Download Externalities

Externalities
© Allen C. Goodman 2009
Ideal Market Processes are desirable if …
• We accept the value judgment that “personal wants of
individuals should guide the use of society’s resources.”
• Three structural characteristics are necessary:
– All markets are competitive.
– All participants are fully informed.
– All valuable assets can be individually owned and managed
without violating the competition assumption.
• If these hold, government’s best role involves determining
an income distribution, providing rules of property and
exchange and enforcing competition.
Markets
If markets behave properly, COST of item equals the PRICE
that buyers are willing to pay.
Value to consumer = Value to producer
With competition, in the short run, the firm produces to where:
MC = MR = P
Value of resources in production = MR = Value to consumer
We can do a little bit of geometry to show this:
Typical Firm Diagram
Mkt.
Firm
S
AC
P
MR
P*
D
Economy Q
MC
Firm q
Pareto Efficiency
Context of trade.
One can’t make oneself better off,
without making someone else
worse off.
We usually do this with an
exchange Edgeworth Box.
Abner’s Preferences
Belinda’s Preferences
Abner
Belinda
Pareto Efficiency
Start at Point A.
Is this an Equilibrium?
Belinda
No, they can trade
Belinda can be better
off.
B
So can Abner.
A
Abner
Pareto Efficiency
We can plot similar points, which
we recognize as a “contract
curve”
Belinda
And so on.
B
A
Abner
Pareto Efficiency
We must recognize that point X is
Pareto Optimal.
Belinda
Y
So is point Y.
B
A
X
Abner
Utility Possibility Frontier
We can plot Abner’s utility against
Belinda’s Utility.
X
Why do we draw it
this way?
What if we want a perfectly
egalitarian society?
Does equal utility mean
equal allocations?
Y
Abner’s Utility
So, are markets always great?
• Externality – A cost or
benefit in production or
consumption that does
NOT accrue to the producer
or the consumer of the
commodity.
• No single person can own
or manage air or water.
•
Consider a person who
wants to heat a house with a
wood fire.
1. More wood  more heat.
2. W/ more heat, willingness to
pay for additional heat .
3. More wood and more heat
 more smoke
Heat and smoke
Individual sees price of wood as
P1.
Compares price to marginal
benefit (demand curve).
Individual purchases quantity A
of wood.
BUT…
Wood  Smoke.
Assume that more burning 
more smoke.
We get MSC curve
D = WTP
$
MSC
P1
MC
B
Heat, smoke
A
Heat and smoke
•
•
•
•
•
Wood  Smoke.
Assume that more burning
 more smoke.
We get MSC curve
If we go past B the marginal
benefits are:
D = WTP
$
MSC
P1
MC
Inc.
Inc.
Ben.
Costs
If we go past B the marginal
costs are:
B
Heat, smoke
A
Heat and smoke
•
If we go past B we get
societal losses.
D = WTP
$
MSC
•
This is a NEGATIVE
externality.
P0
•
•
•
How to remedy?
A tax of P0 – P1.
Called a Pigovian Tax, after,
Arthur Pigou early 20th
century economist
Losses
P1
MC
Inc.
Ben.
B
Heat, smoke
A
Heat and smoke
•
Tax of P0 – P1.
D = WTP
$
MSC
•
•
•
•
Has nothing (necessarily) to
do with cleaning up the air.
We must set up a market for
a resource that no one Tax
specifically owns.
Think of it as taking
revenues and refunding it
back to population.
Who gains? Who loses?
P0
Losses
Tax
P1
MC
Inc.
Ben.
B
Heat, smoke
A
A general problem – the Lake
Externalities Equations
n industrial firms
Yi = output
Pi = price
xi units of labor at wage W
Production Function
+++
Yi = Yi (zi, xi, q),
where:
zi = waste discharges
q = quality of lake
L = assimilative capacity of Lake
- - +
q = Q (z1, z2, ..., zn, L)
Society’s Objective
Societal Objective:
Max U =  Pi Yi (xi, zi, q) -  W xi - C (L) -  [q - Q (z1, z2, ..., zn, L)]
Pi is the willingness to pay (related to utility of goods).
PiYi is the amount spent (related to utility of goods).
 is the valuation of the extra unit of environmental quality.
First Order Conditions:
U / xi = Pi Yixi - W = 0.
U / zi = Pi Yizi +  Qzi = 0
U / q =  Pj Yjq -  = 0
U / L =  QL - C' = 0
(a)
(b)
(c)
Public
Good
(d)
Society’s Objective
First Order Conditions:
U / xi = Pi Yixi - W = 0.
U / zi = Pi Yizi +  Qzi = 0
U / q =  Pj Yjq -  = 0
U / L =  QL - C' = 0
For Firm 1:
P1 Y1x1 = W
P1 Y1z1 = -  Qz1
P1 Y1q = 
Eq'm:
P1 Y1z1 = [P1 Y1q] [- Qz1]
(a)
(b)
(c)
(d)
P1 Y1z1
$
[P1 Y1q] [- Qz1]
z1
z*1
Society’s Objective
First Order Conditions:
U / xi = Pi Yixi - W = 0.
U / zi = Pi Yizi +  Qzi = 0
U / q =  Pj Yjq -  = 0
U / L =  QL - C' = 0
For Firm 1:
P1 Y1x1 = W
P1 Y1z1 = -  Qz1
P1 Y1q = 
(a)
(b)
(c)
(d)
[P1 Y1q +  2,n Pj Yjq ] [- Qz1] > [P1 Y1q] [- Qz1]
P1 Y1z1
$
For Society:
P1 Y1x1 = W
P1 Y1z1 = -  Qz1
 Pj Yjq = 
Optimum: P1 Y1z1 =
[P1 Y1q +  2,n Pj Yjq ] [- Qz1] > [P1 Y1q] [- Qz1]
[P1 Y1q] [- Qz1]
Amount TAX
Collected
z*1
z1
z*1
So …
• Societal optimum dictates that each firm
produce less than in an autarkical system.
• Remedy, again, would be a tax.
• Once again, a situation where ownership is
not well-defined and one’s actions affect
others.
Coase Theorem
The output mix of an economy is identical, irrespective of the
assignment of property rights, as long as there are zero
transactions costs.
Does this mean that we don’t have to do pollution taxes, that
the market will take care of things?
Some argue that it’s not really a theorem.
It does set out the importance of transactions costs.
Let’s analyze.
Externalities and the Coase Theorem
+ + X  F ( Lx , K x , Y )
Y  G ( Ly , K y )
Production of Y decreases
production of X, or FY < 0.
L  Lx  Ly
K  Kx  K y
If we maximize U (X, Y) we get:
U [ F ( Lx , K x , Y ), G ( Ly , K y )]
U [ F ( Lx , K x , G ( L  Lx , K  K x )), G ( L  Lx , K  K x )]
Planning Optimum
If we maximize U (X, Y) we get:
U [ F ( Lx , K x , Y ), G ( Ly , K y )]
U [ F ( Lx , K x , G ( L  Lx , K  K x )), G ( L  Lx , K  K x )]
If we maximize U (X, Y) w.r.t. Lx and Kx, we get:
UY
FL
FL

 FY 
 FY
U X GL
GL
Does a market get us there?
(*)
Planning optimum  Market Optimum
UY
FL
FK

 FY 
 FY
U X GL
GK
(*)
Does a market get us there?
If firms maximize conventionally, we get:
p X FL  pY GL  w
p X FK  pY GK  r
FL G L w


FK GK r
FL
FK
pY


G L GK p X
So?
UY
FL
FK

 FY 
 FY
U X GL
GK
UY
pY
FL
FK



UX
p X G L GK
(*)
(**)
Society’s optimum
Market optimum
Since FY < 0, pY/pX is too low by that factor. Y is
underpriced.
Coase Theorem
The output mix of an economy is identical, irrespective of the
assignment of property rights, as long as there are zero
transactions costs.
Suppose that the firm producing Y owns the right to use water
for pollution (e.g. waste disposal). For a price q, it will sell
these rights to producers of X.
Reduced by
Profits for the firm producing X are:
paying to pollute
Y  Y  T (Tickets )
 X  p X F ( LX , K X , Y )  wLX  rK X  q (Y  Y ) (***)
 X
 p X FY  q  0
Y
Coase Theorem
Y Y T
 X  p X F ( LX , K X , Y )  wLX  rK X  q (Y  Y ) (***)
 X
 p X FY  q  0
Y
Y  pY G ( LY , KY )  wLY  rKY  q (Y  Y )
 Y
 ( pY  q )G L  w  0
α  1 gets to Y;
LY
Like the iceberg model
 Y
 ( pY  q )GK  r  0
KY
We know that q = -pXFY
Coase Theorem
 X
 p X FY  q  0
Y
 Y
 ( pY   q)GL  w  0
 LY
 Y
 ( pY   q)GK  r  0
 KY
FL
FK
pY
 FY 
 FY 
GL
GK
pX
If   1, this looks like (*)
We know that q = -pXFY
Change the ownership - X owns
 X  p X F ( LX , K X , Y )  wLX  rK X  qY (****)
 X
 p X FY  q  0
Y
Y  pY G ( LY , KY )  wLY  rKY  qY
Y
 ( pY  q )G L  w  0
LY
Y
 ( pY  q )GK  r  0
KY
We know that q = -pXFY/
If X owns
FL FY FK FY
pY




G L  GK 
pX
If   1, this looks like (*)
If Y owns
FL
FK
pY
 FY 
 FY 
GL
GK
pX
If   1, this looks like (*)
If  = 1
We are at a Pareto optimum
We are at same P O.
If  is close to 1
We may be Pareto superior
We are not necessarily at
same place.
Where we are depends on
ownership of prop. rights.
Remarks
• These are efficiency arguments.
• Clearly, equity depends on who owns the
rights.
• We are looking at one-consumer economy.
If firm owners have different utility
functions, the price-output mixes may differ
depending on who has property rights.
Graphically
X’s demand (if Y holds)
Y’s supply (if Y holds)
Py -r/GK = Py -w/GL
-pxFY
q
If Y holds, X pays this much
T = Tx + Ty
If X holds, Y pays this much
T*
But, with transactions costs 
X’s demand (if Y holds)
Y’s supply (if Y holds)
Py -r/GK = Py -w/GL
-pxFY
q
q
q
If Y holds, X pays this much
If X holds, Y pays this much
Y gets this much
T = Tx + Ty
X gets this much
T*
The equilibria are not the same!