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]
Quantity of Y | Quantity of X | MRS 5 | 1 | 5
4 | 2 | 2 3 | 3 | 1
2 | 4 | 0.5 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 consumer should consume Answer 1 Question 5[input] units of X and Answer 2 Question 5[input] units of Y.

Question

BlackTom AI · Accepted Answer

MRS equals the price ratio at an interior optimum, so set MRS = Px/Py to find the chosen bundle.

1) Relevant knowledge points and concepts
- Marginal Rate of Substitution (MRS) = MUx/MUy measures how many units of Y the consumer is willing to give up for one more unit of X (slope of the indifference curve).
- At an interior utility-maximizing point given prices, MRS = Px/Py (the slope of the indifference curve equals the slope of the budget line).
- Budget line slope (absolute value) = Px/Py. Here Px = $10, Py = $2, so Px/Py = 10/2 = 5.

2) Complete reasoning process step by step
- Compute the market trade-off between X and Y: Px/Py = 10/2 = 5.
- The optimal interior point on the given indifference curve must have MRS equal to 5.
- Look up the table of (Y, X, MRS) to find which row has MRS = 5.

3) Intermediate calculation steps
- Px/Py = 10 ÷ 2 = 5.
- Match MRS = 5 in the table: the row with MRS = 5 shows Quantity of X = 1 and Quantity of Y = 5.

4) Why the correct answer is correct
- Because at the bundle (X=1, Y=5) the consumer’s marginal willingness to trade Y for X (MRS = 5) exactly equals the market trade-off (Px/Py = 5), there is no profitable reallocation of spending between X and Y given prices. Thus that bundle is the utility-maximizing choice on that indifference curve.

5) Why the other options are incorrect
- Other table rows have MRS values 2, 1, 0.5, 0.2 which do not equal the price ratio 5. If MRS < Px/Py, the consumer values X less than the market requires and would want relatively more Y; if MRS > Px/Py, the consumer would want relatively more X. Only MRS = 5 satisfies the tangency condition.

6) Conclusion
The optimal consumption bundle is X = 1 unit and Y = 5 units, which matches the provided answer.

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