Around p = p* the own-price elasticity of demand is approximately
Dq
Dpbq*p*
p*
pbp*DD qpq**.
Tax Incidence and Own-Price
Elasticities
p
Market demand
Market supply
p * p s b a c d a b c d b t b b t d .
Quantity Taxes & Market Equilibrium
psabcdbt pbabcddt
qtadbcbdt bd
The total tax paid (by buyers and sellers combined) is
Market Equilibrium
p
Market demand
Market quantity supplied is fixed, independent of price.
S(p) = c+dp, so d=0 and S(p) c.
q* = c
D-1(q) = (a-q)/b q
Market Equilibrium
/ Chapter Sixteen
Equilibrium
What Do We Do in This Chapter?
We study the concept of equilibrium We will study external changes to
And buyers pay pb = ps + t.
Quantity Taxes & Market Equilibrium
Who pays the tax of $t per unit traded?
The division of the $t between buyers and sellers is the incidence of the tax.
pb
buyers
p* ps
Tax paid by sellers
qt q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
E.g. suppose the market demand and supply curves are linear. D (p b ) a b p b
Quantity Taxes
p bp st and D (p b ) S (p s ) describe the market’s equilibrium. Notice that these two conditions apply no matter if the tax is levied on sellers or on buyers. Hence, a sales tax rate $t has the same effect as an excise tax rate $t.
Quantity Taxes & Market Equilibrium
p
Market demand
Market supply
pb p* ps
qt q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
p
Market demand
Market supply
Tax paid by
T tq tta d b c b d t. b d
Tax Incidence and Own-Price
Elasticities
p
Market demand
Market supply
pb
$t
p*
ps
qt q*
D(p), S(p)
Tax Incidence and Own-Price
Elasticities
p
Market demand
pb p* ps
Market
supply An sales tax lowers
the market demand
curve by $t, lowers
the sellers’ price and
reduces the quantity
$t
traded.
qt q*
D(p), S(p)
p
Market demand
Market quantity supplied is
extremely sensitive to price. S-1(q) = p*.
p* D-1(q) = (a-q)/b q
Quantity Taxes
A quantity tax levied at a rate of $t is a tax of $t paid on each unit traded.
psabcdbt pbabcddt
qtadbcbdt bd
The tax paid per unit by the buyer is
p b p * a b c d d t b a c d b d t d .
The tax paid per unit by the seller is
Quantity Taxes & Market Equilibrium
p

Market demand
Market supply
No tax
p*
q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
p
Market demand
p*
Market
supply An excise tax
p
Market demand
Market supply
Change to buyers’
pb
$t
price is pb - p*.
p*
Change to quantity
ps
demanded is Dq.
qt q* Dq
D(p), S(p)
Tax Incidence and Own-Price Elasticities
S (p s ) c d p s
Quantity Taxes & Market Equilibrium
D (p b ) a b p b and S ( p s ) c d p s . With the tax, the market equilibrium satisfies
p bp st and D (p b ) S (p s )so p bp st and a b p b c d p s .
Change to sellers’
pb
$t
price is ps - p*.
p*
Change to quantity
raises the market
$t
supply curve by $t,
raises the buyers’
price and lowers the
quantity traded.
qt q*
D(p), S(p)
And sellers receive only ps = pb - t.
Quantity Taxes & Market Equilibrium
p
Market demand
p*
Market supply
An sales tax lowers the market demand curve by $t
$t
q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
p
Market demand
p* ps
Market
supply An sales tax lowers
the market demand
curve by $t, lowers
the sellers’ price and
reduces the quantity
$t
traded.
qt q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
Quantity Taxes
Even with a tax the market must clear.
I.e. quantity demanded by buyers at price pb must equal quantity supplied by sellers at price ps.
qt D(pb)S(ps) abpbadbbcd bdt.
Quantity Taxes & Market Equilibrium
psabcdbt pbabcddt
qtadbcbdt bd
As t increases, and
ps falls, pb rises, qt falls.
Quantity Taxes & Market Equilibrium
raises the market
$t
supply curve by $t
q*
D(p), S(p)
Quantity Taxes & Market Equilibrium
p
Market demand
pb p*
Market
supply An excise tax
raises the market
$t
supply curve by $t,
raises the buyers’