in slope (due to price changes) typically alters the tangency condition, so a different point on a higher indifference curve might become optimal.
- If income or prices shift such that the budget line moves in a way that makes a different bundle (with a higher or different combination of x and y) affordable and preferred (on a higher indifference curve), the original point would not remain optimal.

Because the statement in the provided answer—"No. It will not. The new optimal basket will be to the left of the original optimal basket."—asserts a specific directional move (to the left, i.e., with less of x and/or y) without context about the new budget line’s slope, the original indifference curve, or the consumer’s preferences, this claim cannot be guaranteed to hold in all scenarios. In some cases, the optimal could stay at (50, 50); in others, it could move to a point with a different mix, or away from the origin depending on whether the budget constraint becomes more or less favorable for combinations of goods.

In summary, with the information given (only that (50,50) is just affordable on the new budget line), we cannot definitively conclude that the original optimal basket will not remain optimal or that the new optimum lies to the left. The actual outcome hinges on the new budget line’s slope relative to the consumer’s marginal rate of substitution at (50,50) and on whether a higher indifference curve becomes affordable under the new constraints.

If you intended a multiple-choice analysis, please provide the complete set of answer options so I can evaluate each one specifically and explain why each option is correct or incorrect.

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

[Continuation of question 14] Given that the original optimal basket (x = 50, y = 50) is just affordable on the new budget line, will the original optimal basket remain the optimal basket at the new income and prices?

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