Question

Suppose there are 20 consumers for a good and they have identical demand functions: 

D(p) = 10 − 3p for any price less than or equal to`10/3` and d₁(p) = 0 at any price greater than `10/3`.
What is the market demand function?

Answer 1

d(p) = 10 − 3p if p ≤ `10/3`

d₁ (p) = 0 if p >`10/3`

Market demand = Summation of demand of all the consumers in the market

For price ≤ `10/3` 

Market demand = 20 ∑d (p) ( ∵ Since consumers have identical demand curve)

= 20 × (10 − 3p)

= 200 − 60p

For price >  `10/3`  

Market demand = 20 × d₁(p)

= 20 × 0

= 0 

Market demand function = 200 - 60p `{("If", p, ≤ ,10/3 ) ,("If",p ,> ,10/3):}`

                                         = 0