Taxes
© Peter Berck 1999,2010
Some Questions
• What does an energy tax really do and why?
• Did US agricultural policy result in too
much land in farming?
• What does the left wing believe about
supply curves when they talk about taxing
firms? What does the right wing believe
when it says that taxes are “job killers.”
Specific Tax
• A specific tax is a tax per unit sold.
– e.g. 2 cents per crate of oranges.
• Or $25/acre foot of water sold.
• An ad valorem tax is based on value. e.g.
8% of the value of the transaction, like a
sales tax.
• We analyze a specific tax.
Consumer and Producer Price
• Consumers pay Pd per unit,
– which consists of the amount the producers
receive Ps and the tax, t.
– That is Pd = Ps + t.
– Producers respond to what they receive, S(Ps) is
their supply curve.
– Consumers purchase according to what it costs
them, D(Pd) is their demand curve.
Tax Algebra
•
•
•
•
S(Ps) = D(Pd) and
Pd = Ps + t.
Solve for the prices Ps and Pd.
An obvious solution technique is S(Ps) =
D(Ps +t).
Algebraic Example
Q = 3 Ps is S(Ps)
• Q = 12 – 4 Pd is D(Pd)
• No Tax Equilibrium: P= Ps = Pd.
– Q*= 36/7; P*= 12/7
– I put the stars (*) on P and Q to indicate that
these are the (no tax) equilibrium values
Algebra with Tax
• Let t = 2; We have 3 Eq in 3 variables
Eq 1: Q = 12 – 4 Pd is D(Pd)
Eq 2: Q = 3 Ps
is S(Ps)
Eq 3: Ps + t = Pd
12 – 4 (Ps + t) = 3 Ps
12 – 8 – 4 Ps = 3 Ps
Ps = 4/7. Pd = 18/7
Inverse Function will work better
for Graphs
Eq 1: Q = 12 – 4 Pd is D(Pd)
D-1(Q) = Pd = (12-Q)/4
Eq 2: Q = 3 Ps
is S(Ps)
S-1(Q)= Ps= Q/3
Graphical Solution
•
•
•
•
D-1(Q) = Pd
S-1(Q)= Ps.
Equilibrium is D-1(Q) = Pd = Ps + t,
so [D-1(Q) - t] = Ps = S-1(Q).
– The term in brackets [ ] is just the demand curve shifted
downward by t;
– for every value of Q, find the associated value of p and
subtract t from it!
– Talk through why this makes sense
Graphical Tax
3
2.5
Pd
P
2
S
D
D -2
t
1.5
1
Ps
0.5
0
0
2
4
6
Q
8
10
“Shift” supply
• make the algebraic substitution in the other
order.
• Equilibrium is S-1(Q) = Ps = Pd - t,
• so S-1(Q) + t = Pd = D-1(Q).
• Now the supply curve from the consumer's
point of view appears to have shifted up by
t.
Graph—Supply “Shifts”
4
P
3.5
3
2.5
2
1.5
S
D
S +2
t
1
0.5
0
0
2
4
6
Q
8
10
Incidence
• Tax incidence means finding the tax caused price
changes to consumers and producers.
• P* is the price with no tax
• We say Pd – P* is the incidence upon consumers
• We say P* - Ps is incident upon the producers
• Go back to graph and show it on the graph
Algebra for incidence in the
example
• P* = 12/7
• The consumer sees price rise by 18/7 – 12/7
• The producer sees the price fall by 12/7 –
4/7
• Of the $2 tax, $6/7 was incident upon
consumers while $8/7 was incident upon the
producers
At your seat…
• Draw supply demand with a flat horizontal
supply curve. Usual downward sloping
demand
–
–
–
–
Add a tax
Calculate incidence
Now think about whether a tax is a good political idea.
Does it matter who gets taxed (consumer or producer)
Tax Take
• One (obvious) purpose of taxes is to raise
revenue.
• Revenue = t Q
– where Q is the quantity bought with the tax
Revenue
4
P
3.5
3
2.5
S
D
S +2
2
1.5
1
0.5
0
0
2
4
6
Q
Price is $/unit; Q is units; Area is $
8
10
Tax’s can induce desired
behavior
• Firm’s don’t pay for the use of air to
dispose of waste.
• Suppose a unit of output causes a unit of waste
(unavoidably so.)
• Suppose waste causes damage of $t/unit
• A tax of $t/unit will induce the proper
behavior
• Market Based Incentives
Some Details
•
•
•
•
S(Pout,Pin,…) is the supply curve
Pin is clean air services
It should cost t but it actually costs 0.
Supply is outward shifted with cheaper
inputs
• Charging t as a tax puts things back where
they belong.
A standard
• The government could calculate the correct
output and order the firm to make it.
• Why does the firm prefer the standard to the
tax?
– Aren’t standards (Command and Control) the
essence of central planning, that is, they are
communist?
– Back to the picture; where does the Green go?
Who Gets the Revenue with a
quota or a tax?
4
P
3.5
3
2.5
S
D
S +2
2
1.5
1
0.5
0
0
2
4
6
Q
Price is $/unit; Q is units; Area is $
8
10
Loan Rate
• Ag. Adustment Act of 1933
– Depression
– Deflation (prices go down.)
– Point was to raise farm prices
• US still does things like this but more
complicated
Loan Rate
Demand
Gov’t Purchases
PL
Supply
QD
QL
Set Aside
Set
aside
shifts
supply
in.
Demand Gov’t Purchases
PL
Supply
QD
QL-after set aside
QL
Why the set aside
• Reduce government outlay.
• But Conservation became important with
both the dustbowl and the Hoosac Mills
Decision of 1936.
– Soil conservation
– Conservation as reason for AAA to make it
constitutional
Decoupling
• How would you raise revenue to farmers
without creating an incentive to plant more?
• Is our biofuel policy decoupled?
Electricity
• Example in book comes from California
• Electricity is made from Nat. Gas, Hydro,
and out of state coal.
• Look at http://www.eia.doe.gov/emeu/aer/pdf/aer.pdf
Energy Flow, 2009
(Quadrillion Btu)
Figure 2.1: Hourly California
Supply Curve for Fossil-Fueled
Electricity.
2-30
© 2011 Pearson Addison-Wesley. All
rights reserved.
Figure 2.5:
Equilibrium.
2-31
© 2011 Pearson Addison-Wesley. All
rights reserved.
Carbon Policy
• CA and other western states are setting up a
program to limit the carbon from electricity
and other sources.
Figure 2.8:
An Electricity Output Quota.
2-33
© 2011 Pearson Addison-Wesley. All
rights reserved.