Question

Suppose there are two consumers in the market for a good and their demand functions are as follows:

d₁(p) = 20 − p for any price less than or equal to 20 and d₁(p) = 0 at any price greater than 20.

d₂(p) = 30 − 2p for any price less than or equal to 15 and d₁(p) = 0 at any price greater than 15.

Find out the market demand function.

Answer 1

d₁ (p) = 20 - p `{(p, £, 20),(p ,>,20):}`

d₂ ( p) = 30 - 2p  `{(p, £, 15),(p ,>,15):}`

For price less than Rs 15 (p≤ 15)

Market demand for a good = d₁ (p) + d₂ (p)

= 20 − p + 30 − 2p

= 50 − 3p

For price more than Rs 15 but less than Rs 20 (15 <p≤ 20)

Market demand = d₁(p) + d₂ (p)

= 20 − p + 0 (∵ for p > 15, d₂ (p) = 0)

= 20 − p

For price more than Rs 20 (p > 20)

Market demand = d₁(p) + d₂ (p)

= 0 + 0 (∵ for p > 10, d₁ (p) = 0, d₂ (p) = 0)

= 0

Thus, market demand

= 50 − 3p if p ≤ 15

=20 − p if 15 < p ≤ 20

= 0 if p > 20