A consumer has an income of Rs 90. Bananas cost Rs 9 each and mangoes Rs 4 each. She buys 6 bananas and 9 mangoes. At this bundle she is willing to give up 2 mangoes for one more banana. Which of the following is correct?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → She can be better off by buying fewer bananas and more mangoes.
At the optimum, the rate at which she is willing to swap the goods (MRS) must equal the rate at which the market lets her swap them (the price ratio). Here the two rates differ.
Given:
Income = Rs 90
Price of bananas, p1 = Rs 9; price of mangoes, p2 = Rs 4
Bundle = 6 bananas and 9 mangoes
MRS = 2 mangoes for one banana
\( \displaystyle \text{Cost of the bundle} = 9 \times 6 + 4 \times 9 = 54 + 36 = 90 \)
\( \displaystyle \text{Price ratio} = \frac{p_1}{p_2} = \frac{9}{4} = 2.25 \)
Option (1) The bundle is her optimum, since it costs exactly her income. — Incorrect. Costing her whole income only puts the bundle on the budget line. The optimum also needs MRS = price ratio, and 2 is not 2.25.
Option (2) She can be better off by buying more bananas and fewer mangoes. — Incorrect. One more banana costs her 2.25 mangoes in the market, but she values it at only 2 mangoes. She would lose.
Option (3) She can be better off by buying fewer bananas and more mangoes. — Correct. Giving up one banana saves Rs 9, which buys 2.25 mangoes. She needs only 2 mangoes to stay as well off, so each swap leaves her 0.25 mango better off.
Option (4) She cannot afford this bundle with her income. — Incorrect. The bundle costs Rs 90, which is equal to her income.
NCERT (2026-27): “2.3 Optimal Choice of the Consumer 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 (MRS) and that of the budget line (price ratio) are same at that point. Recall from our earlier discussion that 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 MRS 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.” |