Lecture 1 Oligopoly, Entry Investment

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              Cournot competition
                         Free entry
    Investment and strategic effects

Lecture 1: Oligopoly, Entry & Investment
         MFE Industrial Organization 2009

                         Charles Roddie

                      Nuffield College, Oxford


                    Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
                       Cournot competition
                                  Free entry
             Investment and strategic effects

Cournot competition

     n firms, costs Ci (qi ), market demand function D(p), inverse
     demand function P(Q) = D −1 (Q).
     Each firm chooses qi to maximize profit π = qi P(Q) − Ci (qi ),
     where Q = qj , given choices of other firms: Nash
     First-order condition for maximum:
     δqi = P(Q) + qi P (Q) − Ci (qi ) = 0.
     Simultaneous solution of these equations is NE.

                             Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
Constant returns to scale, identical firms

      Cost c.q for producing q.
      Linear demand D(p) = A − Bp
      Implies P(Q) =     B .
      FOCs: A−Q +
              B      qi B −    c = 0 or Q + qi = A − B.c; assume
      A − B.c > 0.
      So qi s are identical, qi = Q and Q = nq, and
      (n + 1)q = A − Bc; Q = n+1 (A − B.c) and
                   1   A
      P(Q) = c + n+1 ( B − c) > c
      Profit per firm
                             1    A            1    1
      π = q.(P(Q) − c) = q. n+1 ( B − c) =   (n+1)2 B
                                                      (A   − Bc)2
Efficiency measurement

     One measurement of efficiency is “total surplus”, sum of:
         producer surplus = profits
         consumer surplus=what market is worth to consumers
                                                        1 (A−BC )2
     Competitive market maximizes surplus:              2    B       (see
     graphs). Call this Smax .
         all goes to consumer
     Here producer surplus is n.π = 2 (n+1)2 Smax
     Consumer surplus, since demand is linear, is
          1    A             1 n                 n    A            n
          2 Q( B   − P)] =   2 n+1 (A   − B.c)[ n+1 ( B − c)] = ( n+1 )2 Smax
     Difference is “deadweight loss”,                 S
                                               (n+1)2 max
Graphs: A Monopolist’s Marginal Revenue
  Marginal revenue of an extra unit:
      Earn the price on the unit, but
      depress price on existing sales
  MR is below the demand curve, MR = P − Q.P (Q)
Graphs: An Oligopolist’s Marginal Revenue
      Firm produces a share of output,
      feels price depression on less,
                                           Q.P (Q)
      hence MR is higher, MR = P −            n    .
  E.g., duopoly:   2   the price depression.
Surplus analysis
Surplus: numbers

     Increasing entry reduces concentration, enhances performance.
     Write performance as a percentage of maximum feasible value

   No. of Firms       1      2      3      4      5   ...      ∞
   Single Firm π   50.0   22.2   12.5    8.0    5.6   ...     0.0
   Industry π      50.0   44.4   37.5   32.0   27.8   ...     0.0
   Cons. Surplus   25.0   44.4   56.3   64.0   69.4   ...   100.0
   Surplus         75.0   88.9   93.8   96.0   97.2   ...   100.0
   DWL             25.0   11.1    6.2    4.0    2.8   ...     0.0

     With 5+ firms, performance is close to perfect competition.
Discussion: What if costs are different?

      In a competitive setting
          Only firm(s) with lowest cost produce; price=lowest cost
      In an oligopoly setting
          A range of firms still produce
               lower cost firms produce a greater share, make greater profits.
               no production for firms above a certain cost
               entry would help
                        Cournot competition
                                   Free entry
              Investment and strategic effects

What if there is free entry?

      Firms decide simultaneously whether to enter market, how
      much to produce
      Just like oligopoly with infinite number of firms:
          competitive prices, total quantities; surplus maximization, all
          going to consumers

                              Charles Roddie    Lecture 1: Oligopoly, Entry & Investment
Fixed costs and increasing returns to scale

      Assume identical firms again
      Analysis above extends to diminshing returns to scale without
      major differences
          more competition leads to efficiency, competitive equilibrium,
          in a large market,
      What if there are increasing returns to scale?
          Fixed cost is special case (or limiting case)
          What happens in competitive equilibrium? No equilibrium
      If you could control actions of firms, what is most efficient
      Discussion: examples of fixed costs, increasing returns to scale
Fixed costs and free entry

      Suppose firm has to pay fixed cost F to enter market.
      Model: firms decide to enter; once they enter, there is
      Cournot competition equilibrium
      Equilibrium number of firms entering:
          Given by: if one more firm were to enter, profits would be less
          than zero
                                 1   1               2
          n of firms given by: (n+1)2 B (A − Bc)2 = (n+1)2 Smax ≥ F :
          maximal n satisfying this
          approximately n ≈ 2Smax /F − 1: does this fit reality? (see
Fixed costs and entry: total surplus analysis

      Effect of firm entering on total surplus:
           Increase in total surplus when fixed costs are ignored:
                DWL is (n+1)2 Smax
                Change is (take derivative): − (n+1)3 Smax : very small compared
                to F
           Additional fixed cost F
      How do they compare?             S
                                 (n+2)2 max
                                               < F so
          2                   2               2               (n+2)2
      [ (n+1)3 Smax ]/F > [ (n+1)3 Smax ]/[ (n+2)2 Smax ] =   (n+1)3
      when n > 1
      So if there is more than one firm, the last firm is decreasing
      total surplus.
      Calculation not very revealing; you don’t need to know it.
Excess entry

      “Business-stealing” effect: when a firm enters, it causes other
      firms to reduce quantities - an efficiency loss. It doesn’t
      internalize this: See Mankiw & Whinston (1986)
      Causes “excess entry”: entry is more than efficient level
      Efficient number of firms if you can control everything (first
      best): 1
      Number of firms that actually enter:       2Smax /F − 1
      Efficient if you can control only the number of firms:
      somewhere in between
          Under the specific conditions that isolate this effect

  “Regulatory Reform” by Armstrong, Cowan, and Vickers:
  “Does this result imply that partial liberalization—restricting the
  number of entrants—is a better policy than total liberalization? For
  a number of reasons we believe that it would be dangerous to draw
  any such conclusion.”
    1   Result may fail if the welfare measure puts more weight on
    2   Restricting entry may facilitate collusion.
    3   Intervention to limit entry may encounter information
    4   Excess entry ignores firm asymmetries.
    5   Equilibrium entry may be a result of entry-deterring behaviour.
    6   “Product diversity effect” of entry can reverse result.
Entry/exit in the automobile industry

      1913: Ford Assembly line
      High associated fixed costs likely played role in short and long
      Other factors such as technological exclusion
Industry examples: discussion

      What caused rises and drops in firm numbers in automobile
      and tyre industries?
      How well would the theory (prediction about number of firms)
      apply within industries today? Across industries?
          Variables: capital costs and increasing/constant/decreasing
          RTS, demand

     Suppose the cost varies according to investment
         Investing I leads to cost c(I).q, with c(I) decreasing in q
         Suppose all decisions are taken simultaneously by all firms?
              They decide investments and quantities and compete in
              Cournot competition.
              Effective cost function C (q) = min(C (I).q + I)
              Analysis same as before
         What if investment is done first?
Investment to influence expectations

      Suppose investment decisions are made before quantity
      production decisions
          Think of building factories and actually using them to produce
      How does this differ from the simultaneous game?
          If investment lowers costs of producing, what effect does that
          have on how the other player will behave?
      In what direction does it differ from equilibrium where
      everything is simultaneous?
          Do we get under/over-investment?
      What about Cournot competition?
Strategic effects: general principles

      Effects of investment on a firm’s profits:
          A direct effect. For instance, investment may lower its
          marginal cost.
          An own-action effect. It adjusts its output. But this is
          second-order (doesn’t affect FOC)
          A “strategic effect”. Competitors adjust their own actions.
      In a Cournot competition, the strategic effect of cost
      reduction helps:
          A firm’s expansion leads its competitors to contract their
          which raises price and helps the investing firm.
      In a price-setting Betrand competition, the strategic effect of
      cost reduction hinders:
          A firm’s cost reduction leads it to lower its price
          which prompts competitor price reductions, harming profits.
Theory: commitment

     Nash equilibrium with two players for simplicity:
      ∗          ∗    ∗         ∗
     a1 = BR1 (a2 ), a2 = BR2 (a1 ), best responses to each other
     That was simultaneous moves; suppose now one firm moves
         “Stackelberg leadership”
         Now a1 maximizes u1 (a1 , BR2 (a1 ))
         Do at least as well because you can always play a1 and do as
         well as before
                   ∗         ∗           ∗    ∗
              u1 (a1 , BR2 (a1 )) = u1 (a1 , a2 )
         But generally do better because there are now new strategic
         effects, since own action changes other’s action.
         Player 2 does better or worse depending on game.
     Examples: want to commit to higher quantities, higher prices,
     matching competitors prices, product quality, predatory pricing
Ways to effectively commit, fully or partially

      If you can’t move first/make a binding commitment to, say, a
      high quantity of production, what actions can you take to
      influence expectations?
      Quite a few:
          Investment was one example: only partial so not as good as
          full commitment, but it let other players know you can be
          expected to produce more.
          Repeatedly producing more (and building up a reputation):
          this is the most standard explanation in economics
          Appointing executives that want to increase market
          share/using contracts that reward this?

    Cournot competition: effect of number of firms on prices,
    profits, quantities, efficiency.
    The determinants of entry (and exit); possibility of excess
    entry under fixed costs/increasing RTS. Industry examples.
    Various factors that can hinder entry.
    Strategic effects: the effects benefits of commitment; how to
    achieve it. Influencing expectations via capital investment.