The figure shows Karim’s budget constraint, or feasibility frontier, on the same graph as Karim’s indifference curves. Based on this information, read the following statements and select the correct one(s).

Question

BlackTom AI · Accepted Answer

At the utility-maximizing choice, the consumer attains the highest attainable indifference curve consistent with the budget — this occurs where a convex indifference curve is tangent to the budget line. Point E is shown as that tangency and therefore is the most likely choice.

1. Relevant knowledge points and concepts
- Budget constraint (feasibility frontier): all bundles affordable given prices and income; feasible choices lie on or below this line.  
- Indifference curves: represent combinations giving the same utility; they are convex to the origin when marginal rate of substitution (MRS) diminishes.  
- Utility maximization condition: with an interior solution, the optimal bundle is where the budget line is tangent to the highest reachable indifference curve, i.e., MRS = price ratio (slope of indifference curve = slope of budget line).

2. Step-by-step reasoning
- Identify feasible region: all points on or under the budget line.  
- Rank indifference curves: curves farther from the origin represent higher utility.  
- Find the highest indifference curve that still touches the feasible region. If one of the indifference curves is tangent to the budget line, that tangency is the interior optimum. The figure places such a tangency at E.

3. Intermediate logical steps (no numerical calculation required)
- At E the indifference curve is convex and touches the budget line without crossing it → E is feasible and on the highest attainable indifference curve.  
- Tangency implies MRS = price ratio, satisfying the first-order condition for an interior maximum.

4. Why the correct answer is correct
- Because E is feasible and lies on the highest indifference curve reachable given the budget, and convexity ensures uniqueness, E is the utility-maximizing choice.

5. Why other options are incorrect
- Option 2: “All points A through E are possible choices, but E represents the best choice if Karim is maximizing his consumption.” Incorrect because consumers maximize utility, not raw “consumption”; also not all points give the same utility—only E lies on the highest attainable indifference curve.  
- Option 3: “Points B and D are better than point E as Consumption is higher and thus utility is higher.” Incorrect because having more of one good does not guarantee higher overall utility if utility depends on both goods; B and D lie on lower indifference curves (or are not the tangency), so utility is not higher.

6. Conclusion
Therefore the correct statement is: Point E represents the most likely choice as this represents a point that is both feasible and on an indifference curve that is convex to the origin. This matches the provided answer.

The figure shows Karim’s budget constraint, or feasibility frontier, on the same graph as Karim’s indifference curves. Based on this information, read the following statements and select the correct one(s). 多项选择题

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