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