In the graph below, what statement is true about points A and B (assume the red lines are two budgets, of $20 and $40).

Question

BlackTom AI · Accepted Answer

To begin, let me restate what the question is asking: identify a true statement about points A and B given two budget lines and the standard consumer choice framework. The core concept here is the equality of the marginal rate of substitution to the ratio of prices at a utility-maximizing point, i.e., MUx/Px = MUy/Py.

Option analysis:
- If we examine the statement MUx/MUy = Px/Py at A, this is one way to express the same condition as MUx/Px = MUy/Py, because MUx/MUy = Px/Py implies MUx/Px = MUy/Py after a simple cross-multiplication and division by Px*Py. So, algebraically, MUx/MUy = Px/Py is equivalent to MUx/Px = MUy/Py. This equivalence means that a point where the consumer is maximizing utility given prices will satisfy this ratio equality.
- The same reasoning applies to point B: if B is a tangency point where the budget line touches a higher or lower indifference curve optimally, it will also satisfy MUx/Px = MUy/Py, which again is equivalent to MUx/MUy = Px/Py. Therefore, at both A and B, the marginal condition for optimality aligns with the price ratio.

Now, considering potential misconceptions:
- If one thought the condition was MUx/Px = MUy/Py alone, that is correct in standard theory, but recognizing its equivalence to MUx/MUy = Px/Py clarifies why the statement can be considered true for points A and B in this setup.
- If someone claimed the condition only applies to one point or only to A or only to B, that would be incorrect; in a standard two-good, two-budget setting, utility maximization occurs at the tangency points where the MRS equals the price ratio, which would apply to any optimal point on the budget constraint, here both A and B if they are tangencies.

Putting it together, the statement MUx/MUy = Px/Py at A is equal to MUx/MUy = Px/Py at B expresses the same optimality condition at both points, reflecting that both A and B are tangency (utility-maximizing) points on their respective budgets. This aligns with the fundamental rule MUx/Px = MUy/Py (the marginal rate of substitution equals the price ratio) and its equivalent form MUx/MUy = Px/Py when manipulated algebraically.

In summary, both A and B satisfy the marginal condition for utility maximization, making the given statement true for both points.

SA.999.600.91.SU25 Module 5 Cumulative Exam

In the graph below, what statement is true about points A and B (assume the red lines are two budgets, of $20 and $40).

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