Tax Incidence

Friday, September 21, 2001

Dr. Schwab spoke briefly about the ideas of statutory and economic tax incidence and will get to something called tax shifting. First let's review the definitions we got in class:

The statutory incidence tells you which economic agent is legally responsible for paying the tax.
The economic incidence tells you the final distribution of the burden of a tax.
Tax shifting describes the difference between the statutory incidence and the economic incidence of a tax.

Take Dr. Schwab's example from class. Suppose gas costs $1. Now suppose a law is passed to tax each gallon of gas $0.30 when it is sold, to be paid by gas station owners. If the gas station owners can't raise the price, then they bear the full burden of the tax. Instead of getting $1 for each gallon of gas they sell, the gas station owner effectively gets $0.70 per gallon ($1 price minus the $0.30 paid in tax). Now suppose the gas station owners can raise the price to $1.30. Who bears the burden of the tax? The consumers, because for each gallon of gas the station owners are receiving $1 ($1.30 price minus the $0.30 paid in tax).

Per Unit Tax on Suppliers

Suppose we look at the market for food. This table of data is identical to the one from the purple book of Dr. Schwab's Powerpoint Slides on page 2 of Chapter 6. The first thing we will do is duplicate what was done in lecture.

Suppliers are willing to sell 24 units of food when they receive $13 per unit. When there is no tax on suppliers, this means they are willing to sell 24 units when the price paid by demanders is $13 per unit. When there is no tax, the price paid by demanders and the revenue received by suppliers are identical. Similarly, Suppliers are willing to sell 7 units of food when they receive $7 per unit of food. When there is no tax on suppliers, this means they are willing to sell 7 units of food when demanders pay a price of $7 per unit. This is the no-tax equilibrium: P=7, Q=12.

Suppose government passes a $2 per unit tax on food that is paid by the suppliers of food.

These guys would like to try and dodge having to pay the tax. The tax creates a gap between the price paid by demanders and the revenue received by suppliers. This is because the demanders pay the market price, but government steps in and takes the tax burden out of the suppliers' revenue.

After the tax is imposed on sellers, what happens to supplier willingness to sell? Let's look at the price $13 paid by demanders. When there was no tax, the sellers received the full $13 per unit and were willing to sell 24 units of food. However, now the government is taking $2 per sale out of the price paid by demanders. Thus, suppliers only end up with $11 of the $13 paid by demanders. How many units of food are producers willing to sell when they only receive $11? They will only sell 20 units of food when they end up with $11. So at P=13, suppliers are willing to sell less.

Price Paid by Demanders	Demand	Supply
13	1	24
12	2	22
11	4	20
10	6	18
9	8	16
8	10	14
7	12	12
6	14	10
5	16	8
4	18	6

Price Paid by Demanders	Demand	Old Supply	New Supply After $2 Tax
13	1	24	20
12	2	22	18
11	4	20	16
10	6	18	14
9	8	16	12
8	10	14	10
7	12	12	8
6	14	10	6

What happens is that at every price paid by demanders, suppliers are willing to sell less. This is the definition of a leftward shift of the supply curve. Of course, demand stayed the same, so now we have the same amount of demanders fighting over fewer units supplied at each price. What's the new equilibrium after the tax gets passed? It occurs at the intersection of the unchanged demand curve and the new leftward shifted post-tax supply curve. When we look at the table, this happens at P=8 and Q=10.

Now the 64 dollar question is: where did the economic incidence of the tax fall? Who actually bore the burden of the tax? In this food example, the equilibrium changed from P=7, Q=12 to P=8, Q=10. Two things happened here:

Price rose from 7 to 8. This makes demanders worse off because they pay higher prices for food. However, they did not bear the entire burden of the tax, because if that happened, we should have seen a price rise equal to the entire tax (remember Dr. Schwab's example with the gas station owners?) from 7 to 9.
Quantity fell from 12 to 10. The demanders did not bear the entire burden of the tax because the suppliers bear some of it in the form of lower sales. If the suppliers shifted the entire burden onto demanders, there would have been no drop in sales, only a rise in prices.

Per Unit Tax on Demanders

Suppose government passes a $2 per unit tax on food that is paid by the demanders of food.

Just like the suppliers, demanders would like to dodge having to pay this tax. The most obvious thing that will happen is that demanders will shift to untaxed substitutes. In the case of food, that kind of doesn't make sense. A story we could tell here is that maybe people were overeating before the tax and after the tax cut down to only eating enough to survive.

After the tax is imposed on demanders, what happens to demanders' willingness to buy food? Let's look at the price $11 paid by demanders. When there was no tax, the demanders paid just the $11 per unit price and were willing to buy 4 units of food. However, now the government is adding additional $2 tax to the price paid by demanders. Thus, when price is $11, the demanders must really pay $13 to cover the price and the tax charge. How many units of food are demanders willing to buy when they must pay $13? They will only buy 1 unit of food when they must pay $13. So at P=11, demanders are willing to buy less.

Price Paid by Demanders	Demand	Supply
13	1	24
12	2	22
11	4	20
10	6	18
9	8	16
8	10	14
7	12	12
6	14	10
5	16	8
4	18	6

Price Paid by Demanders	Old Demand	Supply	New Demand After $2 Tax
11	4	20	1
10	6	18	2
9	8	16	4
8	10	14	6
7	12	12	8
6	14	10	10
5	16	8	12
4	18	6	14

What happens is that at every price paid by demanders, demanders are willing to buy less. This is the definition of a leftward shift of the demand curve. Of course, supply stayed the same, so now we have the fewer demanders fighting over the same number of units supplied at each price. What's the new equilibrium after the tax gets passed? It occurs at the intersection of the unchanged supply curve and the new leftward shifted post-tax demand curve. When we look at the table, this happens at P=6 and Q=10.

Again, the 64 dollar question is: where did the economic incidence of the tax fall? Who actually bore the burden of the tax? In this second food example, the equilibrium changed from P=7, Q=12 to P=6, Q=10. Two things happened here:

Price fell from 7 to 6. This makes suppliers worse off because they get lower prices for food. However, they did not bear the entire burden of the tax, because if that happened, we should have seen a price drop equal to the entire tax from 7 to 5.
Quantity fell from 12 to 10. The suppliers did not bear the entire burden of the tax because the demanders bear some of it in the form of lower sales. If the demanders shifted the entire burden onto suppliers, there would have been no drop in sales, only a rise in prices. What's the difference from the tax on suppliers case? Here, food is cheaper, so demanders would have liked high quantity. In the tax on suppliers case, price went up so it was the suppliers, not the demanders, who wanted high quantity.

Okay, so the chain of events we have so far is this:

Government passes a law that taxes somebody.
- A tax can be on suppliers (producers) OR
- A tax can be on demanders (consumers)
Whoever is legally responsible for the tax will try to dodge the burden of the tax and push it onto somebody else. Whoever is trying to dodge the tax undergoes a curve shift.
- Taxed Suppliers will shift their supply curve left in hopes of raising the price and passing the tax onto demanders.
- Taxed Demanders will shift their demand curve left as they substitute away from the taxed good.
- Anyone who is untaxed will not shift their curve - only the party that has the statutory incidence will!
A new equilibrium is reached and tax shifting can be evaluated.