1. “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. 1

2. By “rational economic order” Hayek means Pareto efficient
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… 2

3. 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! 3

4. Beer Pizza 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
Beer U3 U2 U1
Pizza 4

5. They can be as close as you can make them -- but don’t let them touch!
Make sure slope
EVERWHERE negative!
Don’t let them cross!
They can be as close as you
can make them --
but don’t let them touch!
This one’s upside down! 5

6. 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 6

7. Note that the slope changes as we move along an indifference curve
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
Pizza
Small run
Big run 7

8. For indifference curves we need to work with tangents
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 8

9. Beer X
MRSX > MRSY Y U1
Pizza 9

10. 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 10

11. Beer Beer Person B Person A 0A 0B Pizza Pizza Pizza 0B Beer Person A
flipped over
Now slide together
to get...
Beer 0A
Pizza 11

12. … an Edgeworth Box Pizza 0B Beer Beer 0A Pizza B1 B2 B3 B4 A5 A4 A3 A2
NOTE: Each axis represents total
amount of each good available. 12

13. 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 13

14. Pizza 0B B1 B2 B3 X B4
Beer
Beer Y Z A4 A3 A1 A2 0A
Pizza 14

15. 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 15

16. 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 16

17. 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 17

18. Pizza 0B Beer Beer 0A Pizza B1 B2 B3 X B4 Y Z A5 H A4 G A3 A2 A1 18
Contract
curve
Beer
Beer Y Z A5 H A4 G A3 A2 A1 0A
Pizza 18

19. 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? 19

20. 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... 20

21. “This. is emphatically not the economic problem which society faces
“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.” 21

22. 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 22

23. 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 23

24. 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 24

25. The Budget Constraint Beer Pizza 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.
Pizza 25

26. 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 26

27. Beer Pizza 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.
What is MRS at point X?
Beer A X U3 B U2 U1
Pizza 27

28. 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 28

29. 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 29

30. 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 30

31. There is no such mechanism in planned socialism
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