Question

Part I. Partial Equilibrium Tax Incidence under Competition 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
1. What is the market equilibrium quantity of a cau-hot-dog?
2. What is the market equilibrium price of a cau-hot-dog? Suppose the government requires the seller to pay 10% of the final price of a cau-hot-dog as an ad valorem tax.  
3. What is the gross price of a cau-hot-dog in this case?
4. What is the after-tax quantity of cau-hot-dog?
5. How much is the price paid by the buyers for a cau-hot-dog in this case?
6. How much will the seller receive for each sale of a cau-hot-dog in this case?
7. Whose tax burden is greater in this case?
8. How much is the total tax revenue for the government in this case?
9. 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?
10. 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. Demand = Supply,

So,1300-Q=180+9Q

=>1300-180=9Q+Q

=>1120=10Q

=> Q= 1120/10=112

So, market equilibrium of quantity = 112.

2. Price => 1300-Q= 1300-112= 1188

So, market equilibrium price of cau hot dog is 1188

Govt requires seller to pay 10% as ad-valorem tax so, tax= 118.8

3. So, price after tax = 1188-118.8=1069.20

4. After tax quantity of cau-hot -dog =

=> 1069.20=1300-Q

=> Q= 1300-1069.20 = 230.8

So, It round figure quantity = 230 units of cau-hot-dogs