The demand equation for a certain product is p = 400 - 2q,where p is the price per unit (in dollars)for q units.If its supply equation is p = q + 100,then the consumers' surplus when market equilibrium is established is
A) $9000.
B) $9500.
C) $10,000.
D) $10,500.
E) $11,000.

Question

Quizplus · Accepted Answer

To find the market equilibrium, we set the demand equation equal to the supply equation:
400 - 2q = q + 100
3q = 300
q = 100
Then we can find the equilibrium price by plugging q = 100 into either equation:
p = 400 - 2(100) = 200
p = 100 + 100 = 200
So the equilibrium price is $200 per unit.
To find the consumers' surplus, we need to integrate the demand equation from 0 to 100 units:
∫(400 - 2q) dq from 0 to 100
= [(400q - q^2)/2] from 0 to 100
= [20000 - 10000]/2
= $10,000
Therefore, the consumers' surplus when market equilibrium is established is $10,000.

The Demand Equation for a Certain Product Is P =