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Supply. Demand, and a Tax
(Class notes by E.S. de Dios)
How do equilibrium price and quantity change when a tax is imposed?
Let the demand and supply functions be given as usual by
Q
D
=
a
–
bP
(1a)
Q
S
=
–
c
+
dP
(1b)
(Here,
a
,
b
,
c
, and
d
are all arbitrary
positive
numbers.) Then without a tax,
equilibrium price is given (as we all know) by equating
Q
D
and
Q
S
and solving for
P
.
a
–
bP
= –
c
+
dP
(2)
which yields
P
+
=
a
+
c
b
+
d
and
Q
+
=
a
–
b
a
+
c
b
+
d
=
ad

bc
b
+
d
.
(3)
How must this change when a tax equal to
T
per unit is imposed?
Remember that sellers react to the price they receive while buyers act on the price
they observe. Without a tax, these two prices were the same, namely
P
. But when
there is a tax, the two are different, and we can distinguish
P
B
, the price the buyer
pays, and
P
S
, the price the seller receives.
The price the buyer pays equals the price the seller receives
plus
the tax, i.e.,
P
B
=
P
S
+
T
.
(4)
If the price the buyer pays is the price we observe, then
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 Spring '09
 Dean

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