A consumer has an income of Rs 48. Both the bundles (6, 4) and (5, 6) lie on her budget line, where the first number is good 1 and the second is good 2. What are the prices of the two goods?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Good 1 Rs 6, good 2 Rs 3
Every bundle on the budget line costs the whole income, M = p1x1 + p2x2.
Given:
Income = Rs 48
Bundles on the budget line: (6, 4) and (5, 6)
\( \displaystyle 6p_1 + 4p_2 = 48 \quad \text{and} \quad 5p_1 + 6p_2 = 48 \)
Both equal 48, so set them equal:
\( \displaystyle 6p_1 + 4p_2 = 5p_1 + 6p_2 \;\Rightarrow\; p_1 = 2p_2 \)
\( \displaystyle 6(2p_2) + 4p_2 = 48 \;\Rightarrow\; 16p_2 = 48 \)
\( \displaystyle p_2 = 48 / 16 = 3 \)
\( \displaystyle p_1 = 2 \times 3 = 6 \)
Check: 5 × 6 + 6 × 3 = 30 + 18 = 48
So good 1 costs Rs 6 and good 2 costs Rs 3.
Option (3) Good 1 Rs 4, good 2 Rs 6 — these prices fit (6, 4), as 24 + 24 = 48, but not (5, 6), as 20 + 36 = 56.
Option (4) Good 1 Rs 5, good 2 Rs 4.50 — these prices fit (6, 4), as 30 + 18 = 48, but not (5, 6), as 25 + 27 = 52.
NCERT (2026-27): “2.2.1 Budget Set and Budget Line If both the goods are perfectly divisible6, the consumer’s budget set would consist of all bundles (x1, x2) such that x1 and x2 are any numbers greater than or equal to 0 and p1x1 + p2x2 ≤ M. The budget set can be represented in a diagram as in Figure 2.9. All bundles in the positive quadrant which are on or below the line are included in the budget set. The equation of the line is p1x1 + p2x2 = M” “The line consists of all bundles which cost exactly equal to M. This line is called the budget line. …” |