CAPITALISM

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.

2

• 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 Hayeks argument we have to
  figure out what hes talking about with this
  marginal rate of substitution stuff. To do that
  we have to learn about

3
Indifference Curves

• Consider two goods, say beer and pizza. Holding
  a persons 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!

4
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
0
Pizza
5
Make sure slope EVERWHERE negative!
Dont let them cross!
They can be as close as you can make them --
but dont let them touch!
This ones upside down!
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

7

• That is, its 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
Pizza
Small run
Big run
8

• Rise over run works fine for straight lines, but
  its 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

9
Beer
MRSX gt MRSY
X
Y
U1
0
Pizza
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

11
Beer
Beer
Person B
Person A
0A
0B
Pizza
Pizza
Pizza
0B
Beer
Person A
Person B flipped over
Now slide together to get...
Beer
0A
Pizza
12
an Edgeworth Box
Pizza
0B
B1
B2
B3
B4
Beer
Beer
A5
A4
A3
A2
A1
0A
Pizza
NOTE Each axis represents total amount of each
good available.
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

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

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

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

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

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 elses
• But...

21

• 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.

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

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

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

25
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
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

27
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
U2
B
U1
0
Pizza
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

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,
  everyones 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 everyones MRS will be the same

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

31

• 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