Question

The demand curve for tickets to concert is given as follows: Q = 20 - P. If the price falls from €5 to €3, what is the change in consumer surplus from concert tickets?

an increase of €32

an increase of €225

an increase of €176.50

an increase of €112.50

which is correct ?

Answer 1

The given demand function is

Q = 20 - P

Consumer surplus is the difference between maximum price willing to pay by the consumers and the actual market price. It is the area below the demand curve.

The maximum price willing to pay is the price when quantity demanded is zero

0 = 20 - P

P = 20

The maximum price willing to pay = 20

Consumer surplus when price is 5

​​​​The difference between maximum price and actual price = 20 - 5 = 15

Quantity demanded when price is 3 = 20 -P

= 20 - 5 = 15

Demand = 15

Consumer surplus when price is 5 = (1/2) * 15 *15 = 112.5

Consumer surplus when price is 3

The difference between maximum price and actual price = 20 - 3 = 17

Demand when price is 3 = 20 - 3 = 17

Consumer surplus when price is 3 = (1/2) * 17 *17 = 144.5

Change in consumer surplus = 144.5 -112.5 = 32

Correct answer : An increase of 32