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The demand for football tickets is Q = 360 â 10P and the supply of football tickets is Q= 20P. The government levies a per-ticket tax of $4, which is paid by consumers. Calculate the after-tax price paid by consumers. Calculate the gross price received by ticket sellers. What are consumerâs and producerâs tax burdens?

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Answer:

After tax price paid by consumers

Supply function n terms of price;

P = Q / 20

P = 0.05Q

Add the tax;

P = 0.05Q + 4

Demand function in terms of price is;

Q = 360 – 10P

P = (Q - 360) / -10

Price will be;

Demand = Supply

(Q - 360) / -10 = 0.05Q + 4

36 - 0.1Q = 0.05Q + 4

0.15Q = 32

Q = 213

After tax price = 36 - 0.1Q

= 36 - 0.1 * (213)

= $14.70

Gross price for ticket sellers is;

= Price - tax

= 14.7 - 4

= $10.70

Consumer and Producer tax burden.

Without tax, price is;

36 - 0.1Q = 0.05Q

0.15Q = 36

Q = 240

P = 36 - 0.1 * 240

= $12

Consumer tax burden = 14.70 - 12 = $2.70

Producer tax burden = Tax - consumer tax burden = 4 - 2.7 = $1.30