“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

Pizza0

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

U1

U2

U3

Make sure slope EVERWHERE negative!

Don’t let them cross!

This one’s upside down!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

Pizza

Big rise

Small run0

Same rise

Big run

• 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

Pizza0

U1

X

Y

MRSX > MRSY

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

Beer

Pizza Pizza

Pizza

0A 0B

0BBeer

Pizza0A

Person A Person B

Person Bflipped over

Person A

Now slide togetherto get...

A1A2

A3

A4

A5

B1B2B3

B4

0A

0B

Bee

r

Pizza

PizzaB

eer

NOTE: Each axis represents total amount of each good available.

… an Edgeworth Box

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

A1 A2

A3

A4

B1B2B3

B4

X

YZ

0A

0B

Bee

r

Pizza

PizzaB

eer

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

A1A2

A3

A4

A5

B1B2B3

B4

X

YZH

G

0A

0B

Bee

r

Pizza

PizzaB

eer

Contract curve

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

Pizza0

I = PBQB + PPQP

Where I is income for the periodPB and QB are price and quantity of beer consumedPP and QP are price and quantity of pizza consumed

Rearrange (why?) to get:

QB = I/PB - (PP/PB) QPVerticalintercept

Slope

Illustration: Say I is $100 and beer is $2.If person spends all his income on beer, thenQP is zero and QB is fifty beers.

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

U1U2

U3

Pizza

Beer

0

A

X

B

Say our consumer is enjoying the combinationrepresented 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 isthe 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.

What is MRS at point X?

• 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

A Special Characteristic of the Equilibrium

• 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

Perfect Competition Closes the Loop

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