Question #54938

1. There is a fruit seller who has 30 Kgs of apples to be sold and he wants to fix a price so that all the apples are sold. There are three customers in the market and their individual demand functions are given below:
D1=25-.05P
D2=20-.025P
D3=15-.075P
Where D is the demand and P is the price
Determine :
Market demand equation for the fruit seller
Price at which he can sell all the apples
Individual demands of each of the three customers

Expert's answer

Market demand (D) equation for the fruit seller:

D=D1+D2+D3=25-0.05*P+20-0.025*P+15-0.075*P => D=60-0.15*P

Price at which apples will be sold:

Total quantity of apples = 30 => 30=60-0.15*P => P=200 (for price equal to 200 all the apples will be sold).

Individeal demands of each of three customers:

D1=25-0.05*200=15 => D1=15

D2=20-0.025*200=15 => D2=15

D3=15-0.075*200=0 => D3=0

So, D=D1+D2+D3=15+15+0=30 => all apples are sold

D=D1+D2+D3=25-0.05*P+20-0.025*P+15-0.075*P => D=60-0.15*P

Price at which apples will be sold:

Total quantity of apples = 30 => 30=60-0.15*P => P=200 (for price equal to 200 all the apples will be sold).

Individeal demands of each of three customers:

D1=25-0.05*200=15 => D1=15

D2=20-0.025*200=15 => D2=15

D3=15-0.075*200=0 => D3=0

So, D=D1+D2+D3=15+15+0=30 => all apples are sold

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