Regarding indifference curves in consumer theory, which of the following statements are correct?

Introduction / Context:
Indifference curves are an important tool in modern microeconomics for analyzing consumer preferences and choices. Each indifference curve represents combinations of two goods that give a consumer the same level of satisfaction. This question lists three statements about indifference curves and asks which are correct. You must recall both the shape and properties of indifference curves and the rule that they cannot intersect if preferences are consistent.

Given Data / Assumptions:

• Statement 1: Indifference curves are convex to the origin.
• Statement 2: A higher indifference curve represents a higher level of satisfaction.
• Statement 3: Two indifference curves cut each other.
• Consumer is rational, with consistent and transitive preferences.

Concept / Approach:
Under usual assumptions, indifference curves are downward sloping and convex to the origin because of diminishing marginal rate of substitution. Convexity reflects a preference for balanced bundles over extreme ones. A higher indifference curve means that at least one good is in greater quantity while the other is not less, so it represents a higher utility level. Indifference curves for a given consumer cannot intersect; if they did, it would violate the transitivity and consistency of preferences, because one point would then appear to provide both higher and lower satisfaction at the same time.

Step-by-Step Solution:
Step 1: Evaluate Statement 1. Indifference curves are generally convex to the origin due to diminishing marginal rate of substitution, so Statement 1 is correct. Step 2: Evaluate Statement 2. A higher indifference curve is further from the origin and reflects a bundle with more of at least one good without less of the other, so it represents a higher satisfaction level. Statement 2 is correct. Step 3: Evaluate Statement 3. If two indifference curves intersected, the common point would have the same satisfaction as two different curves which represent different satisfaction levels, which is inconsistent. Therefore, Statement 3 is incorrect. Step 4: Combine the results. Only Statements 1 and 2 are correct, so the correct choice is “1 and 2”.

Verification / Alternative check:
You can visualize typical indifference curves in the quantity of good X on the horizontal axis and quantity of good Y on the vertical axis. For a rational consumer, higher curves are outward and to the right of lower curves. If you try to draw two curves that intersect, you will find that the assumption that more of a good is preferred to less is violated at some points, confirming that intersection is not allowed. This supports the conclusion that only the first two statements are correct.

Why Other Options Are Wrong:
1 only: This ignores the fact that higher indifference curves do represent higher satisfaction, so it is incomplete.
2 and 3: This incorrectly assumes that indifference curves can cut each other, which contradicts basic theory.
3 only: This is clearly wrong, because the third statement itself is incorrect and the first two are correct.

Common Pitfalls:
One common mistake is to forget the rule that higher indifference curves imply higher utility and to treat all curves as equivalent. Another pitfall is to think that curves can intersect like simple graphs, ignoring the implications for preference consistency. Remember that the entire indifference curve represents the same satisfaction level, and curves for different levels must never cross if the consumer is rational and preferences are transitive.

Final Answer:
The correct combination is that Statements 1 and 2 are true, while Statement 3 is false, so the answer is “1 and 2”.