Question

Demand: QD = 100 - 2p Supply: QS = 3p

If government imposes a 10% ad valorem tax to be collected from sellers, what is the price consumers will pay? How much tax revenue is collected?

Answer 1

ANSWER:

Qs = 3p

p = Qs / 3

sellers recieve price + 10% tax = (1 + 10%) * Q / 3 = 1.1Q / 3

now substituting the price in demand we get:

Q = 100 - 2p = 100 - 2 * (1.1q / 3) = 100 - 2.2q / 3

q = 100 - (2.2q / 3)

q + 2.2q / 3 = 100

5.2q / 3 = 100

5.2q = 300

q = 300 / 5.2 = 57.69

solving for price + tax we get

100 - 2p = q

100 - 2p = 57.69

100 - 57.69 = 2p

42.31 = 2p

p + tax= 42.31 / 2

p + tax = 21.15

p + 10% = 21.15

p = 21.15 / 10%

p = 19.23

tax revenue = (21.15 - 19.23) * 57.69 = 110.76

price paid by consumers is 21.15