XVII. THE INCIDENCE AND DEADWEIGHT LOSS (WELFARE LOSS) OF EXCISE TAXES: NORMATIVE ANALYSIS OF SUPPLY AND DEMAND
A. Introduction
Here we use perunit based taxes for example purposes, but the basic analysis holds for other taxes, as well. When a tax is passed by the legislature or Congress, they specify from whom the tax will be collected. We know that the party who is responsible for paying the tax to the government, usually the seller, is not always the one who really pays the tax, sometimes that party is able to pass the tax along to the consumer. Our study of the incidence of a tax enables us to analyze to what extent sellers can pass a tax along to buyers in terms of higher prices. The incidence of a tax, then, refers to the party, the buyer or the seller, who pays the tax, through higher prices paid or through lower prices received. Welfare effects of taxes are also examined here using consumer and producer surplus analysis.
Usually, as we shall see, the incidence is shared by the buyers and the sellers. The buyers pay a higher price after the tax than before, but the price rises by less than the tax. If the price paid by the buyers rises by less than the increase in the tax, the sellers will receive a lower price, net of taxes paid, than they got before the tax was imposed. After examining the incidence of the tax, we will turn to an examination of the welfare effects of taxation.
Before looking at the welfare effects and incidence of excise taxes, let's see how they affect the buyers and sellers in a market and the equilibrium prices and quantities in markets. When an excise tax is levied, there will be a difference between the price the buyer pays and the price the seller receives. This difference is the amount of the tax. For example, an excise tax is levied on cartons of cigarettes to the tune of $1.00 per carton ($0.10 per pack, a modest tax). If the seller is receiving $5.00, net of taxes, then the buyer must be paying $6.00 per carton. This will be true whether the tax is collected from the buyer or from the seller.
Take a look at FIGURE IX. Before any tax is levied, the demand curve is D1 and the supply curve is S1. The consumer surplus is the area of the triangle from $10.50 to the equilibrium price of $5.50 with a base of 100 cartons per day, or $250 (1/2 base times height) per day. The producer surplus here is the area of the triangle from $.50 to $5.50 with a base of 100 cartons per day, also $250. The total surplus is $500 per day.
After a tax of $1.00 per carton is levied, the supply curve facing the buyers is St, and so the new equilibrium price and quantity are $6.00 and 90 cartons, respectively. The new consumer surplus is the area of the triangle from $10.50 to $6.00, with a base of 90 cartons, or $202.50. The new producer surplus can be seen as either the triangle from $.50 to $5.00 with a base of 90 cartons per day or from $1.50 to $6.00 with a base of 90 cartons per day, in either case, the producer surplus is also $202.50 per day. There are 90 cartons of cigarettes sold per day with a tax of $1.00 per carton, so the government is collecting $90 per day in taxes.
Producer and consumer surplus now totals $405, with $90 going
to the government. What happened to the other $5 in surplus?
Neither the producers, the consumers, nor the government gets
that surplus, because the units upon which that original $500
surplus was made are not all still being traded. Consumer
and producer surplus are gains to buyers and sellers from trade.
Since fewer units are now being traded there will be less surplus.
The $5 surplus is lost to society. No one makes those gains
because those units are not traded.
We can also see that of the $90 made by the government, $45 came from buyers who now pay $.50 more per carton than they did without the tax, $45 dollars came from sellers who received $.50 less per carton (after taxes). We see that in the case given true burden of the tax, the incidence of the tax, falls equally on buyers and sellers, because the sellers can only pass half of the tax increase along to the buyers.
Three propositions will be proven about tax incidence: 1)
the incidence of a tax is independent of party that is responsible
to pay the tax; 2) the incidence of the tax will fall more
heavily on the buyer, the less elastic the demand; and 3) the
incidence of the tax will be shifted more to the buyer the less
elastic the supply. It will also be shown that the more
elastic the demand curve, the lower the revenues from a given
tax and the higher the deadweight loss and that the more elastic
the supply curve, the lower the revenues to the government and
the higher the deadweight loss.
B. The incidence of the tax is the same, no matter which party pays the tax
When the tax is collected from the seller, how will a dollar tax on a carton of cigarettes affect the market for cigarettes? In FIGURE IX, the market is initially at equilibrium at a price of $5.50 with 100 cartons per day being purchased. With the sellers responsible for paying the tax, there will be two supply curves relevant: the original supply curve, S1, and the supply curve after taxes, St, which is S1 plus the tax of $1.00 per carton. The supply curve, S1, tells us the price that the sellers must receive in order to induce them to bring a particular quantity to the market. The supply curve, St, tells us the price buyers must pay (including tax) for the sellers to bring a certain quantity to the market. A dollar excise tax will reduce the equilibrium quantity to 90 cartons per week, increase the price the buyers pay to $6.00, and reduce the price that the sellers receive to $5.00.
If the tax were to be collected from the buyers instead of the
sellers, there would be no change in supply curve, S1,
but now there would be two relevant demand curves, D1,
the original demand curve, and Dt, which is D1
minus the dollar per carton tax, as we see in FIGURE X.
The demand curve Dt shows the price that the sellers
receive from the buyers for a particular quantity, if the buyers
are also paying the government a $1.00 tax per carton. Notice
that the price paid by the buyer is once again $6.00 and the price
received by the seller is $5.00 with the difference going to the
government in tax revenues. It doesn't matter which party
pays the tax, the incidence will be the same.
C. Elasticity of demand, tax incidence, tax revenues and
deadweight loss
Since it does not matter which party the tax is collected from,
let us assume that the tax will be collected from the sellers,
as this will keep our diagram as uncluttered as possible.
In FIGURE XI the original supply curve is S1, where
the original equilibrium price and quantity are $5.50 and 100
per week, respectively. The supply curve St is
the supply curve as the buyers see it, after the tax is imposed.
If the demand were D1, a perfectly elastic demand,
the buyers' price would still be $5.50 after the tax, but only
cartons would be purchased. The sellers now receive
only $4.50 per carton, as the buyers will pay no more than a total
of $5.50 per carton, tax and all. The sellers bear the full
burden of the tax, receiving a dollar less per carton than before.
The tax is not shifted to the buyers at all.
If the demand were less elastic, as with D2, we see that the new price paid by the buyers will be $6.00 per carton, only $.50 higher than the original price. The sellers receive a price of $5.00, a dollar less than the buyers pay, which is $.50 more than they would have been paid with demand D1 with the dollar tax. Some of the tax is paid by the buyers in a higher price, but the sellers still pay most of the tax.
If the demand were completely inelastic, as in the case with demand curve D3, the price the buyers pay will be $6.50, a dollar higher than the original price. The sellers receive the original price of $5.50. The incidence of the tax is borne completely by the buyers.
Notice that the tax revenue rectangles are all of the same height, the tax is always $1.00 in the case above. What should be noted is that with the most elastic demand curve, D1, the smallest quantity of cigarettes is traded, only 80 cartons per day. More is traded with D2 (90 cartons) and there is no diminution of demand with the perfectly inelastic demand curve, D3. With D1, the government gets $80 per day, with D2, $90, and with D3, $100.
Let us now look at the deadweight loss of the tax, also called the excess burden of the tax, and the welfare loss triangle with the three demand curves. With D1, the deadweight loss is the area of the triangle aeg. This triangle can be thought of as being made up of two congruent triangles, acd and dfe, as well as the rectangle gcdf, which can be seen to be twice the area of acd or dfe. With D2, the deadweight loss is the area of the triangle abd, which can also be seen to be made up of two congruent triangles, acd and acb. Triangle acb then has the same area as dfe, and so triangle aeg has twice the area of abd, because subtracting acb and acd from aeg, we are left with the rectangle gcdf, which is twice the area of dfe. Notice that there is no deadweight loss with the perfectly inelastic demand, D3, because the same units are traded after the tax as before, with ALL of the lost consumer and producer surplus going to the government.
We conclude, then, that more of the tax will be shifted to the buyers, the less elastic the demand. More tax revenues are collected, the less elastic the demand. Also, deadweight loss of a tax is lower, the less elastic the demand.
D. Elasticity of supply, tax incidence, tax revenues and
deadweight loss
Again we have a $1.00 tax, but this will be collected from the buyers, again to keep the diagram as free of clutter as possible (remember, it doesn't matter if the tax is collected from the buyers or from the sellers, the results are the same). From FIGURE XII, we have D1 as our original demand curve before the tax and Dt as our demand after tax. The original price is again $5.50 and the original quantity traded is 100 cartons per day. We have three supply curves: 1) S1, the perfectly elastic supply curve; 2) S2, a moderately, but not perfectly, elastic supply; and 3) S3, a perfectly inelastic supply curve.
It is easy to see that with the most elastic supply curve, S1,
the buyers will be paying a price of $6.50 after the tax, bearing
the entire burden of the tax, yet with the perfectly inelastic
supply curve, S3, the buyers pay no more than the original
price of $5.50, with the sellers bearing the entire burden of
the tax, receiving a dollar less than the original price.
With S2, the burden is shared by both the sellers and
the buyers.
We see that the incidence of the tax is shifted more to the sellers,
the less elastic the supply, or the more difficulty the sellers
have in altering their behavior. It is left to the reader
to show that the less elastic the supply, the more the government's
revenues will be raised from a given size tax and the lower the
deadweight loss of a tax. We see that ideally, the more
inelastic the demand and/or supply, the more revenues will be
raised for the government (which is not a good thing, in and of
itself, as it may just provide the government with more to waste)
and the lower the deadweight loss of the tax.
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