“The Price System As A
Mechanism For Using
Knowledge”
– Friedrick Hayek, AER, 1945
• “What is the problem we wish to solve when we try
to construct a rational economic order? On certain
familiar assumptions the answer is simple enough. If
we possess all the relevant information, if we start
out from a given system of preferences, and if we
command complete knowledge of available means,
the problem is purely one of logic. That is, the
answer to the question of what is the best use of
available means is implicit in our assumptions.
• The conditions which the solution of this
[optimization] problem must satisfy have been fully
worked out and can be stated best in mathematical
form: put at their briefest, they are that the marginal
rates of substitution between any two commodities
or factors must be the same in all their different
uses.”
• By “rational economic order” Hayek means
Pareto efficient
• Before we go on with Hayek’s argument we
have to figure out what he’s talking about
with this marginal rate of substitution stuff.
To do that we have to learn about…
Indifference Curves
• Consider two goods, say beer and pizza.
Holding a person’s consumption of all other
goods constant, an indifference curve shows
all combinations of the two goods that gives
this person the same utility.
• For a given level of utility, there exists a
UNIQUE indifference curve.
• Utility cannot be measured, but indifference
curves can be observed -- thus very useful!
Beer
Characteristics of indifference curves:
-- negative slope
-- cannot cross
-- convex to origin because of law of diminishing
marginal utility
-- infinitely dense as long as goods infinitely divisible
-- utility rises as distance from origin rises
U3
U2
U1
0
Pizza
Make sure slope
EVERWHERE negative!
This one’s upside down!
Don’t let them cross!
They can be as close as you
can make them -but don’t let them touch!
Marginal Rate of Substitution
• MRS is the trade-off of one good for
another so as to maintain same level of
utility
• That is, rate at which one good traded off
for the other along an indifference curve
• Note that this trade-off rate is a change
along the vertical axis divided by the
resulting change along the horizontal axis
• That is, it’s rise over run -- MRS is the slope
of the indifference curve
• Note that the slope changes as we move
along an indifference curve
Beer
Big rise
Same rise
0
Small run
Big run
Pizza
• Rise over run works fine for straight lines,
but it’s too inaccurate for curvy lines
• For indifference curves we need to work
with tangents
• For a given point on an indifference curve,
the MRS is the slope of the tangent to that
point
Beer
X
MRSX > MRSY
Y
U1
0
Pizza
Edgeworth Box
• To understand what Hayek means with his
equality of MRS, we need to construct an
Edgeworth Box which shows relationship
between two individuals
• An Edgeworth Box is two indifference
graphs (representing two persons)
superimposed to form a rectangle
– to do this, one of the graphs has to be inverted
Beer
Beer
Person A
0A
Pizza
0B
Pizza
Beer
Person B
Pizza
0B
Person A
Person B
flipped over
0A
Now slide together
to get...
Pizza
Beer
… an Edgeworth Box
Pizza
0B
B1
B2
B3
B4
A5
A4
A1
0A
A2
Pizza
A3
NOTE: Each axis represents total
amount of each good available.
How To Use the Edgeworth Box
To Illustrate Pareto Efficiency
• Choose a point where indifference curves
intersect
• Note MRS for each person
– not equal
• Show how it would be possible to make one
better off without making other worse off by
moving along an indifference curve
• How far can we go?
• Note MRS at this limit
– equal
Pizza
0B
B1
B2
B3
X
B4
Y
Z
A4
A1
0A
Pizza
A2
A3
Pareto Efficiency and Equality of
Marginal Rates of Substitution
• At any point like X where MRSA is not
equal to MRSB it can be shown that one
person can be made better off without
harming the other simply by redistributing
the available goods between them
• Once a tangency is reached, such as points
Y or Z, this is no longer possible
• Thus X is not efficient, but both Y and Z are
• There are an infinite number of such
tangencies
– our graph shows only six, but lots more could
be packed in!
– a line connecting these efficient points is called
the contract curve
Efficiency and Movements
Toward Efficiency As An Ethical
Judgement -- The Pareto
Criterion
• Ethical judgment that society is better off
when someone is made better off and no
one is made worse off
• Provides partial ranking of states of the
world
– society better off at Y or Z than at X
– society better off at H than at X
– provides no ranking between X and G
Pizza
0B
B2
B3
B1
X
B4
Contract
curve
Y
Z
H
G
A1
0A
Pizza
A2
A5
A4
A3
Numerical Example
• Say MRSA = 3/2 and MRSB = 3/1.
• That is, A would trade off 2 slices of pizza
for three beers while B will trade off one
slice for three beers
• Take two slices from A and give them to B
• Take three beers from B and give them to A
• A is no worse off but B is better off
• What happens to each MRS?
Back To Hayek
• So “if we possess all the relevant
information, if we start out from a given
system of preferences, and if we command
complete knowledge of available means,”
then all we have to do is make sure that
everyone is consuming where his or her
marginal rate of substitution between any
two goods is the same as everyone else’s
• But...
• “This ... is emphatically not the economic
problem which society faces. And the
economic calculus which we have
developed to solve this logical problem,
though an important first step ..., does not
yet provide an answer to it. The reason for
this is that the data from which the
economic calculus starts are never for the
whole society given to a single mind, and
can never be so given.”
What Does Hayek Mean?
• Pareto efficiency/equality of MRS is merely
a state of being -- nothing we have modeled
says it will happen
• Is there an institutional arrangement, an
economic framework, which would bring
about a state of efficiency?
• If perfect information holds, then a central
planner, using his or her perfect knowledge,
could simply organize production and
consumption so as to achieve efficiency
• But perfect information does not exist
Capitalism Uses Available
Information To Reach Efficiency
• The market based capitalist system (when it
works right) does not require perfect
information
• All any one person needs to know is
information about his or her own
preferences and circumstances
• Price signals provide the rest
Modeling Efficiency in a
Capitalist System
• We can build a simple model of a well
functioning capitalist economy which
achieves efficiency as an equilibrium
outcome
• Return to the indifference curve graph and
add the budget constraint
• The budget constraint shows all possible
combinations of the two goods the
consumer is ABLE to buy out of income
The Budget Constraint
Beer
I = PBQB + PPQP
Where I is income for the period
PB and QB are price and quantity of beer consumed
PP and QP are price and quantity of pizza consumed
Rearrange (why?) to get:
QB = I/PB - (PP/PB) QP
Vertical
intercept
Slope
Illustration: Say I is $100 and beer is $2.
If person spends all his income on beer, then
QP is zero and QB is fifty beers.
0
Pizza
Consumer Equilibrium
• Consumers are assumed to maximize utility
• A utility maximizing consumer will choose
that one combination of goods that gives the
highest possible utility within his budget
• That is, he or she will choose the one point
on the budget constraint that is just tangent
to an indifference curve
• Only one indifference curve is tangent to
the budget constraint and that will be the
highest possible one
Say our consumer is enjoying the combination
represented by point A. Can he do better?
He can trade off beer for more pizza, moving
along his budget line. As he does so, he moves
to higher and higher indifference curves until
he reaches point X on curve U2. Note that U2 is
the indifference curve tangent to the budget line.
Any further and his utility starts to fall. Point X
represents the utility maximizing combination of
beer and pizza for this consumer.
Beer
A
What is MRS at point X?
X
U3
U2
B
U1
0
Pizza
A Special Characteristic of the
Equilibrium
• The slope of the budget line is -PP/PB (i.e.,
the negative of the price ratio)
• The slope of an indifference curve at a point
is the MRS
• At equilibrium, the consumer is at the point
on an indifference curve that is tangent to
the budget line
• At that point, therefore, MRS equals the
negative of the price ratio
– slopes are equal at point of tangency
Perfect Competition Closes the
Loop
• In a well functioning, perfectly competitive
market where there are no market failures or
distortionary taxes, everyone faces the same
set of market prices
• Since everyone faces the same set of prices,
everyone’s budget constraints will have the
same slope, the negative of the price ratio
• Each will attain equilibrium where his or
her MRS is equal to this common slope
• So everyone’s MRS will be the same
Final Comments on Hayek
• Similar mechanisms occur on the
production side
– intuition simple: say you are a producer who
uses tin as an input. Something happens to tin
production making it more scarce. Tin users
must somehow be induced to use less tin.
Markets automatically respond to the greater
scarcity by making tin prices go up. How will
tin users respond?
– No Such Mechanism Exists Under Planned
Socialism
– someone would have to tell tin users to cut back
• The conclusion is that there is a mechanism
in capitalism that automatically brings about
an efficient outcome
– at least under ideal conditions
• There is no such mechanism in planned
socialism
• Thus, we conclude that capitalism is, in
principle, a more efficient system