Question

The inverse demand function for video games is p = 240 ? 2q and the inverse supply function is p = 3 + q. The government imposes a $6 tax on each video game purchased. a) Find CS and PS before tax

b. Find CS and PS after tax

c. Does the CS fall by more than the PS or not?

(SHOW THE PROOF USING VALUES OF ELASTICITES OF DEMAND AND SUPPLY)

Answer 1

Solution : Equating demand and supply :

240-2Q = 3+ q

240-3 = 3Q

237/3 = Q

Q = 79

And P= 3 + 79 =82.

Let us draw the demand and the supply curve :

Producer surplus : The area below the price line and above the supply curve :

1/2 * (82-3) * 79 = 3120.5

Consumer surplus = : The area above the price line and below the demand curve :

1/2 *( 240-82) * 79 = 6241.

Now if a tax of 6 $ is imposed then :

Supply will shift upward by the amount of tax : and supply curve will be

P=3+ q+ 6

p= 9 +q

Now equate demand with the supply :

240-2q = 9+q

231=3q

q =77.

P =9+77 = 86

Now the diagram will be :

COnsumer surplus = (240 -86) * 77 * 1/2 = 5929

Producer surplus =( 86-9) *1/2 * 77 = 2964.5

Change in consumer surplus = 6241 -5929 = 312

change in producer surplus = 3120.5 -2964.5 = 156.

yes the fall in the consumer surplus is more than the change in producer surplus .

Let us see this by using elasticity :

= -2

=-1/2

elasticity of demand = -1/2 * 82/79 = - 0.51

elasticity of supply = * P/Q = 1 * 82/79 = 1.03

the elasticity of supply is higher than the elasticity of demand this implies that loss in the consumer surplus will be higher than the loss in the producer surplus .