Use the graph below to answer the questions that follow.Basic Indifference Curve If the slope of the indifference curve at C is 3, then

Question

BlackTom AI · Accepted Answer

At the tangency between an indifference curve and a budget line the marginal rate of substitution equals the price ratio: MRS = p_x / p_y.

1) Relevant concepts
- Slope of an indifference curve (IC) at a point is related to the marginal rate of substitution (MRS). Conventionally MRS = MU_x / MU_y and equals the absolute value of the slope of the IC (since the IC slopes downward).
- The budget line slope is -p_x / p_y (change in y per unit change in x given prices).
- At a utility-maximizing tangency, the slope of the IC equals the slope of the budget line in magnitude, so MRS = p_x / p_y.

2) Step-by-step reasoning
- Let the slope of the IC at C be s. Because ICs slope downward, the mathematical slope dy/dx = -s; the absolute slope (MRS) is s.
- The budget line slope is -p_x/p_y. For tangency (consumer is optimizing at C), the magnitudes must match: s = p_x / p_y.
- The problem states the slope of the indifference curve at C is 3 (interpreted as the magnitude/MRS = 3). Therefore p_x / p_y = 3.

3) Intermediate steps / equations
- dy/dx|IC = -MRS
- Budget slope = -p_x/p_y
- Tangency: -MRS = -p_x/p_y => MRS = p_x/p_y
- Given MRS = 3 => p_x/p_y = 3

4) Why the correct answer is correct
Because at the tangency the consumer equates marginal willingness to trade (MRS) with the market trade-off between goods (price ratio). If the IC’s slope (MRS) is 3, the market price trade-off must also be 3.

5) Why other choices are incorrect
- “The price of x is $3”: you cannot infer an absolute price level from the slope alone; the slope gives only the ratio p_x/p_y.
- “The price of y is $3”: same reasoning—slope provides a ratio, not an individual price.
- “p_x/p_y is 0.33”: this is the reciprocal; it contradicts the given slope of 3.

6) Conclusion
Therefore the price of x divided by the price of y equals 3, which matches the provided answer.

Use the graph below to answer the questions that follow.Basic Indifference Curve If the slope of the indifference curve at C is 3, then单项选择题

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