[Continuation of question 13]
If the price of food doubles to $2 per unit, the price of other goods remains at $1, and Tom's income increases to $150, would Tom still afford the original optimal basket of question 1 (x = 50 and y = 50)?

Question

BlackTom AI · Accepted Answer

First, I will restate the key pieces of the problem to ensure clarity: the price of food (x) has risen to 2, the price of the other good (y) remains 1, and Tom's income is 150. The original basket in question 1 was x = 50 and y = 50. We need to determine if that same basket is still affordable under the new prices and income.

Option analysis:
- Evaluate affordability: Compute the total expenditure for the original basket under the new prices. With x = 50 and y = 50, total cost = (price of x)*x + (price of y)*y = 2*50 + 1*50 = 100 + 50 = 150. Since Tom’s income is 150, this expenditure exactly equals his income, so the basket lies on the new budget line. This shows that the original basket is affordable under the updated price and income.

- Link to the concept of the budget line: An affordable basket is any combination (x,y) that satisfies 2x + y ≤ 150. The original basket satisfies 2(50) + 50 = 150, so it is on the boundary, i.e., just affordable. If the question intends merely affordability, this confirms the basket is reachable given the revised prices and income.

- Consideration of optimality: The question asks whether Tom would still “afford the original optimal basket.” Affordability is one thing; optimality depends on Tom’s preferences and the resulting utility-maximizing choice given the new budget constraint. Since we are not provided with the utility function or the original optimal (in question 1) conditions, we cannot definitively conclude that the original basket remains the utility-maximizing choice solely from price and income changes. However, in many microeconomics problems, if the income adjusts to exactly compensate the higher price (i.e., nominal income is raised to keep the original bundle affordable), the interpretation is that the bundle remains attainable but not necessarily optimal unless the preference structure implies the same bundle remains optimal under the new constraint.

- Why this option can be correct: The calculation shows that the expenditure equals the new income, so the original basket is indeed just affordable and lies on the new budget line. If the question’s intended answer is about affordability rather than unchanged optimality under a shift in price, this option accurately describes the situation.

- Why this option could be misleading if misinterpreted: If one assumes that affordability automatically implies optimality regardless of preferences, that would be an overreach. The mere fact that 2x + y = 150 holds true confirms affordability on the budget line, but without knowledge of the utility maximization given the new prices, we cannot conclusively state it remains the optimal bundle.

- Missing alternative options note: The provided data shows only one answer option, so there are no other choices to contrast here. If there were alternative statements, we would assess each in terms of budget feasibility, budget line position, and implications for utility maximization under the new prices and income.

In summary, the analysis confirms that the original basket (x = 50, y = 50) is affordable under the new prices and income because its total cost equals 150, placing it on the new budget line 2x + y = 150. Whether it remains the utility-optimal choice would depend on Tom’s preferences and the resulting utility maximization under the updated budget constraint, information which is not provided in this prompt.

[Continuation of question 13] If the price of food doubles to $2 per unit, the price of other goods remains at $1, and Tom's income increases to $150, would Tom still afford the original optimal basket of question 1 (x = 50 and y = 50)?单项选择题

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