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.
Solution
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
