Read the passage carefully and answer the questions based on the passage:

Equality of the Marginal Rate of Substitution and the Ratio of the Prices

The optimum bundle of the consumer is located at the point where the budget line is tangent to one of the indifference curves. If the budget line is tangent to an indifference curve at a point, the absolute value of the slope of the indifference curve and that of the budget line are the same at that point. The slope of the indifference curve is the rate at which the consumer is willing to substitute one good for the other. The slope of the budget line is the rate at which the consumer is able to substitute one good for the other in the market. At the optimum, the two rates should be the same. To see why, consider a point where this is not so. Suppose the marginal rate of substitution at such a point is 2 and suppose the two goods have the same price. At this point, the consumer is willing to give up 2 mangoes if she is given an extra banana. But in the market, she can buy an extra banana if she gives up just 1 mango. Therefore, if she buys an extra banana, she can have more of both the goods compared to the bundle represented by the point, and hence, move to a preferred bundle. Thus, a point at which the MRS is greater, the price ratio cannot be the optimum. A similar argument holds for any point at which the MRS is less than the price ratio.

The optimum bundle of the consumer is located at the point where ................?

Budget line is tangent to one of the indifference curves.

The correct answer is Option (2) → Budget line is tangent to one of the indifference curves.

The optimal bundle for a consumer is the point where they achieve the highest possible satisfaction (utility) given their limited income. This occurs where the consumer's budget line is tangent to an indifference curve. At this tangency point, the rate at which the consumer is willing to substitute one good for another (Marginal Rate of Substitution, or MRS) is exactly equal to the rate at which the market allows them to do so (the price ratio of the two goods). In other words, the slope of the indifference curve is equal to the slope of the budget line. At any point other than this, the consumer can reallocate their spending to reach a higher level of satisfaction.