Question

Suppose that the market demand curve for residential water is:

Q

D

= 10 – 2.25

P

and the market supply curve is:

Q

S

= –10 + 2.75

P

where the quantity is measured in millions of gallons per month and the price is in dollars

per thousand gallons.

a. Calculate the equilibrium price and quantity.

b. Calculate the consumer surplus at the equilibrium price

Answer 1

a. At equilibrium, demand equals supply.

So, at the equilibrium,

10 – 2.25P = –10 + 2.75P

or, – 2.25P - 2.75P = -10 - 10

or, -5P = -20

or, P = -20/-5 = 4 dollars

Putting the value of P in demand equation, we get

Demand = 10 - 2.25P = 10 - 2.25*4 = 10 - 9 = 1 million dollars.

b. Consumer surplus is the difference between the maximum price a consumer is willing to pay and the price actually paid by the consumer.

Let us first calculate the maximum price the consumer is willing to pay. At this price, demand will be 0.

10 – 2.25P = 0

or, 2.25 P = 10

or P = 10/2.25 = 4.44

Consumer surplus is given triangular area between the price line and the demand curve. The area of the triangle - 1/2 * base * height = 1/2 * equilibrium quantity * maximum willingness to pay = 1/2 * 1 * 4.44 = 2.22 millions dollars.