Transcript Document

Chapter 17
THE EFFICIENCY OF
PERFECT COMPETITION
MICROECONOMIC THEORY
BASIC PRINCIPLES AND EXTENSIONS
EIGHTH EDITION
WALTER NICHOLSON
Copyright ©2002 by South-Western, a division of Thomson Learning. All rights reserved.
Smith’s Invisible Hand
Hypothesis
• Adam Smith believed that the
competitive market system provided a
powerful “invisible hand” that ensured
resources would find their way to where
they were most valued
• Reliance on the economic self-interest
of individuals and firms would result in a
desirable social outcome
Smith’s Invisible Hand
Hypothesis
• Smith’s insights gave rise to modern
welfare economics
• The “fundamental theorem” of welfare
economics suggests that there is a
close correspondence between the
efficient allocation of resources and the
competitive pricing of these resources
Pareto Efficiency
• An allocation of resources is Pareto
efficient if it is not possible (through
further reallocations) to make one person
better off without making someone else
worse off
• The Pareto definition identifies allocations
as being “inefficient” if unambiguous
improvements are possible
Efficiency in Production
• An allocation of resources is efficient in
production (or “technically efficient”) if no
further reallocation would permit more of
one good to be produced without
necessarily reducing the output of some
other good
• Technical efficiency is a precondition for
Pareto efficiency but does not guarantee
Pareto efficiency
Efficient Choice of Resources
for a Single Firm
• A single firm with fixed inputs of labor
and capital will have allocated these
resources efficiently if they are fully
employed and if the RTS between
capital and labor is the same for every
output the firm produces
Efficient Choice of Resources
for a Single Firm
• Assume that the firm produces two
goods (X and Y) and that the available
levels of capital and labor are K’ and L’
• The production function for X is given by
X = f (KX, LX)
• If we assume full employment, the
production function for Y is
Y = g (KY, LY) = g (K’ - KX, L’ - LX)
Efficient Choice of Resources
for a Single Firm
• Technical efficiency requires that X
output be as large as possible for any
value of Y (Y’)
• Setting up the Lagrangian and solving for
the first-order conditions:
L = f (KX, LX) + [Y’ – g (K’ - KX, L’ - LX)]
L/KX = fK + gK = 0
L/LX = fL + gL = 0
L/ = Y’ – g (K’ - KX, L’ - LX) = 0
Efficient Choice of Resources
for a Single Firm
• From the first two conditions, we can see
that
fK g K

fL g L
• This implies that
RTSX (K for L) = RTSY (K for L)
Efficient Allocation of
Resources among Firms
• Resources should be allocated to those
firms where they can be most efficiently
used
– the marginal physical product of any
resource in the production of a particular
good should be the same across all firms
that produce the good
Efficient Allocation of
Resources among Firms
• Suppose that there are two firms
producing X and their production
functions are
f1(K1, L1)
f2(K2, L2)
• Assume that the total supplies of capital
and labor are K’ and L’
Efficient Allocation of
Resources among Firms
• The allocational problem is to maximize
X = f1(K1, L1) + f2(K2, L2)
subject to the constraints
K1 + K2 = K’
L1 + L2 = L’
• Substituting, the maximization problem
becomes
X = f1(K1, L1) + f2(K’ - K1, L’ - L1)
Efficient Allocation of
Resources among Firms
• First-order conditions for a maximum
are
X
f1
f2
f1
f2




0
K1 K1 K1 K1 K 2
X f1 f2 f1 f2




0
L1 L1 L1 L1 L2
Efficient Allocation of
Resources among Firms
• These first-order conditions can be
rewritten as
f1
f2

K1 K 2
f1
f2

L1 L2
• The marginal physical product of each
input should be equal across the two
firms
Efficient Choice of Output
by Firms
• Suppose that there are two outputs (X
and Y) each produced by two firms
• The production possibility frontiers for
these two firms are
Yi = fi (Xi ) for i=1,2
• The overall optimization problem is to
produce the maximum amount of X for
any given level of Y (Y*)
Efficient Choice of Output
by Firms
• The Lagrangian for this problem is
L = X1 + X2 + [Y* - f1(X1) - f2(X2)]
and yields the first-order condition:
f1/X1 = f2/X2
• The rate of product transformation
(RPT) should be the same for all firms
producing these goods
Efficient Choice of Output
by Firms
Firm A is relatively efficient at producing cars, while Firm B is
relatively efficient at producing trucks
Cars
Cars
RPT 
2
RPT 
1
100
1
1
100
50
Trucks
Firm A
50
Trucks
Firm B
Efficient Choice of Output
by Firms
If each firm was to specialize in its efficient product, total
output could be increased
Cars
Cars
RPT 
2
RPT 
1
100
1
1
100
50
Trucks
Firm A
50
Trucks
Firm B
Theory of Comparative
Advantage
• The theory of comparative advantage
was first proposed by Ricardo
– countries should specialize in producing
those goods of which they are relatively
more efficient producers
• these countries should then trade with the rest
of the world to obtain needed commodities
– if countries do specialize this way, total
world production will be greater
Theory of Comparative
Advantage
• Suppose that this is the marginal cost
data for England and Portugal for the
production of wine and cloth
Marginal Costs
Wine
England
8
Portugal
2
Cloth
4
2
Theory of Comparative
Advantage
• In Ricardo’s analysis, marginal costs
were assumed to be constant
• If we let total resource costs be fixed for
each country at 100, the production
possibility frontier for England is
8W + 4C = 100
and for Portugal it is
2W + 2C = 100
Theory of Comparative
Advantage
• The RPTs differ between these countries:
dC
RPT (England)  
2
dW
dC
RPT (Portugal)  
1
dW
Theory of Comparative
Advantage
• Although Portugal has an absolute
advantage in the production of both
goods, both countries could benefit from
trade
– wine is relatively less costly in Portugal
• Portugal has a comparative advantage in wine
– cloth is relatively less costly in England
• England has a comparative advantage in cloth
Theory of Comparative
Advantage
• Suppose that, prior to trade, each country
devotes half its resources to each good
– For England:
W = 50/8 = 6.25
C = 50/4 = 12.5
– For Portugal:
W = 50/2 = 25
C = 50/2 = 25
Theory of Comparative
Advantage
• World output can be increased if England
was to produce less wine and more cloth
and Portugal was to produce more wine
and less cloth
• Suppose that England decided to devote
all of its resources to the production of
cloth
W = 0/8 = 0
C = 100/4 = 25
Theory of Comparative
Advantage
• Suppose that Portugal decided to devote
70% of its resources to the production of
wine, with the remaining 30% used to
produce cloth
W = 70/2 = 35
C = 30/2 = 15
• World output of wine has increased from
31.25 to 35, and cloth output has risen
from 37.5 to 40
Efficiency in Product Mix
• Technical efficiency is not a sufficient
condition for Pareto efficiency
– demand must also be brought into the
picture
• In order to ensure Pareto efficiency, we
must be able to tie individual’s
preferences and production possibilities
together
Efficiency in Product Mix
• The condition necessary to ensure that
the right goods are produced is that the
marginal rate of substitution for any two
goods must be equal to the rate of
product transformation of the two goods
MRS = RPT
– the psychological rate of trade-off between
the two goods in people’s preferences must
be equal to the rate at which they can be
traded off in production
Efficiency in Product Mix
Output of Y
Suppose that we have a one-person (Robinson
Crusoe) economy and PP represents the
combinations of X and Y that can be produced
P
Any point on PP represents a
point of technical efficiency
P
Output of X
Efficiency in Product Mix
Output of Y
Only one point on PP will maximize
Crusoe’s utility
At the point of
tangency, Crusoe’s
MRS will be equal to
the technical RPT
P
U3
U2
U1
P
Output of X
Efficiency in Product Mix
• Assume that there are only two goods
(X and Y) and one individual in society
(Robinson Crusoe)
• Crusoe’s utility function is
U = U(X,Y)
• The production possibility frontier is
T(X,Y) = 0
Efficiency in Product Mix
• Crusoe’s problem is to maximize his
utility subject to the production
constraint
• Setting up the Lagrangian yields
L = U(X,Y) + [T(X,Y)]
Efficiency in Product Mix
• First-order conditions for an interior
maximum are
L U
T


0
X X
X
L U
T


0
Y Y
Y
L
 T ( X ,Y )  0

Efficiency in Product Mix
• Combining the first two, we get
U / X T / X

U / Y T / Y
or
dY
MRS ( X for Y )  
(along T )  RPT ( X for Y )
dX
Competitive Prices and
Efficiency
• Attaining a Pareto efficient allocation of
resources requires that the rate of
trade-off between any two goods be the
same for all economic agents
• In a perfectly competitive economy, the
ratio of the prices of the two goods
provides the common rate of trade-off to
which all agents will adjust
Efficiency in Production
• In minimizing costs, a firm will equate
the RTS between any two inputs (K and
L) to the ratio of their competitive prices
(w/v)
– this is true for all outputs the firm produces
– RTS will be equal across all outputs
Efficiency in Production
• A profit-maximizing firm will hire
additional units of an input (L) up to the
point at which its marginal contribution
to revenue is equal to the marginal cost
of hiring the input (w)
PXfL = w
Efficiency in Production
• If this is true for every firm, then with a
competitive labor market
PXfL (for firm 1) = w = PXfL (for firm 2)
fL (for firm 1) = fL (for firm 2)
• Every firm that produces X has
identical marginal productivities of
every input in the production of X
Efficiency in Production
• Recall that the RPT (of X for Y) is
equal to MCX /MCY
• In perfect competition, each profitmaximizing firm will produce the output
level for which marginal cost is equal to
price
• Since PX = MCX and PY = MCY for
every firm, RTS = MCX /MCY = PX /PY
Efficiency in Production
• Thus, the profit-maximizing decisions
of many firms can achieve technical
efficiency in production without any
central direction
• Competitive market prices act as
signals to unify the multitude of
decisions that firms make into one
coherent, efficient pattern
Efficiency in Product Mix
• The price ratios quoted to consumers
are the same ratios the market presents
to firms
• This implies that the MRS shared by all
individuals will be equal to the RPT
shared by all the firms
• An efficient mix of goods will therefore
be produced
Efficiency in Product Mix
Output of Y
P
X* and Y* represent the efficient output mix
PX*
slope  
P*
Only with a price ratio of
PX*/PY* will supply and
demand be in equilibrium
Y
Y*
U0
X*
P
Output of X
Laissez-Faire Policies
• The correspondence between
competitive equilibrium and Pareto
efficiency provides some support for the
laissez-faire position taken by many
economists
– government intervention may only result in
a loss of Pareto efficiency
Departing from the
Competitive Assumptions
• The ability of competitive markets to
achieve efficiency may be impaired
because of
– imperfect competition
– externalities
– public goods
Imperfect Competition
• Imperfect competition includes all
situations in which economic agents
exert some market power in determining
market prices
– these agents will take these effects into
account in their decisions
• Market prices no longer carry the
informational content required to achieve
Pareto efficiency
Imperfect Competition
• Suppose that there are two goods that
are produced (X and Y)
– X is produced under imperfectly competitive
conditions
• MRX < PX
– Y is produced under conditions of perfect
competition
• MRY = PY
Imperfect Competition
• The profit-maximizing output choice is
that combination of X and Y for which
MCX MRX PX*
RPT ( X for Y ) 

 *  MRS (of X for Y )
*
MCY
PY
PY
• This will result in a nonoptimal choice of
outputs
– less X and more Y will be produced than
would be optimal
Imperfect Competition
Imperfect competition in the market for X
will result in less X and moreY produced
than is Pareto efficient
Output of Y
Y’
Y*
slope  
U2
U1
X’
X*
PX*
P*
Y
Production is
efficient and supply
and demand are in
equilibrium, but the
outcome is not
Pareto efficient
Output of X
Externalities
• An externality occurs when there are
interactions among firms and individuals
that are not adequately reflected in
market prices
• With externalities, market prices no
longer reflect all of a good’s costs of
production
– there is a divergence between private and
social marginal cost
Public Goods
• Public goods have two properties that
make them unsuitable for production in
markets
– they are nonrival
• additional people can consume the benefits of
these goods at zero cost
• should their prices be zero?
– they are nonexclusive
• extra individuals cannot be precluded from
consuming the good
• consumers will become free riders
Market Adjustment and
Information
• The efficiency properties of a
competitive price system may be
affected by the level of information in
the market
Establishing Competitive
Equilibrium Prices
• What market signals do suppliers and
demanders use to move toward equilibrium?
– Suppose that the competitive market price for a
good starts at P0
– We know that under certain circumstances
there exists an equilibrium price (P*) such that
D(P*) = S(P*)
– How does the market move from P0 to P*?
Walrasian Price Adjustment
• Changes in price are motivated by
information about the degree of excess
demand at any particular price
• The Walrasian adjustment mechanism
specifies that the change in price over
time is given by
dP/dt = k[D(P) - S(P)] = k[ED(P)]
k>0
Walrasian Price Adjustment
• Price will rise if there is positive excess
demand and fall if there is negative
excess demand
• This mechanism is called a tâtonnement
process
Walrasian Price Adjustment
Price
ED < 0
If excess demand is positive,
price will rise.
S
P
If excess demand is negative,
price will fall.
P*
This equilibrium price (P*) will
be stable because the forces
will move price toward P*
P
ED > 0
D
Quantity
Walrasian Price Adjustment
If excess demand is positive,
price will rise.
Price
P
If excess demand is negative,
price will fall.
ED > 0
P*
ED < 0
S
P
This equilibrium price (P*)
will not be stable because
the forces will move price
away from P*
D
Quantity
Walrasian Price Adjustment
• The Walrasian price adjustment
procedure is a differential equation
• We can use a Taylor approximation of
the form
dp/dt = k[ED’(P*)](P - P*)
• This is called a first-order differential
equation
Walrasian Price Adjustment
• An important theorem in the study of
first-order differential equations is that
their solutions have the same stability
properties as do the nonlinear
equations they approximate
Walrasian Price Adjustment
• The general solution to this type of
problem will be of the form
P(t) = (P0 - P*)ekED’(P*)t + P*
where P0 represents the initial price at
t=0
– for this system to be stable, it must be the
case that ED’ (P*) < 0
• an increase in price must reduce excess demand
• a fall in price must increase excess demand
Marshallian Quantity
Adjustment
• A somewhat different picture of the
adjustment process was suggested by
Marshall
– individuals and firms should be viewed as
adjusting quantity in response to imbalances
in quantity demanded and quantity supplied
– price changes follow from these changes in
quantity
Marshallian Quantity
Adjustment
• Let D -1(Q) represent the price that
buyers are willing to pay for each quantity
• Let S -1(Q) represent the price that
suppliers require for each quantity
• The Marshallian adjustment mechanism
can be represented by
dQ/dt = k[D -1(Q) - S -1(Q) ] = k[ED -1(Q)]
k>0
Transactions and
Information Costs
• To develop a behaviorally oriented
theory of market adjustment, one must
examine the costs involved in reaching
market equilibrium and illustrate how
economic actors will seek to minimize
these costs
• Will market adjustments be primarily of
the Walrasian or Marshallian type?
Transactions and
Information Costs
• If prices can be easily changed and if
information about price changes is
readily disseminated among buyers and
sellers, Walrasian price adjustment may
dominate
• If prices are difficult to alter and if the
quantity traded can be changed with little
cost, markets are more likely to exhibit
Marshallian quantity adjustment
Disequilibrium Pricing
and Expectations
• The traditional model pictures supply and
demand decisions as being made
simultaneously
• The theory offers no guidance on how
demanders or suppliers act in
disequilibrium situations
• If the simultaneity assumption could be
relaxed, this problem would be simplified
Disequilibrium Pricing
and Expectations
• Assume that demand responds to the
current market price which is known with
certainty
• Demand is given by
QtD = c - dPt
Disequilibrium Pricing
and Expectations
• However, suppliers can respond only to
what they expect the market price to be
• Therefore, supply is given by
QtS = a + bE(Pt)
where E(Pt) is what suppliers expect the
market price to be at time t
Disequilibrium Pricing
and Expectations
• The behavior of this model will depend
on how suppliers form price expectations
• If suppliers always expect the price in
period t - 1 to prevail in period t
E(Pt) = Pt - 1
• In this case, the model would become a
cobweb model
The Cobweb Model
Price
Initially, price is set at P0, and
Q1 will be produced
S
Demanders will bid for Q1 thus
establishing the market price
at P1
P0
P2
At a price of P1, suppliers will
choose to produce Q2 which
will lead to a price of P2
P1
D
Q2
Q1
Quantity
The Cobweb Model
Price
The process is repeated until
price works its way to the
equilibrium price (P*)
S
P0
P2
Before reaching equilibrium, a
number of disequilibrium (and
inefficient) outcomes occur
P*
P1
D
Q2
Q1
Quantity
Rational Expectations
• A separate hypothesis about the formation
of price expectations was proposed by
Muth in the early 1960s
• In his model, expectations are made on a
“rational” basis by incorporating all
available information about the market in
question
Rational Expectations
• A supplier who know the precise forms of
the demand and supply curves could
calculate the equilibrium price
c d
P* 
ba
• This value could then be used to form the
price expectation
c d
E (Pt )  P * 
ba
Rational Expectations
• Using this expected price, supply will be at
its equilibrium level
– the market will be free of the inefficient
fluctuations observed in the cobweb model
• In the absence of any other information or
transactions costs, equilibrium will be
established instantly
Price Expectations and
Market Equilibrium
• Suppose the demand for handmade
violins is given by
QtD = 10 - 3Pt
• Because producing a violin takes longer
than one period, makers base their
decision on what they expect the price
to be
QtS = 2 + E(Pt)
Price Expectations and
Market Equilibrium
• In equilibrium
E(Pt) = Pt
P* = 2
Q* = 4
Price Expectations and
Market Equilibrium
• With adaptive expectations, other pricequantity combinations might be
observed
• Suppose that
E(Pt) = Pt -1
Price Expectations and
Market Equilibrium
• If P0 = 1, supply in period 1 is
Q1 = 2 + P0 = 3
and P1 is determined by the demand
curve
3 = 10 - P1
P1 = 7/3
• Proceeding in this way yields the
following prices and quantities over time:
Price Expectations and
Market Equilibrium
Period
0
Quantity
NA
Price
1.00
1
3.00
2.33
2
4.33
1.89
3
3.89
2.04
4
4.04
1.99
5
3.99
2.00
6
4.00
2.00
Information and Inefficient
Equilibria
• The proof of the efficiency of
competitive prices assumed that these
equilibrium prices were known to all
economic actors
• If some actors are not fully informed
about prevailing prices or product
quality, inefficient allocations may result
Asymmetric Information and
the Lemons Model
• Assume that used cars come in a number
of qualities (n)
– each of these qualities has a price
associated with it (P1,…,Pn) representing the
value these cars would have to buyers and
sellers in a fully informed situation
• Sellers know precisely the value of their
car
Asymmetric Information and
the Lemons Model
• Buyers have no way of knowing a car’s
quality until they own it and base their
evaluation of cars on the average quality
of all cars available (P’)
– equilibrium price must be P’
• this is what demanders will pay for a car of
average quality
Asymmetric Information and
the Lemons Model
• At a price of P’, quantity supplied will be
QS 
 S (P )
Pi P '
i
i
where Si s the supply of cars of quality Pi
and the sum is taken over qualities less
than P’
• For cars with better quality (Pi > P’), the
seller will choose to hold on to the car
Asymmetric Information and
the Lemons Model
• In this situation, buyers will be unsatisfied
because the quality of used cars is lower
than they expect
– this situation will deteriorate even further
over time
• The inefficiency in this market occurs
because sellers have no way to convince
buyers that their cars are not lemons
Distribution
• Although there are forces in competitive
price systems that direct resources
toward efficent allocations, there are no
guarantees that these allocations will
exhibit desirable distributions of welfare
among individuals
Distribution
• Assume that there are only two people
in society (Smith and Jones)
• The quantities of two goods (X and Y) to
be distributed among these two people
are fixed in supply
• We can use an Edgeworth box diagram
to show all possible allocations of these
goods between Smith and Jones
Distribution
OJ
UJ1
UJ2
US4
UJ3
Total Y
US3
UJ4
US2
US1
OS
Total X
Distribution
• Any point within the Edgeworth box in
which the MRS for Smith is unequal to
that for Jones offers an opportunity for
Pareto improvements
– both can move to higher levels of utility
through trade
Distribution
OJ
UJ1
UJ2
US4
UJ3
US3
UJ4
US2
A

OS
Any trade in this area is
an improvement over A
US1
Contract Curve
• In an exchange economy, all efficient
allocations lie along a contract curve
– points off the curve are necessarily
inefficient
• individuals can be made better off by moving to
the curve
• Along the contract curve, individuals’
preferences are rivals
– one may be made better off only by making
the other worse off
Distribution
OJ
UJ1
UJ2
US4
UJ3
US3
UJ4
US2
A

Contract curve
OS
US1
Distribution
• Suppose that the two individuals
possess different quantities of the two
goods at the start
– it is possible that the two individuals could
both benefit from trade if the initial
allocations were inefficient
Distribution
• Neither person would engage in trade
that would leave him worse off
• Only a portion of the contract curve
shows allocations that may result from
voluntary exchange
Distribution
OJ
Suppose that A represents
the initial endowments
UJA
A

OS
USA
Distribution
OJ
Neither individual would be willing
to accept a lower level of utility
than A gives
UJA
A

OS
USA
Distribution
OJ
Only allocations between M1 and
M2 will be acceptable to both
UJA
M2

M1

A

OS
USA
Distribution
• If the initial endowments are skewed in
favor of some economic actors, the
Pareto efficient allocations promised by
the competitive price system will also
tend to favor those actors
– voluntary transactions cannot overcome
large differences in initial endowments
– some sort of transfers will be needed to
attain more equal results
Important Points to Note:
• Pareto’s definition of an efficient
allocation of resources -- the point at
which no one person can be made
better off without making someone else
worse off -- provides the basis for
normative welfare theory
Important Points to Note:
• Productive or technical efficiency is a
necessary though not sufficient
condition for Pareto efficiency
– achieving technical efficiency requires that
three marginal conditions hold:
• equality of rates of technical substitution
across different outputs
• equality of marginal productivities among firms
• equality of rates of product transformation
across firms
Important Points to Note:
• Pareto efficiency requires productive
efficiency and efficiency in the choice
of output mix
– this latter goal can be attained by
choosing that technically efficient output
for which the rate of product
transformation between any two goods is
equal to individuals’ marginal rate of
substitution for these goods
Important Points to Note:
• Reliance on competitive equilibrium prices
will yield a technically efficient allocation
of resources because profit-maximizing
firms will make choices consistent with the
three marginal allocation rules
– existence of competitive equilibrium prices for
outputs will also result in an efficient output
mix
• the correspondence between Pareto efficiency
and competitive equilibrium is complete
Important Points to Note:
• Violations of the competitive
assumptions may distort the allocation of
resources away from Pareto efficiency
– imperfect competition
– externalities
– existence of public goods
Important Points to Note:
• Imperfect information may affect the
speed with which markets achieve
equilibrium, perhaps yielding inefficient
disequilibrium outcomes over the short
term
– informational asymmetries may also affect
the Pareto efficiency of competitive
equilibria
Important Points to Note:
• Distributional outcomes under
competitive markets may sometimes be
considered undesirable from the
perspective of equity
– initial endowments may constrain the range
of outcomes achievable through voluntary
transactions