A consumer has an income of Rs 100. Good 1 costs Rs 5 and good 2 costs Rs 10, and she buys the bundle (10, 5). The price of good 1 rises to Rs 6. By how much must her income rise so that she can still just buy (10, 5), and what is then the absolute slope of her budget line?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 10; 0.6
Her income must cover the new cost of the same bundle. The absolute slope of the budget line is p1/p2, so it depends only on the prices.
Given:
Income = Rs 100
p1: Rs 5 → Rs 6; p2 = Rs 10
Bundle = (10, 5)
\( \displaystyle \text{New cost} = 6 \times 10 + 10 \times 5 = 60 + 50 = 110 \)
\( \displaystyle \text{Rise in income} = 110 - 100 = 10 \)
\( \displaystyle \text{Absolute slope} = \frac{p_1}{p_2} = \frac{6}{10} = 0.6 \)
Income must rise by Rs 10, and the slope becomes 0.6.
Option (1) Rs 10; 0.5 — 0.5 is the old slope (5/10). The extra income shifts the line out but does not change its slope.
NCERT (2026-27): “2.2.2 Changes in the Budget Set Note that the slope of the new budget line is the same as the slope of the budget line prior to the change in the consumer’s income. However, the vertical intercept has changed after the change in income. …” “… If the price of bananas increases, ie if p’1> p1, the absolute value of the slope of the budget line increases, and the budget line becomes steeper (it pivots inwards around the vertical intercept and horizontal intercept decreases). …” |