An automobile owner reduced his monthly petrol consumption when the prices went up. The price-consumption relationship is as follows : Price (in ₹ per litre) 40 50 60 75 Monthly consumption (in litres) 60 48 40 32 If the price goes up to ₹ 80 per litre, his expected consumption (in litres) will be

(a) 30 ✓ UPSC's answer
(b) 28
(c) 26
(d) 24

Why the answer is (a)

• Calculate the price elasticity of demand (PED) using the midpoint method for the interval from ₹75 to ₹60: PED = [(40 - 32) / ((40 + 32) / 2)] / [(60 - 75) / ((60 + 75) / 2)] = (8 / 36) / (-15 / 67.5) = 0.2222 / -0.2222 = -1.

• The absolute value of the elasticity is 1, indicating unitary elastic demand in this range.

• Apply this elasticity to the next price increase from ₹75 to ₹80: Percentage change in price = (80 - 75) / ((80 + 75) / 2) = 5 / 77.5 ≈ 0.0645 (6.45%).

• Since |PED| = 1, the percentage change in quantity demanded is also approximately 6.45% (decrease).

• Calculate the new consumption: 32 litres * (1 - 0.0645) ≈ 29.92 litres, which rounds to 30 litres.

• Therefore, the expected consumption is 30 litres, corresponding to option (a).

Why the other options are wrong

(b) 28: 28 litres implies a higher elasticity than the observed unitary elasticity, resulting in an excessive drop in consumption.
(c) 26: 26 litres suggests a significantly higher price sensitivity that is not supported by the data points provided.
(d) 24: 24 litres represents a 25% drop in consumption, which is inconsistent with the calculated 6.45% price increase and unitary elasticity.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2015, held on 23 August 2015. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.