Separate the buyer price from the seller price.
A per-unit tax on sellers increases the buyer price needed for each quantity to be supplied. Draw supply vertically above its original position by the tax. With downward-sloping demand and upward-sloping supply, the resulting equilibrium has fewer units traded, a higher buyer price and a lower price retained by sellers after tax.
- Supply
- A per-unit seller tax is a charge for each unit sold. At any given quantity, sellers need a higher buyer price to pay the tax and retain the original amount. Supply measured at the buyer price shifts up by the tax.
- Prices
- The seller net price is the amount kept per unit after paying the tax, before other costs. Buyer price minus seller net price equals the tax per unit.
- Revenue
- Government tax revenue = tax per unit x actual quantity sold after the policy. Use the new sales quantity, which may be lower than before.
The tax amount and what it applies to
Specific tax
A specific tax is a fixed charge per unit sold. For example, if sellers previously needed $5 for a given quantity, a $2 tax means buyers must pay $7 for sellers to keep that $5. This compares the two supply curves at the same quantity; it does not say the final market price rises by the full tax.
Ad valorem tax
Ad valorem means a percentage of value. The tax base is the quantity or value to which a tax applies. Here the specified base is the seller price before tax: 20% of $10 is $2, giving a $12 buyer price; 20% of $20 is $4. The dollar gap varies, unlike a fixed $2 per-unit tax.
Tax revenue over time
For a per-unit tax, revenue is the tax per unit times taxable quantity sold. For an ad valorem tax, it is the percentage rate times the specified taxable sales value. A higher rate can shrink the tax base; a higher rate alone does not prove higher total revenue.
Worked example: A $2 tax on each bottle
Demand is P = 10 - 0.05 Q; supply is P = 2 + 0.05 Q. Price is dollars per bottle and Q is bottles per day.
- Before tax, set demand price equal to supply price: 10-0.05 Q=2+0.05 Q. This gives Q=80 and P=$6.
- Add $2 to the original supply price: the new buyer-price supply curve is P=4+0.05 Q. At the old $6 price, quantity supplied is 40 while demand is 80, creating upward price pressure.
- The new intersection is Q=60 and buyer price $7. The original supply curve at 60 gives seller net price $5.
- Buyers spend 7x 60=$420. Government collects 2x 60=$120; sellers retain 5x 60=$300.
Watch out for this
A $2 tax means the buyer price rises by exactly $2.
The tax is the gap between the buyer price and seller net price. Here that gap is $2, but the buyer price rises by $1.
Check your understanding
After a $3 per-unit tax, buyers pay $11 and 30 units trade. How much do sellers retain before other costs?
- $330
- $90
- $240