Two consumers have the demand curves \( d_1(p) = 12 - 2p \) for prices up to 6 and \( d_2(p) = 8 - p \) for prices up to 8; each demand is zero at higher prices.
Statement I: At a price of 4, the market demand is 8 units.
Statement II: For any price between 6 and 8, the market demand is \( 8 - p \).
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Both Statement I and Statement II are true.
Market demand at a price is the sum of the two demands at that price. A consumer whose price limit is passed demands zero.
Statement I: At a price of 4, the market demand is 8 units. — True. d1(4) = 12 − 8 = 4 and d2(4) = 8 − 4 = 4, so the total is 8.
Statement II: For any price between 6 and 8, the market demand is \( 8 - p \). — True. Above 6, consumer 1 demands zero, so only consumer 2’s demand, 8 − p, is left.
NCERT (2026-27): “2.5 Market Demand … Thus, the market demand for the good at each price can be derived by adding up the demands of the two consumers at that price. …” “Adding up Two Linear Demand Curves Consider, for example, a market where there are two consumers and the demand curves of the two consumers are given as d1(p) = 10 – p (2.14) and d2(p) = 15 – p (2.15) Furthermore, at any price greater than 10, the consumer 1 demands 0 unit of the good, and similarly, at any price greater than 15, the consumer 2 demands 0 unit of the good. The market demand can be derived by adding equations (2.14) and (2.15). At any price less than or equal to 10, the market demand is given by 25 – 2p, for any price greater than 10, and less than or equal to 15, market demand is 15 – p, and at any price greater than 15, the market demand is 0.” |