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

0

0.5

1

1.5

2

2.5

3

0 2 4 6 8 10

Q

P

SDD -2

t

Ps

Pd

“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”

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Q

P

SDS +2t

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

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Q

P

SDS +2

Price is $/unit; Q is units; Area is $

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?

0

0.5

1

1.5

2

2.5

3

3.5

4

0 2 4 6 8 10

Q

P

SDS +2

Price is $/unit; Q is units; Area is $

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

QLQD

Gov’t PurchasesPL

Demand

Supply

Set Aside

QLQD

Gov’t PurchasesPL

Demand

Supply

Set aside shifts supply in.

QL-after set aside

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)

© 2011 Pearson Addison-Wesley. All rights reserved.

2-30

Figure 2.1: Hourly California Supply Curve for Fossil-Fueled

Electricity.

© 2011 Pearson Addison-Wesley. All rights reserved.

2-31

Figure 2.5: Equilibrium.

Carbon Policy

• CA and other western states are setting up a program to limit the carbon from electricity and other sources.

© 2011 Pearson Addison-Wesley. All rights reserved.

2-33

Figure 2.8: An Electricity Output Quota.