Question textConsider the following table. It provides you with the Marginal Rate of Substitution between two goods. These values describe the consumer's indifference curve. [table]
Choice | Quantity of X | Quantity of Y | MRS a | 1 | 5 | 5
b | | 2 | 2 c | | | 1 d | 2 | | 0.5 e | 1 | 5 | 0.2
[/table] Suppose the Price of X is $10 and the Price of Y is $2. The consumer's income is sufficient to reach only the optimal consumption point on this indifference curve. Given these prices, the utility maximising consumer should choose the bundle Answer 1 Question 3[select: , a, b, c, d, e].

Question

Question textConsider the following table. It provides you with the Marginal Rate of Substitution between two goods. These values describe the consumer's indifference curve. [table]
Choice | Quantity of X | Quantity of Y | MRS a | 1 | 5 | 5
b |  | 2 | 2 c | |  | 1 d | 2 | | 0.5 e | 1 | 5 | 0.2
[/table] Suppose the Price of X is $10 and the Price of Y is $2. The consumer's income is sufficient to reach only the optimal consumption point on this indifference curve. Given these prices, the utility maximising consumer should choose the bundle Answer 1 Question 3[select: , a, b, c, d, e].

BlackTom AI · Accepted Answer

At an interior utility-maximizing bundle the marginal rate of substitution equals the price ratio: MRS = Px / Py.

1) Relevant knowledge points and concepts
- MRS (marginal rate of substitution) = MUx / MUy measures how many units of Y the consumer will trade for one unit of X while remaining on the same indifference curve.
- The tangency (first-order) condition for an interior optimum is MRS = Px / Py. If this equality cannot be met, a corner solution may occur.
- Here Px = $10 and Py = $2, so the relevant price ratio is Px/Py = 10/2.

2) Step-by-step reasoning
- Compute the market price ratio:
  Px / Py = 10 / 2 = 5.
- Compare this to the MRS values given for each bundle:
  a: MRS = 5
  b: MRS = 2
  c: MRS = 1
  d: MRS = 0.5
  e: MRS = 0.2

3) Intermediate calculation steps
- Px/Py calculation shown explicitly: 10 ÷ 2 = 5.
- Check equality: For bundle a, MRS (5) = Px/Py (5) — exact match.
- For bundles b–e, MRS < Px/Py (2 < 5, 1 < 5, 0.5 < 5, 0.2 < 5).

4) Why the correct answer is correct
- The tangency condition requires MRS = Px/Py. Only bundle a satisfies MRS = 5 which equals the market price ratio 10/2. Therefore the indifference curve is tangent to the budget line at bundle a, making it the utility-maximizing choice given these prices (and given income sufficient to reach that point).

5) Why the other options are incorrect
- Bundles b–e have MRS strictly less than the price ratio. That means the consumer values an extra X less relative to Y than the market requires (they would not be willing to give up enough Y for X at the market terms), so these points are not tangency optima. If the consumer were at any of those points, they would want to move away (purchase less Y and more X) until MRS rises to the price ratio; since only a meets equality, b–e are suboptimal.

6) Conclusion
- The utility-maximising consumer should choose bundle a. This matches the provided correct answer: a.

类似问题

Consider the indifference curves below and answer the following questionsGraph 1c At point E on U1 the MRS is

Consider the indifference curves below and answer the following questionsGraph 1c At point E on U1 the MRS is

Consider the following indifference curves and answer the questions that follow:Indifference Curves 1d Suppose the consumer is on the highest budget constraint. The consumer is currently consuming at point E. In order to maximise their utility they should

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

The figure shows the indifference curves of a student for the two ‘goods’, free time and final grade. Based on this information, read the following statements and select the correct one(s).

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单