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CAPITALISM Powered By Docstoc
					    “The Price System As A
     Mechanism For Using
– 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
• 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!
       Characteristics of indifference curves:
Beer    -- 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



Make sure slope                 Don’t let them cross!
EVERWHERE negative!

                                They can be as close as you
      This one’s upside down!   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
• 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

         Big rise

        Same rise

                        Small run   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

       X   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               Person B
        Person A

   0A               Pizza            0B                  Pizza

                                    Pizza                        0B
         Person A

                                     Person B
                                     flipped over

                            Now slide together
                            to get...                             Beer
   0A               Pizza
      … an Edgeworth Box

      B3        B2


           A1        A2
                               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
• 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
      B3            B2
               A1        A2
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
  – 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
• 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
  – 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
      B3            B2
 B4                                 Contract
                          Z                    A5
                          H              A4
               A1        A2
         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
• 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
• 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    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.
       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
Beer                   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.

               X       What is MRS at point X?

                   B           U2

  A Special Characteristic of the
• 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
• 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
  – 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
• Thus, we conclude that capitalism is, in
  principle, a more efficient system