In a market, demand is q = 180 - 2p and supply is q = 4p - 60. What is the price elasticity of demand (in absolute value) at the equilibrium, and what happens to consumers’ total expenditure on the good if supply falls slightly?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0.8; total expenditure rises
Given:
Demand: q = 180 − 2p
Supply: q = 4p − 60
First find the equilibrium, then the elasticity there. Whether spending rises with price depends on whether demand is elastic or inelastic.
\( 180 - 2p = 4p - 60 \)
\( 6p = 240 \)
\( p = 40 \)
\( q = 180 - 80 = 100 \)
For a straight-line demand curve q = a − bp, the elasticity is |eD| = bp ÷ q. Here b = 2.
\( \displaystyle |e_D| = \frac{bp}{q} = \frac{2 \times 40}{100} = 0.8 \)
A fall in supply raises the price. Demand is inelastic (0.8 is less than 1), so quantity falls by a smaller percentage than price rises. Total expenditure therefore rises.
This question uses Market Equilibrium and Theory of Consumer Behaviour (elasticity and expenditure) together.
NCERT (2026-27): “Supply Shift Now, suppose due to some reason, the market supply curve shifts leftward to SS2 with the demand curve remaining unchanged, as shown in panel (a). Because of the shift, at the prevailing price, p0, there will be excess demand equal to 0 q’’ qo in the market. Some consumers who are unable to obtain the good will be willing to pay higher prices and the market price tends to increase. …” Theory of Consumer Behaviour: “2.6.3 Elasticity and Expenditure … On the other hand, if the percentage decline in quantity is less than the percentage increase in the price, the expenditure on … the good will go up …” |