Two consumers have demand curves \( d_1(p) = 20 - p \) for any price up to 20 (zero above it) and \( d_2(p) = 30 - 2p \) for any price up to 15 (zero above it). What is the market demand at a price of 10 and at a price of 18?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 20 units and 2 units
Given:
d1(p) = 20 − p up to Rs 20, zero above
d2(p) = 30 − 2p up to Rs 15, zero above
Market demand at a price = the sum of the two demands at that price.
At p = 10: d1 = 20 − 10 = 10, d2 = 30 − 20 = 10
Market demand = 10 + 10 = 20 units
At p = 18: d1 = 20 − 18 = 2, d2 = 0 (price above 15)
Market demand = 2 + 0 = 2 units
Using 30 − 2p at Rs 18 would give a negative quantity; consumer 2 buys nothing there.
NCERT (2026-27): “2.5 Market Demand … The market demand for a good at a particular price is the total demand of all consumers taken together. The market demand for a good can be derived from the individual demand curves. Suppose there are only two consumers in the market for a good. Suppose at price p′, the demand of consumer 1 is q′1 and that of consumer 2 is q′2. Then, the market demand of the good at p′ is q′1 + q′2. … 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 … 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. …” |