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EC325 Public Economics Notes
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In-depth lecture, class and textbook notes for lent term of EC325. Writer got a first class grade in this module.
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Public Economics Notes LTAnya Shah
2023
,1 Tax Incidence
Incidence is a term defining who the tax actually affects.
Who receives the money is actually meaningless when it comes to
measuring who actually benefits the most.
o When low-income people receive housing benefits, landlords
have an incentive to increase rent so they capture some of
these benefits.
o Earned Income Tax Credit (EITC); subsides poor people who
work – but this may cause employers to keep wages low.
1.1 Partial Equilibrium Incidence
Model Set-Up:
Two goods: x and y (background good – numeraire = 1)
Per-unit tax on good x q= p+t
o q effective buyer’s price (price consumers pay)
o p seller’s price (price sellers receive and keep)
o Ad Valorem (q=( 1+τ ) p ¿ and excise tax (q= p+t ¿ are equiva-
lent in a competitive case
Market for x is small to minimize income effects affecting demand for
goods in other markets
No close substitutes and complements rule out spillovers into other
markets
Tax revenue not spent on taxed good to avoid feedback effects
Perfect Competition
Demand:
Consumer have Quasi-Linear Utility u ( x , y )=u ( x ) + y and
wealth z
Total demand D ( q ) = ∑ x (q)
Price elasticity of demand: ε D = ( dDdq )( Dq( q ) )
o q after-tax price for buyers
o Percentage change in total demand when there is a 1%
change in price.
o Change in total demand with respect to after-tax buyers price
o q= p+t tax levied on consumers
Supply:
Firms maximize profits π= pS−c ( S )
Total Supply p S
, dS p
Price elasticity of supply: ε S=( )( )
dp S ( p )
o Percentage change in total supply when there is a 1% change
in price.
o p=q−t tax levied on producers
Equilibrium:
D ( q ) =pS demand = supply
D ( p ( t ) +t )=S( p ( t ) )
o Total demand is based on buyer’s price q
dD
dp dp ε
= = D
dt dS dD ε S −ε D
−
dp dp
dp
o effect of tax on seller’s price: incidence on sellers (if this
dt
is -1 then producers bear the full burden of the tax)
o Gives us demands share of the overall response
o If demand is inelastic, ε D would be small so incidence on sell-
ers is small as we would expect.
o Being elastic as an agent is beneficial as you can avoid
the burden.
dD
dp dp ε
Prove that = = D holds:
dt dS dD ε S −ε D
−
dp dp
We start with demand = supply Qd =Qs
Qd=D ( q )=D (p +t) and Qs=S (p)
Therefore, D ( q ) =S ( p)
dD dq dS dp
Derivative of this expression · = ·
dq dt dp dt
dq
o total derivative of argument with respect to the tax
dt
dq dp dt dp
Now take the derivative of q= p+t = + = +1 and sub that
dt dt dt dt
into the above.
· (
dD dp
dq dt )
dS dp
+1 = ·
dp dt
dD dp dD dS dp
· + = ·
dq dt dq dp dt
dD dS dp dD dp dD dp dS dD
= · − · = ( − )
dq dp dt dq dt dq dt dp dq
, dD
dp dq q
= now multiply all parts by
dt dS dD D(q)
−
dp dq
dD q
·
dp dq D ( q )
=
dt dS q dD q
· − ·
dp D ( q ) dq D ( q )
εD
Then split up the bottom left into p+t dS p dS t
· + · −ε
dp D ( q ) dp D ( q ) D
dS p
As D ( q ) =S ( p ), · =ε
dp D ( q ) S
dS t
· increase in tax proportional to the price change is a very
dp D ( q )
small number, we start at t=0 ; so, we approximate that to 0.
dp εD
Therefore, we get =
dt ε S−ε D
We have made two important assumptions:
1. Market is in equilibrium at the beginning: Qd=Qs
2. t=0 is the starting point
Now let’s consider the case where the tax is levied on producers:
We start with demand = supply Qd =Qs
Qd=D ( q ) and Qs=S (p)
However, now p=q−t
Derivative of the above
(
dD dq dS dq dt
· = −
dq dt dp dt dt )
dD dq dS dq dS
· = · −
dq dt dp dt dp
dS
(
dS dq dS dD
=
dp dt dp dq
−
) dq
=
dt dS dD
dp
−
dp dq
p
Multiply all parts by
S( p)
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