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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:
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
Belinda
Abner’s Preferences
Belinda’s Preferences
Pareto Efficiency
Start at Point A.
Is this an Equilibrium?
Abner
Belinda
No, they can trade
Belinda can be better off.
ASo can Abner.
B
Pareto Efficiency
We can plot similar points, which we recognize as a “contract curve”
Abner
Belinda
And so on.
A
B
Pareto Efficiency
We must recognize that point X is Pareto Optimal.
Abner
Belinda
So is point Y.
A
B
X
Y
Utility Possibility Frontier
We can plot Abner’s utility against Belinda’s Utility.
Why do we draw it this way?
Abner’s Utility
Bel
inda
’s U
t ili
ty
X
Y
What if we want a perfectly egalitarian society?
Does equal utility mean equal allocations?
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 smokeIndividual sees price of wood as
P1.
Compares price to marginal benefit (demand curve).
Individual purchases quantity A of wood.
BUT…
Heat, smoke
$
MC
MSC
D = WTP
P1
A
Wood Smoke.
Assume that more burning more smoke.
We get MSC curve B
Heat and smoke
• If we go past B the marginal benefits are:
Heat, smoke
$
MC
MSC
D = WTP
P1
A
• Wood Smoke.
• Assume that more burning more smoke.
• We get MSC curve
B
Inc.Ben.Inc.
Costs• If we go past B the marginal
costs are:
Heat and smoke• If we go past B we get
societal losses.
Heat, smoke
$
MC
MSC
D = WTP
P0
P1
AB
Inc.Ben.
Losses
• This is a NEGATIVE externality.
• How to remedy?
• A tax of P0 – P1.
• Called a Pigovian Tax, after, Arthur Pigou early 20th century economist
Tax
Heat and smoke• Tax of P0 – P1.
Heat, smoke
$
MC
MSC
D = WTP
P0
P1
AB
Inc.Ben.
Losses
Tax
• Has nothing (necessarily) to do with cleaning up the air.
• We must set up a market for a resource that no one specifically owns.
• Think of it as taking revenues and refunding it back to population.
• Who gains? Who loses?
A general problem – the LakeExternalities Equations
n industrial firmsYi = outputPi = pricexi units of labor at wage W
Production Function+ + +
Yi = Yi (zi, xi, q), where:
zi = waste dischargesq = quality of lakeL = assimilative capacity of Lake - - - +q = Q (z1, z2, ..., zn, L)
Society’s ObjectiveSocietal 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 Yi
xi - W = 0. (a) U / zi = Pi Yizi + Qzi = 0 (b) U / q = Pj Yj
q - = 0 (c) U / L = QL - C' = 0 (d)
Public Good
Society’s ObjectiveFirst Order Conditions:
U / xi = Pi Yixi - W = 0. (a)
U / zi = Pi Yizi + Qzi = 0 (b) U / q = Pj Yj
q - = 0 (c) U / L = QL - C' = 0 (d)
For Firm 1:P1 Y1
x1 = WP1 Y1
z1 = - Qz1
P1 Y1q =
Eq'm:P1 Y1
z1 = [P1 Y1q] [- Qz1]
z1
$P1 Y1
z1
[P1 Y1q] [- Qz1]
z*1
AmountCollected
Society’s ObjectiveFirst Order Conditions:
U / xi = Pi Yixi - W = 0. (a)
U / zi = Pi Yizi + Qzi = 0 (b) U / q = Pj Yj
q - = 0 (c) U / L = QL - C' = 0 (d)
For Firm 1:P1 Y1
x1 = WP1 Y1
z1 = - Qz1
P1 Y1q =
z1
$P1 Y1
z1
[P1 Y1q] [- Qz1]
z*1
For Society:P1 Y1
x1 = WP1 Y1
z1 = - Qz1
Pj Yjq =
Optimum: P1 Y1z1 =
[P1 Y1q + 2,n Pj Yj
q ] [- Qz1] > [P1 Y1
q] [- Qz1]
[P1 Y1q + 2,n Pj Yj
q ] [- Qz1] > [P1 Y1q] [- Qz1]
z*1
TAX
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 TheoremThe 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 L K Y
Y G L K
L L L
K K K
x x
y y
x y
x y
( , , )
( , )Production of Y decreasesproduction of X, or FY < 0.
+ + -
If we maximize U (X, Y) we get:
U F L K Y G L K
U F L K G L L K K G L L K K
x x y y
x x x x x x
[ ( , , ), ( , )]
[ ( , , ( , )), ( , )]
Planning Optimum
U F L K Y G L K
U F L K G L L K K G L L K K
x x y y
x x x x x x
[ ( , , ), ( , )]
[ ( , , ( , )), ( , )]
If we maximize U (X, Y) we get:
If we maximize U (X, Y) w.r.t. Lx and Kx, we get:
U
U
F
GF
F
GFY
X
L
LY
L
LY (*)
Does a market get us there?
Planning optimum Market Optimum
U
U
F
GF
F
GFY
X
L
LY
K
KY (*)
Does a market get us there?
If firms maximize conventionally, we get:
p F p G w
p F p G rX L Y L
X K Y K
F
F
G
G
w
rL
K
L
K
F
G
F
G
p
pL
L
K
K
Y
X
So?
U
U
F
GF
F
GFY
X
L
LY
K
KY (*)
U
U
p
p
F
G
F
GY
X
Y
X
L
L
K
K
(**)
Society’s optimum
Market optimum
Since FY < 0, pY/pX is too low by that factor. Y is underpriced.
Coase TheoremThe 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.
Profits for the firm producing X are:
X
( )
( , , ) ( ) (***)
0
X X X X X X
X Y
Y Y T Tickets
p F L K Y wL rK q Y Y
p F qY
Reduced by paying to pollute
Coase Theorem
Y Y Y Y Y Y
Y L
Y K
p G L K wL rK q Y Y
Lp q G w
Kp q G r
( , ) ( )
( )
( )
Y
Y
Y
Y
0
0
Y Y T
p F L K Y wL rK q Y Y
p F q
X X X X X X
X Y
( , , ) ( ) (***)
YX 0
We know that q = -pXFY
α 1 gets to Y;Like the iceberg model
Coase Theorem
Y
Y
Y
Y
( ) 0
( ) 0
Y L
Y K
p q G wL
p q G rK
X
Y p F qX Y 0
We know that q = -pXFY
F
GF
F
GF
p
pL
LY
K
KY
Y
X
If 1, this looks like (*)
Change the ownership - X owns
Y Y Y Y Y Y
Y L
Y K
p G L K wL rK qY
Lp q G w
Kp q G r
( , )
( )
( )
Y
Y
Y
Y
0
0
X X X X X X
X Y
p F L K Y wL rK qY
p F q
( , , ) (****)
YX 0
We know that q = -pXFY/
If Y owns
If 1, this looks like (*)
F
GF
F
GF
p
pL
LY
K
KY
Y
X
If X owns
If 1, this looks like (*)
F
G
F F
G
F p
pL
L
Y K
K
Y Y
X
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.
If X holds, Y pays this muchIf Y holds, X pays this much
Graphically
T = Tx + Ty
q
Y’s supply (if Y holds)X’s demand (if Y holds)
-pxFY Py -r/GK = Py -w/GL
T*