Question

Suppose the market for cau-hot-dogs is characterized by the following daily demand and supply curves. Drawing a diagram of the curves will help you find the right answers. Demand curve: P = 1300 - Q Supply curve: P = 180 + 9Q .Suppose the government requires the seller to pay 10% of the final price of a cau-hot-dog as an ad valorem tax.

1. What is the gross price of a cau-hot-dog in this case? What is the after-tax quantity of cau-hot-dog? How much is the price paid by the buyers for a cau-hot-dog in this case? How much will the seller receive for each sale of a cau-hot-dog in this case? Whose tax burden is greater in this case? How much is the total tax revenue for the government in this case?

3. If the government imposes a unit tax on the buyers instead of the ad-valorem tax on the sellers, how much should be the amount of tax per cau-hot-dog to raise the same amount of the total tax revenue?

4. If the government imposes the ad-valorem tax on the buyers instead of the seller, would the buyers bear a greater tax burden than the seller bears?

Answer 1

1. The after-tax supply would be or or . The demand is . Solving for both, we have (equating the demand price and after-tax supply price) or or . At this quantity, the price would be . The gross price (price paid by consumers) would be hence $1198.90. The after-tax quantity, as found would be 101.1009 units. The price paid by buyers would be the gross price $1198.90. The seller would receive $1089.91.

The pre-tax equilibrium would be as or or , and hence dollars. After the tax is imposed, the consumers pay 1198.90 - 1188 or $10.9 more than pre-tax, while the seller receive 1188 - 1089.91 or $98.09. Hence, the burden of tax is (about nine times) more for the sellers.

The total tax revenue would be tax per unit (0.10*1198.9=119.89) times the units sold (101.1009 units), ie $12120.99.

The graph is as below.

3. Imposing a unit tax of $T on the buyers would change the demand curve as or . The equilibrium quantity would be where or or , and the price paid would be . Of this amount, $T is paid to government. The government tax revenue would be the tax amount (T) times the quantity sold (112 - 0.1T), ie .

For the tax revenue be the same, we must have or , and the solution would be or or or . Hence, for a unit tax of either $121.38 or $998.62 on consumers, the government tax revenue would be same as before.

4. The ad-valorem tax on the buyers would be or . The supply would be the same as . Equating both, we have or or . This would be the price paid by consumers after-tax, and received by sellers. The tax paid per unit would be dollars.

The price paid by consumers is hence . The consumers would pay dollars more than before. The sellers would receive dollars, and hence, are receiving dollars less than before. Hence, the burden on sellers is still more.

The graph is as below.

The below graph compares both the demand and supply tax scenarios.

Note : It is to be noted that due to the rounding errors, the tax amount may change, but would not affect the answer significantly.