Question

for a certain product, the demand curve is given by D(q) = 100e^-.008q and the supply curve is given by s(q) = 4 sqrt q + 10. At the equilibrium price, calculate the consumer surplus.

Answer 1

The consumer surplus is about $51.80.

Step-by-step explanation:

For a certain product, the demand curve is given by

`D(q)=100e^(-0.008q)`

The supply curve is given by

`S(q)=4√(q)+10`

Plot both curves on a coordinate plane.

At equilibrium situation,

Demand = Supply

It means at equilibrium demand and supply curves intersect each other.

From the below graph it is clear that intersection point of both curves is (91.218,48.203). It means equilibrium price is about $48.20.

Substitute q=0 in demand function to find the price the buyer is willing to pay.

`D(0)=100e^(-0.008(0))=100`

Formula for consumer surplus:

Consumer surplus = Price the buyer is willing to pay - Equilibrium price

Consumer surplus = $100 - $48.20

Consumer surplus = $51.80

Therefore the consumer surplus is about $51.80.