A consumer has an income of Rs 100. Good 1 costs Rs 10 and good 2 cos…

A consumer has an income of Rs 100. Good 1 costs Rs 10 and good 2 costs Rs 5.

A. If income rises to Rs 120 and the price of good 2 rises to Rs 6, the vertical intercept of the budget line does not change.

B. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the horizontal intercept does not change.

C. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the bundle (5, 10) is still affordable.

D. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the budget line becomes steeper.

Choose the correct answer from the options given below:

Answer & explanation

Correct answer: option 4

The correct answer is Option (4) → A and B only

The budget line has horizontal intercept M/p₁, vertical intercept M/p₂ and absolute slope p₁/p₂. At first, M = 100, p₁ = 10 and p₂ = 5.

A. If income rises to Rs 120 and the price of good 2 rises to Rs 6, the vertical intercept of the budget line does not change. — Correct. The vertical intercept is 100/5 = 20 before and 120/6 = 20 after. Income and p₂ rise by the same 20%, so it stays at 20.

B. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the horizontal intercept does not change. — Correct. The horizontal intercept is 100/10 = 10 before and 80/8 = 10 after.

C. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the bundle (5, 10) is still affordable. — Incorrect. The bundle now costs 8 × 5 + 5 × 10 = Rs 90. This is more than the new income of Rs 80.

D. If income falls to Rs 80 and the price of good 1 falls to Rs 8, the budget line becomes steeper. — Incorrect. The slope falls from 10/5 = 2 to 8/5 = 1.6. A fall in p₁ makes the line flatter; income does not affect the slope.

NCERT (2026-27): “2.2.1 Budget Set and Budget Line … The horizontal intercept represents the bundle that the consumer can buy if she spends her entire income on bananas. Similarly, the vertical intercept represents the bundle that the consumer can buy if she spends her entire income on mangoes. …”

“2.2.2 Changes in the Budget Set … If the price of bananas decreases, i.e., p’1< p1, the absolute value of the slope of the budget line decreases and hence, the budget line becomes flatter (it pivots outwards around the vertical intercept and horizontal intercept increases). …”