Suppose that Tom's preferences are convex and that Tom's income is $100, the price of food, good X, is $1 per unit and the price of other goods, good Y, is $1 per unit.
Under these circumstances, Tom optimally purchases 50 units of food. Then Tom optimally spends:

Question

Suppose  that Tom's preferences are convex and that Tom's income is $100, the price of food, good X, is $1 per unit and the price of other goods, good Y, is $1 per unit.
Under these circumstances, Tom optimally purchases 50 units of food. Then Tom optimally spends:

BlackTom AI · Accepted Answer

We start by restating the given scenario: Tom has income 100, the price of food X is 1 per unit, and the price of other goods Y is 1 per unit. The information that Tom optimally purchases 50 units of food X tells us he spends 50 on X (since 50 units × $1 per unit = $50).

With a total income of $100, the remaining budget for Y must be 100 − 50 = $50. Since the price of Y is $1 per unit, the quantity of Y purchased would be 50 units if he spends the entire leftover amount on Y.

Given the problem states X=50 units is optimal, the implied allocation is X = 50, Y = 50, spending $50 on Y. This aligns with the budget constraint X + Y ≤ 100 and the prices pX = pY = 1, as well as the assumption of convex preferences that typically yield interior solutions where the consumer reallocates spending smoothly.

If any other options were provided, they would need to be evaluated against these budget and pricing facts: spending on X is 50, so the remaining income for Y is 50, and the price ratio being 1:1 means the remaining expenditure translates directly to 50 units of Y. Therefore, the amount spent on the other goods is $50.

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

Suppose that Tom's preferences are convex and that Tom's income is $100, the price of food, good X, is $1 per unit and the price of other goods, good Y, is $1 per unit. Under these circumstances, Tom optimally purchases 50 units of food. Then Tom optimally spends:

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