(APPX) Refer to the figure below. Given the existing budget line, the consumer maximizes utility:

Question

BlackTom AI · Accepted Answer

A consumer chooses the bundle where the budget line is tangent to the highest indifference curve the consumer can reach. At that tangency the marginal rate of substitution (MRS = slope of the indifference curve) equals the price ratio (slope of the budget line).

1) Relevant concepts
- Indifference curves represent combinations of two goods yielding the same utility; curves farther from the origin represent higher utility.
- The budget line shows all affordable combinations given prices and income.
- Utility is maximized at the tangency between the budget line and the highest attainable indifference curve, where MRS = price ratio.

2) Step‑by‑step reasoning
- Identify which indifference curves are attainable: any curve that intersects or touches the budget line is attainable; curves entirely above the budget line are unaffordable.
- Find the highest indifference curve that touches the budget line. The tangency point on that curve is the utility‑maximizing bundle because any other point on the same budget line lies on a lower indifference curve (lower utility), and any point on a higher indifference curve is unaffordable.
- In the figure the budget line is tangent to the indifference curve labeled C3 at point w. That means the slope of C3 equals the slope of the budget line at w (MRS = price ratio).

3) Calculational/graphical step
- No numeric prices are given, but the graphical condition is MRS (slope of indifference curve at the chosen bundle) = slope of budget line. This equality holds at w, indicating tangency and maximization.

4) Why the correct answer is correct
- Point w is the tangency between the budget line and the highest indifference curve the consumer can reach, so it yields the greatest utility consistent with the budget constraint.

5) Why the other options are incorrect
- Point b and point z lie on lower indifference curves (closer to the origin) and therefore represent lower utility than the tangency at w, even though they may be affordable.
- Point e lies on a higher indifference curve (C4) but does not lie on the budget line, so it is unaffordable and cannot be chosen given the budget.

6) Conclusion
- The consumer maximizes utility at point w. This matches the provided answer: at point w.

(APPX) Refer to the figure below. Given the existing budget line, the consumer maximizes utility: Single choice

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