Partial equilibrium analysis General-equilibrium analysis by vht20013


									                                                                     Key issues
                                                  •    general equilibrium
              Chapter 10                          •    Pareto principle
                                                  •    efficiency and equity
          General Equilibrium and
            Economic Welfare
                ECON 252

    Partial equilibrium analysis                      General-equilibrium analysis
• an examination of equilibrium and changes       • study of how equilibrium is determined in
  in equilibrium in one market in isolation         all markets simultaneously
• problem: by holding prices and quantities of    • an event in one market may have a spillover
  other goods fixed, we ignore possibility that     effect on other markets may be linked
  events in this market affect other markets'         • through demand
  equilibrium prices and quantities                   • through supply
• doing so is fine for small markets (hoola       • because output in one market is an input in
  hoops, for example)                               another

Compromise between partial and
                                                                 Minimum wage
     general equilibrium
 study equilibrium in several - but not all -     • complete coverage (partial-equilibrium
 markets simultaneously                             analysis): minimum wage causes
                                                    unemployment (Puerto Rico)
                                                  • incomplete coverage (general-equilibrium
                                                      • wage differentials across sectors
                                                      • no unemployment

            U.S. minimum wage                                         Effect of incomplete coverage
 • first minimum wage law passed in 1938                         • minimum wage in covered sector causes
    •  Fair Labor Standards Act                                    employment in that sector to fall
    • incomplete coverage: exempted agriculture,
      government, most retail, most service                      • workers who lose their jobs move to the
    • economists joked that its purpose was to maintain            uncovered sector
      family farms                                               • minimum wage leads to wage differential
 • law drove workers out of manufacturing and other                between sectors – not unemployment
   covered industries into agriculture and other
   uncovered sectors

                                                          Figure 10.2 Minimum Wage with Incomplete Coverage

   Uncovered sector supply curve                          (a) Covered Sector                   (b) Uncovered Sector              (c) Total Labor Market

                                                          w, Wage                              w, Wage                           w, Wage
                                                          per hour                             per hour                          per hour
   residual supply curve: market supply not met by
   demanders in other sectors at any given wage:
                Su(w) = S(w) - Dc(w)                            w
    • w = wage
    • w = minimum wage                                          w1                                  w1                                 w1
    • Su(w) = uncovered sector residual supply
    • S(w) = total supply curve
                                                                                      Dc                                Du                                                  D
    • Dc(w) = demand for labor in covered sector                       2        1                              1 2
                                                                      Lc       Lc                             Lu Lu                                               1
                                                                                                                                                     L 1 = L 1 + Lu
                                                                           Lc , Annual hours                 Lu , Annual hours                                   L, Annual hours

Share covered by minimum wage
                                                                   society decides whether a particular
        1938     1947      1962      1978        1991
                                                                   equilibrium (or change in equilibrium) is
        ≈ 50%    56%       61%       86%         88%               desirable by answering 2 questions:
                                                                 • Is the equilibrium efficient?
 today: all industry/government sectors are covered,             • Is the equilibrium equitable?
 but coverage in agriculture and private household
 employment is incomplete

                                                                                                Pareto principle
                               Efficiency                                        allows us to rank different allocations of goods and
                                                                                  services where no interpersonal comparisons need
     • production efficiency (or cost-effectivenss):                              to be made:
       cannot produce more output at current cost                               any allocation where we cannot make one person
       given current knowledge (it involves both technical                        better off without harming another person is
       efficiency and choosing the right output mix, given their price ratio)     Pareto efficient
     • consumption efficiency: goods cannot be
       reallocated across people so that at least
       someone is better off and no one is harmed

         First and second theorems of
               welfare economics
     First Theorem: any competitive equilibrium is                              • trade can benefit both trading partners
       Pareto efficient                                                         • suppose Jane and Denise use labor to
     Second Theorem: any Pareto-efficient                                         produce candy or chop firewood
       equilibrium can be obtained by competition,                              • with a day’s work, their output is
       given an appropriate endowment                                              • Jane: 3 candy bars or 6 cords of firewood
                                                                                   • Denise: 6 candy bars or 3 cords of firewood
                                                                                • they can produce any linear combination

Figure 10.6 Production Possibility Frontiers

         (a) Jane                      (b) Denise
                                                                                        Comparative advantage
        Firewood,                      Firewood,
            Cords                          Cords
                                                                                • they have different marginal rates of
                                                                                  transformation (MRT)
                                                                                   • abilities to change firewood into candy bars
                                                                                   • slope of the production possibility frontier
                6    1
                                                                                • thus, they can benefit from trade
                          MRT = –2
                                                                                • if they consume in equal proportions, they can
                                                    PPFd                          consume
                2                             2             1
                                                                        1          • 2 units of each without trade
                                                                MRT = – –
                                                                        2          • 3 units of each with trade
                          2 3                       2             6
                         Candy, Bars                            Candy, Bars

Figure 10.6 Comparative Advantage and Production
              Possibility Frontiers
                   (c) Joint Production
                                                                                                            More traders
                                                                                         • Harvey can produce 5 cords of wood, 5
                            9      1
                                       MRT = – – (Denise)
                                                                                           candy bars, or any combination
                                                                                         • if he trades with Jane and Denise, all can
                                                                  MRT =
                                                                                         • more traders lead to a PPF that approaches a
                                                                                           concave surface

                                                     6         9
                                                          Candy, Bars

Solved Problem 10.3

                                                                                              Socially desirable decision-

             14                1
                                                                                                    making system
                       MRT = – – (Denise)
                                                                                         • should satisfy
             11                        PPF
                                                                                            • social preferences should be complete and transitive, as
                                                                                              are individual preferences
                                             1                                              • if everyone prefers Allocation a to Allocation b, then a
                                                 MRT = –1 (Harvey)                            should be socially preferred to b
                                                                                            • society's ranking of a and b should depend only on
              6                                                                               individuals' ordering of these two allocations (not on
                                                                                              how they rank other alternatives) independence of
                                                           1                                  irrelevant alternatives
                                                                 MRT = – 2 (Jane)        • dictatorship not allowed: social preferences must
                                                                                           not reflect preferences of only a single individual
                                   6                 11           14       Candy, Bars

 Edgeworth Box
                                                                                                         Edgeworth Box

   • It can be
     used to
     explain how
     is efficient

                                                     A competitive
             Edgeworth Box
                                                     • In a perfectly
                                                       market prices
                                                       adjust so that the
                                                       quantity supplied
                                                       is equal to the

     A competitive equilibrium                            A competitive equilibrium

                                                     • A perfectly competitive equilibrium is
                                                       efficient because MRS=MRT for all
                                                       producers and consumers
                                                     • This is because MRS is made equal to the
                                                       ratio of prices for all consumers (so that
                                                       they maximize utility) and also equal to the
                                                       MRT for each producer who wants to
                                                       maximize profit

     A competitive equilibrium                            A competitive equilibrium
• There is no way to rearrange things in
  consumption or in production in such a way that
  someone can be made better off without having to
  make someone else worse off
• Whether this is fair or not is another issue!!!
• But remember any of the Pareto efficient results
  can be achieved given a suitable reallocation of
  initial endowments
• Society can choose which of the many competitive
  equilibria possible is most desirable, more
  equitable for example.

     A competitive equilibrium                                  Arrow’s impossibility Theorem
                                             Rawls proposed
                                             this type of     • Arrow’s impossibility theorem, or
                                             social welfare     Arrow’s paradox demonstrates the
                                                                impossibility of designing a set of rules for
                                                                social decision making that would obey
                                                                every ‘reasonable’ criterion required by

 Arrow’s impossibility Theorem                                  Arrow’s impossibility Theorem
                                                              • unrestricted domain or universality: the social
• A society needs to agree on a preference order                choice function should be complete (be able to
                                                                rank every possible set of individual preference
  among several different options. Each individual              orders)
  in the society has a particular personal preference         • non-imposition or citizen sovereignty: every
  order.                                                        possible societal preference order should be
• The problem is to find a social choice function,              achievable by some set of individual preference
  which transforms the set of preference orders, one
                                                              • non-dictatorship: the social choice function
  for each individual, into a global societal                   should not simply follow someone’s preferences
  preference order. It should have several desirable            while ignoring all others.

 Arrow’s impossibility Theorem
                                                                Arrow’s impossibility Theorem
• unanimity or Pareto efficiency: if every
  individual prefers a certain option to another, then
  so must the resulting societal preference order.            • Arrow’s theorem says that if the decision-
• independence of irrelevant alternatives: if we                making body has at least two members and
  restrict attention to a subset of options, and apply          at least three options to decide among, then
  the social choice function only to those, then the
  result should be compatible with the outcome for              it is impossible to design a social choice
  the whole set of options. (Changes in individuals’            function that satisfies all these conditions at
  rankings of “irrelevant” alternatives [i.e., ones             once.
  outside the subset] should have no impact on the
  societal ranking of the “relevant” subset.)

• competition produces Pareto
  efficiency…but monopoly does not!
• We will study monopoly next
• Then other types of market structure
• After that, other reasons why markets are
  non-competitive and therefore fail to
  achieve efficiency
• Read Ch. 11!!!


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