This question has been regraded.

Suppose that basket B (x = 5, y = 10) is on Matt's linear budget line, Matt's MRSX,Y (B) = 1/4, PX =$2 and PY = $2. Matt's preferences are represented by smooth curves.

Question

This question has been regraded.

Suppose that basket B (x = 5, y = 10) is on Matt's linear budget line, Matt's MRSX,Y (B) = 1/4, PX =$2 and PY = $2.  Matt's preferences are represented by smooth curves.

BlackTom AI · Accepted Answer

The question presents a linear budget line and a registered MRS along with prices. To analyze, we first restate the key facts: the budget line satisfies 2x + 2y = income, so given a point on the line with x = 5 and y = 10, income must be 30. The budget slope (in x-y terms) is -Px/Py = -2/2 = -1. The marginal rate of substitution at B is MRS_XY(B) = 1/4, which implies the slope of the indifference curve at B is -MRS = -1/4.

Now, compare the MRS to the price ratio Px/Py. We have MRS = 1/4 and Px/Py = 1. Since 1/4 < 1, the consumer values y relatively more than x compared to their prices; in other words, the consumer would prefer to give up x to obtain more y less eagerly than the market would require. On a linear budget, when the MRS is not equal to the price ratio, the optimum occurs at a corner of the budget set rather than at a tangency interior point.

Because MRS_XY < Px/Py, the consumer would optimally spend all income on the good with the relatively higher marginal utility per dollar in this comparison, which is good y in this case. Therefore the optimal bundle lies at the y-rich corner, i.e., x = 0 and y = 15 (since 2x + 2y = 30). This corner is located to the North-West of the current point B (x = 5, y = 10), because NW means increasing y and decreasing x.

Thus, the assertion that B cannot be Matt's optimal choice and that his optimal choice will be to the North West of B is consistent with the standard rule when MRS < Px/Py on a linear budget: move toward the corner with more of the good for which you value more relative to its price, which, in this setup, is y. If there were other options listed, we would evaluate them against the same criteria, but since the only given statement is that NW position is the optimal direction, the reasoning above supports that conclusion.

To summarize in a different light: the interior tangency condition MRS = Px/Py is not satisfied here (1/4 ≠ 1), so an interior optimum cannot occur on the budget line. The correct adjustment is toward the corner that emphasizes y, i.e., NW of B, which aligns with the provided claim.

This question has been regraded. Suppose that basket B (x = 5, y = 10) is on Matt's linear budget line, Matt's MRSX,Y (B) = 1/4, PX =$2 and PY = $2. Matt's preferences are represented by smooth curves.单项选择题

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