15. General Equilibrium and the Origins of the Free-Market and Interventionist Ideologies

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15. General Equilibrium and the Origins of the
Free-Market and Interventionist Ideologies

• free-market advocates or laissez-faire advocates
  believe that government should not interfere with
  perfectly competitive markets, because these are
  efficient and supply goods at lowest possible
  costs
• interventionists believe that perfectly
  competitive markets are rather rare, that they do
  not always function as predicted and even if they
  do, the result might be unfair, so that
  government action is desirable
• furthermore, interventionists doubt that because
  perfectly competitive markets for individual
  goods produce desirable welfare outcomes, a
  perfectly competitive economy as a whole does so,
  too
• General equilibrium analysis studies the
  simultaneous equilibrium on markets for all goods
  

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• 15.1 The Free-Market Argument
• basic assumptions
• existing economy with given stock of capital and
  labor
• large number of people who are both consumers and
  producers
• consumers have convex preferences, producers
  convex technology
• for illustration 2 goods, 2 people one produces
  good 1, the other good 2
• aim allocate inputs efficiently in production,
  distribute goods efficiently to consumers
  (Pareto-efficiency)
• free-market argument beliefs
• perfect competition leads to efficient allocation
  of inputs
• competitive markets lead to efficient
  distribution of goods once they are produced
• the final product mix is determined by the income
  distribution that results from competitive market

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• Efficiency in Consumption
• given some output of the economy, the goods are
  efficiently distributed if the marginal rate of
  substitution between each pair of goods is the
  same for all consumers, allocation must lie on
  the contract curve
• otherwise if, e.g. two consumers have MRS 1/4 and
  1/2, they can both be better off by trading at a
  rate 1/3
• Efficiency in Production
• efficient allocation of inputs can be studied
  analogously
• in an Edgeworth box with dimension given by the
  existing labor force and capital stock, inputs
  spent on good 1 are measured from origin, on good
  2 from upper right
• when isoquants cross, there are other allocations
  of inputs that yield more of both goods (Fig
  15.2)
• hence in efficient allocation isoquants have to
  be tangent and therefore, the marginal rates of
  technical substitution have to be equal for all
  goods otherwise relative productivity of one
  factor is higher for one good than for another
  good

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• Consistency of Production and Consumption
• the various efficient allocations of inputs yield
  the production possibilities frontier that
  describes all combinations of goods that can be
  produced efficiently (Fig 15.3)
• its slope indicates how many units of good 2 have
  to be given up for an additional unit of good 1,
  the marginal rate of transformation (MRT)
• we have MRT2 for 1 MC1 / MC2
• a given product bundle on the frontier now spans
  an Edgeworth box, the points in it represent the
  possible allocations of goods (Fig 15.4)
• production and consumption are consistent for a
  point on the contract curve where MRT MRS for
  all consumers
• otherwise, if e.g. MRS gt MRT there is another
  efficient product mix (more of good 1 and less of
  good 2) that will make all consumers and
  producers better off

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• Perfectly Competitive Markets Satisfy the
  Conditions for Pareto Efficiency
• Efficiency in Consumption in perfectly
  competitive market, all consumers can buy as much
  as they want at identical prices they buy a
  combination such that MRS2 for 1 p1/p2 since
  all consumers do the same, all MRS are equal
• Efficiency in Production if factor markets are
  perfectly competitive, firms can buy inputs at
  identical costs they will use input combination
  such that MRTSc for l wl / wc since all firms
  do the same, all MRTS will be equal
• Consistency of Production and Consumption in a
  long-run equilibrium, prices equal marginal
  costs, hence p1/p2MC1/MC2. Since all consumers
  buy a combination such that MRS2 for 1 p1/p2
  MC1/MC2 and MC1/MC2MRT2 for 1,
  we get MRS2 for 1 MRT2 for 1, as required

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• The Two Fundamental Theorems of Welfare Economics
• first fundamental theorem of welfare economics
  every competitive equilibrium is a Pareto-optimal
  equilibrium for the economy
• second fundamental theorem of welfare economics
  every Pareto-optimal allocation can be achieved
  as a competitive equilibrium for an appropriate
  distribution of income
• hence if one wants to reach a specific
  Pareto-optimal outcome, only redistribution of
  income is necessary, but not intervention in the
  price mechanism of the markets
• thus if one considers Pareto-optimality as
  desirable, government intervention should be
  reduced to income redistribution

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• 15.2 The Interventionist Argument
• basic concern not only Pareto-optimality should
  be considered, but also equity
• in a perfectly competitive economy, for each
  point on the production possibility frontier, a
  Pareto-optimal distribution will be reached (Fig
  15.5)
• different product mixes lead to different utility
  combinations
• utilities possibilities frontier marks the
  maximal achievable utility combinations
• the product mix that is chosen depends on the
  distribution of wealth and labor (i.e. the
  individual productivity of labor)
• interventionists believe that endowments should
  not determine the utility
• hence government should intervene to reach more
  equitable level, even though this might not be
  Pareto-efficient

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• A Basis for Intervention Rawlsian Justice
• Rawls Maximin Justice the welfare of the least
  well-off person should be maximized
• Justification assume people decide upon
  distribution under a veil of ignorance, i.e.
  they do not know their position in society
• under such a veil of ignorance, they would
  probably agree to a distribution that maximizes
  well-being of the least well-off person, because
  they might be that person
• hence increasing inequality can be acceptable if
  the least well-off person is made better off
  (e.g. if tax cuts for the rich lead to more and
  better paid jobs for the poor)

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• A Free-Market Rebuttal to Rawls Nozicks Process
  Justice
• Process Justice if an outcome is reached by
  voluntary agreements of all people involved, it
  is justified
• Problem if the initial distribution of wealth is
  very unequal, even if all agents act voluntarily,
  it may stay unequal
• counter-argument (from a moderate free-market
  advocate) if one wants to rectify inequality,
  one should then redistribute income before market
  process starts, but not interfere with the market
  process
• Equitable Income Distribution Varians Envy-Free
  Justice
• envy-free allocation nobody prefers another
  agents bundle over their own
• envy-free allocation will be reached when all
  start with identical bundles and trade at
  competitive prices no agent will envy another
  because he could have had his bundle
• unequal distribution can be just when it is
  envy-free
• Problems utility levels can still differ,
  envy-freeness does not imply Pareto-efficiency
  and vice versa

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• 15.3 Institutional Failure Another
  Interventionist Argument
• institutions have developed to solve a multitude
  of problems
• perfectly competitive markets for exchange,
  insurance to cover risks, regulatory agencies to
  deal with monopolies
• a competitive market solves a problem
  efficiently so if one wants to reach efficiency,
  a problem that can be solved by a competitive
  market should be left to a market without
  intervention
• however, if problems include asymmetric
  information, public goods, externalities, moral
  hazard and incomplete information, markets do not
  work properly
• in these situations, markets do not only fail to
  reach equity but also efficiency
• non-market institutions may develop to solve the
  problem, but they do not necessarily work
  efficiently either
• if also non-market institutions fail,
  intervention may be necessary

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19. Input Markets and the Origins of Class
Conflict

• capital and labor are unevenly distributed, so
  income will be unequal as well
• this creates the potential for conflicts about
  the appropriate returns to the different factors
• 19.1 Why It Is Important to Determine the Return
  on Each Factor of Production
• apparently market economies are more efficient
  than central planning economies, but this does
  not mean that everybody is happy with the return
  on the factor they provide
• the division into workers, capitalists, and
  landowners provides a source of conflict
• the question is whether the returns are fair and
  reasonable
• hence we have to study how these returns are
  determined in competitive and noncompetitive
  markets

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• 19.2 The Return on Labor
• In an competitive market, the return on labor is
  determined by the supply and demand
• a firms demand for labor is determined by its
  desire to maximize profit, hence it is a derived
  demand
• the output due to an additional unit of labor is
  the marginal physical product due to diminishing
  returns to each factor, the MPP is decreasing
  (Fig 19.1)
• a profit-maximizing firm is interested in the
  increase of revenue an additional unit of labor
  yields, the marginal revenue product which is the
  MPP times the marginal revenue that the output
  yields, hence MRP MR MPP
• in perfectly competitive industry, MR p, MRP
  p MPP
• for a monopolist, the MR is falling, so the MRP
  curve is steeper than for a competitive firm (but
  the MR may initially be higher than p in a
  competitive market, so monopolists MRP does not
  have to be below competitive MRP everywhere) (Fig
  19.2)

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• the optimal quantity of labor is the one where
  the MRP is equal to the MC of labor
• given a perfectly competitive labor market, the
  MC is constant, the firm faces a constant market
  wage
• since a monopolist reduces output, its labor
  demand will be smaller than that of a competitive
  firm (more precisely, than that of a competitive
  industry) (Fig 19.3)
• a firms labor demand curve equals its MRP curve
• the market demand curve is given as usual by
  adding individual firms demand curves
  horizontally
• individual workers decide for each wage how much
  labor they want to supply by choosing optimal
  trade-off between leisure and consumption (this
  is likely to be increasing in some range, but not
  necessarily throughout, e.g. problem 19.2, labor
  supply is independent of wage)
• market supply curve is again horizontal sum
• equilibrium market wage is determined by supply
  demand

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• 19.3 Setting the Stage for Class Conflict
• given the market equilibrium wage w, a firm will
  hire labor up to the point where w MRP (Fig
  19.9)
• since the MRP is falling, the firm hence makes a
  surplus workers may demand a share of this
  surplus, firm argues that surplus is needed for
  return on capital and land
• 19.4 The Return on Capital
• capital consists of manufactured inputs, opposed
  to naturally occurring inputs labor and land
• building capital requires money, either borrowed
  or own
• costs are interest or opportunity cost of
  foregone interest
• if entrepreneurs need money for investments and
  others have savings to invest, institution is
  needed to match them
• financial markets develop
• how is the market interest rate determined?

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• The Supply of Loanable Funds
• given a interest rate, a consumer can trade off
  consumption today and consumption tomorrow (Fig
  19.10)
• for a sufficiently high interest rate the
  consumer would be willing to safe today to
  consume more tomorrow
• the optimal savings decision is such that
• MRStomorrow vs today 1 r, r interest rate
• if consumption tomorrow is a superior good, then
  higher interest rate implies more consumption
  tomorrow (but NOT necessarily less consumption
  today, i.e. higher savings)
• if higher interest imply higher savings, the
  supply of loanable funds is upward sloping (Figs
  19.11, 19.12)
• market supply is derived as usually by adding
  horizontally

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• The Demand for Loanable Funds
• an entrepreneur will take a loan and invest it if
  the expected rate of return of the investment is
  higher than the interest rate
• if an investment of C yields R in one period and
  C(1?) R, then ? is the rate of return
• for a long term investment of C that yields Rk in
  period k, the rate of return is given by ? such
  that
• C ?k Rk / (1?)k
• for a lower market interest rate more investment
  projects will be executed hence the demand curve
  is downward sloping
• market demand is again the horizontal sum
• in market equilibrium supply demand and the
  market interest rate equals the marginal rate of
  return

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• 19.5 The Return on Land
• a rent is the return on a factor in excess of the
  amount necessary to ensure that it will be
  supplied
• the supply of land is fixed, hence the same
  amount will be supplied at any return and hence
  the whole return is a rent
• the return will be determined by the demand alone
  (Fig 19.16)
• 19.6 Resolving the Claims of Different Factors of
  Production The Product Exhaustion Theorem
• marginal productivity theory each factor is paid
  its marginal contribution, i.e. labor is paid the
  MRP of the last worker, capital is paid the rate
  of return of the last unit
• a theory of income distribution should predict
  that the whole value of the goods produced will
  be distributed

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• product exhaustion theorem predicts this in
  long-run equilibrium, when all factors are paid
  their marginal revenue product, the sum equals
  the total value
• let x1,...,xn be the factors, and w1,...,wn be
  the prices and y be the quantity of output
  produced, then in competitive markets all factors
  are paid their MRP, so requirement is
• py w1x1 ... wnxn or p (w1x1 ... wnxn) /
  y
• this means the price of the good should equal the
  long-run average cost, but this holds in long-run
  equilibrium of a perfectly competitive market
• however, workers could argue that they want a
  higher wage at the expense of the return on land,
  because the supply of land would not be reduced

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• 19.7 Determining the Return on Labor in Markets
  That Are Less Than Perfectly Competitive
• labor markets can be less than perfectly
  competitive a union that encompasses all workers
  in an industry is a monopolist, a factory in a
  small town with no other major employers is
  essentially a monopsonist, the only buyer
• an employer in a perfectly competitive labor
  market faces an infinitely elastic supply curve
  and cannot affect wages
• an employer who has a monopsony faces an
  upward-sloping supply curve and hence has a
  choice about the wage level
• if the monopsonist cannot apply wage
  discrimination, i.e. has to pay the same wage to
  all workers, there is an incentive to lower the
  demand to reduce the wage
• the marginal expenditure (ME) is the increase of
  total wage due to hiring one more worker
• ME w in perfectly competitive market, but for
  monopsonist ME w (dw/dL) L and hence ME is
  above supply curve

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• in a perfectly competitive market, the
  equilibrium would be where marginal revenue
  product supply (Fig 19.17)
• a monopolist will hire labor up to the point
  where MRPME
• the wage that he offers is given on the supply
  curve for that employment level
• MRP ME w(dw/dL)Lw 1(dw/dL) (L/w) w
  (11/?)
• where ? being the elasticity of labor supply
• rearranging yields (MRP w) / w 1 / ?
• hence the less elastic the labor supply, the more
  is labor paid below its marginal revenue product,
  or the stronger is the monopsonistic exploitation

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• in a bilateral monopoly there is only one buyer
  and one seller, e.g. only one employer and one
  labor union where all workers are organized
• we cannot follow the approach of monopoly and
  monopsony to treat one side of the market as
  price takers and let the other optimize
  unionized workers will not simply accept a
  monopsonistic wage monopsonist will not simply
  accept a monopoly wage set by the union
• if the union treats the monopsonist as a price
  taker, i.e. assumes that the demand is given by
  the MRP curve, the union will choose a quantity
  such that its marginal revenue (ltdemand) equals
  the marginal cost (Fig 19.18)
• hence both with monopsonist and with monopolistic
  union, the amount of labor would be below
  equilibrium
• in bilateral monopoly, no side is a price taker
  the wage depends on the bargaining power of firm
  and union

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• The Alternating Offer Sequential Bargaining
  Institution as a Stylized Model of Bargaining in
  Bilateral Monopoly
• time is divided in discrete periods (say here 3
  periods)
• the pie to be split shrinks from period to period
• in period 1, player A (say the employer) makes a
  proposal
• if B (the union) accepts, the proposal is
  implemented and the game ends
• if B rejects, period 2 starts the pie shrinks
  and B makes a proposal
• if A accepts, Bs proposal is implemented and the
  game ends
• if A rejects, in period 3 the pie shrinks and A
  makes a new proposal
• if B accepts, the proposal is implemented, if B
  rejects, both get 0, the game is over
• a game with more than 3 periods just continues in
  the same way

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• theorem there is a unique subgame perfect
  equilibrium, where the first offer is accepted
  and each player obtains the sum of the decrements
  of the pie when his or her offers are rejected
• proof backward induction in the last period n
  the player who makes the offer (E) obtains the
  whole pie x (-?)
• hence in period n-1, player D has to offer E
  exactly x (E would reject any lower offer)
• but that means if in period n-1 the pie is y, D
  suggests to keep y-x for himself
• hence in period n-2, E has to offer D y-x
• so if in period n-2 the pie is z, E can suggest
  to keep
• z-(y-x) (z-y)x which is the sum of the
  decrements of the pie in periods n and n-2, where
  E chooses
• by repeated application of the same argument we
  see that both players get the total amount by
  which the pie decreases if their respective
  offers are rejected
• experimental evidence subjects do one period
  b.i., not more