A consumer has Rs 30. Bananas cost Rs 5 each and mangoes Rs 10 each, and both are available only in whole units. How many bundles are in her budget set, and how many of them cost exactly Rs 30?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16 bundles; 4 cost exactly Rs 30
Given:
Income M = Rs 30
Price of bananas = Rs 5, price of mangoes = Rs 10, whole units only
The budget set is every bundle with 5x1 + 10x2 ≤ 30. Count the bundles for each number of mangoes.
0 mangoes: bananas 0 to 6, so 7 bundles
1 mango: bananas 0 to 4, so 5 bundles
2 mangoes: bananas 0 to 2, so 3 bundles
3 mangoes: bananas 0 only, so 1 bundle
Total = 7 + 5 + 3 + 1 = 16 bundles
The last bundle in each row costs Rs 30: (6, 0), (4, 1), (2, 2) and (0, 3). So 4 bundles cost exactly Rs 30; these lie on the budget line.
NCERT (2026-27): “EXAMPLE Consider, for example, a consumer who has Rs 20, and suppose, both the goods are priced at Rs 5 and are available only in integral units. The bundles that this consumer can afford to buy are: (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (1, 0), (1, 1), (1, 2), (1, 3), (2, 0), (2, 1), (2, 2), (3, 0), (3, 1) and (4, 0). Among these bundles, (0, 4), (1,3), (2, 2), (3, 1) and (4, 0) cost exactly Rs 20 and all the other bundles cost less than Rs 20. The consumer cannot afford to buy bundles like (3, 3) and (4, 5) because they cost more than Rs 20 at the prevailing prices.” “2.2.1 Budget Set and Budget Line … The inequality (2.1) is called the consumer’s budget constraint. The set of bundles available to the consumer is called the budget set. …” |