1. The accompanying table shows five consumers’ willingness to pay for one can of diet soda each as well as five producers’ costs of selling one can of diet soda each. Each consumer buys at most one can of soda; each producer sells at most one can of soda. The government asks your advice about the effects of an excise tax of $0.40 per can of diet soda. Assume that there are no administrative costs from the tax.
| Consumer | Willingness to pay |
Producer | Cost |
| Ana | $0.70 | Zhang | $0.10 |
| Bernice | 0.60 | Yves | 0.20 |
| Chizuko | 0.50 | Xavier | 0.30 |
| Dagmar | 0.40 | Walter | 0.40 |
| Ella | 0.30 | Vern | 0.50 |
Without the excise tax, what is the equilibrium price and the equilibrium quantity of soda transacted?
Without the excise tax, Zhang, Yves, Xavier, and Walter sell, and Ana, Bernice, Chizuko, and Dagmar buy one can of soda each, at $0.40 per can. So the quantity bought and sold is 4.
The excise tax raises the price paid by consumers post-tax to $0.60 and lowers the price received by producers post-tax to $0.20. With the excise tax, what is the quantity of soda transacted?
At a price to consumers of $0.60, only Ana and Bernice are willing to buy a can of soda. At a price paid to producers of only $0.20, only Zhang and Yves are willing to sell. So the quantity bought and sold is 2.
Without the excise tax, how much individual consumer surplus does each of the consumers gain? How much with the tax? How much total consumer surplus is lost as a result of the tax?
Without the excise tax, Ana’s individual consumer surplus is $0.70 − $0.40 = $0.30, Bernice’s is $0.60 − $0.40 = $0.20, Chizuko’s is $0.50 − $0.40 = $0.10, and Dagmar’s is $0.40 − $0.40 = $0.00. Total consumer surplus is $0.30 + $0.20 + $0.10 + $0.00 = $0.60. With the tax, Ana’s individual consumer surplus is $0.70 −$0.60 = $0.10 and Bernice’s is $0.60 − $0.60 = $0.00. Total consumer surplus post-tax is $0.10 + $0.00 = $0.10. So the total consumer surplus lost because of the tax is $0.60 − $0.10 = $0.50.
Without the excise tax, how much individual producer surplus does each of the producers gain? How much with the tax? How much total producer surplus is lost as a result of the tax?
Without the excise tax, Zhang’s individual producer surplus is $0.40 − $0.10 = $0.30, Yves’s is $0.40 − $0.20 = $0.20, Xavier’s is $0.40 − $0.30 = $0.10, and Walter’s is $0.40 − $0.40 = $0.00. Total producer surplus is $0.30 + $0.20 + $0.10 + $0.00 = $0.60. With the tax, Zhang’s individual producer surplus is $0.20 − $0.10 = $0.10 and Yves’s is $0.20 − $0.20 = $0.00. Total producer surplus post-tax is $0.10 + $0.00 = $0.10. So the total producer surplus lost because of the tax is $0.60 − $0.10 = $0.50.
How much government revenue does the excise tax create?
With the tax, two cans of soda are sold, so the government tax revenue from this excise tax is 2 × $0.40 = $0.80.
What is the deadweight loss from the imposition of this excise tax?
Total surplus without the tax is $0.60 + $0.60 = $1.20. With the tax, total surplus is $0.10 + $0.10 = $0.20, and government tax revenue is $0.80. So deadweight loss from this excise tax is $1.20 − ($0.20 + $0.80) = $0.20.