Principles of Microeconomics: Sales Taxes and Subsidies
Our understanding of elasticity will help us analyze the impact of sales taxes or subsidies on
equilibrium price and quantity.
1. Per Unit Tax
The simplest sales tax is a fixed tax per unit sold, regardless of the price or quantity of the
units sold. Whether sellers or buyers collect the tax for remission to the government is irrelevant
to the impact of the tax on buyers and sellers but we will assume that sellers collect the tax since
this is the more common occurrence due to the greater ease of remission. Since the sellers
impose the tax on each unit sold, the sellers add the amount of the tax to the price of each unit
sold. This means that the supply function shifts up by the amount of the tax.
If the equation for supply was Ps = S(Q), the Ps Tax= T + S(Q) where T = tax/unit.
e.g. Suppose P = 84 – 0.03Q and P = 26 + 0.02Q describe the market for opera tickets per day.
Initial Equilibrium => 84 – 0.03Q = 26 + 0.02Q
=> Qo = 1160 and Po = $49.20
What is the effect (short-run) of a tax of $12/unit?
=> Supply: P = 12 + 26 + 0.02Q
After Tax Equilibrium => 84 – 0.03Q = 38 + 0.02Q
=> Q 1 920 and P = $16.40
Total Tax Revenue = Tax/unit * Q = $31* 1100 = $3300
NOTE: The equilibrium price after the tax increased by $7.20 ($56.40 - $49.20) not $12. A
graph of these equilibria helps us understand why.
Graph the after-tax equilibrium by shifting up the supply curve by the amount of the tax.
Indicate the original price plus the tax (P0+Ton the vertical axis and shift supply up at Qo by this
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amount. Most individuals shift supply up to intersect D0+Tbut this is incorrect since Supply
clearly shifts by more than the amount of the tax at that point.
P = 84 - 0.02Q, P = 26 + 0.03Q, Tax = $12/unit
0 0 0 0 0 0 0 0 0 0 0 0 0
2 40 60 80 10 10 10 10 10 20 22 24
Q1 Qo Quantity
Sellers add the tax to the price that they charge customers but customers do continue to buy
Qo at the higher price due to the Law of Demand. The higher price results in a fall in quantity
demanded leading to a surplus at0+T, which causes a fall in price to a new equilib1ium P that is
usually less than0+Tthough greater than Po. The increase in price and decrease in quantity as a
result of the tax is a function of the relative elasticities of Demand and Supply. We will see later
that a comparison of the relative slopes of Demand and Supply suffices to determine the change
in price for linear Demand.
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Incidence (or Burden) of a Tax
Economists call the share of the tax paid by Buyers and Sellers the incidence, or burden, of
Definition: The Buyers’ share of a tax is the difference between the pre-tax and post-tax price
paid by Buyers.
Buyers’ Share (BS) = P1– Po
Definition: The Sellers’ share of a tax is the difference between the pre-tax and post-tax price
received by Sellers.
Sellers’ Share (SS) = Po – (P – Tax)
Note: The Sellers’ PriceSel =1P – Tax) is the price sellers receive after they deduct the tax
from the after-tax price paid by buyers.
Note: The tax revenue collected by the government (or total tax paid) is graphically the area with
the tax as the vertical dimensio1 (P 1 (P – tax)), which is the difference between the pre-
tax and post-tax Supply curves a1 Q .
A. Tax collected by Sellers (Tax shifts Supply)
BS Tax Revenue
PSel P 1T
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