12. Market Entry and the Emergence of Perfect Competition

1
12. Market Entry and the Emergence of Perfect
Competition

• 12.1 The Need for Entry-Prevention Strategies
• monopolists profits will attract entrants, which
  diminishes the former monopolists profits. Hence
  he would like to prevent entry
• 12.2 Limit Pricing in the Bain, Modigliani,
  Sylos-Labini Model
• basic idea incumbent chooses a quantity high
  enough such that remaining demand is too low for
  entry to pay
• term limit pricing might appear a bit
  inconsistent since the strategic variable is
  quantity

2

• assumptions
• two periods pre-entry (t0) and entry (t1). In
  period 1 entrant decides whether to enter
• one established firm, incumbent, i, and one
  potential entrant, e
• consumers are not loyal, no switching costs
• demand does not change over time
• in period 0, i will commit to output level xi,
  which it will maintain in future periods
• e believes that if e enters i will maintain xi
  independent of es actions and market price
• last 2 assumptions are critical and problematic

3

• Blockading Market Entry
• assume linear inverse demand p a - b(qiqe)
• in period 0 qe 0, so i faces p a bqi
• profit maximum attains for qi qm (Fig 12.1)
• e faces residual demand p (a bqm) bqe,
  demand is shifted down (Fig 12.2)
• if residual demand is so low (always below
  average cost) that e cannot recover costs for any
  output, e will not enter
• entry is blockaded, i can prevent entry by simply
  producing monopoly quantity (and hence obtains
  the best possible outcome)
• depends of course on assumptions 5 and (in
  particular) 6

4

• Impeding Market Entry
• if the residual demand after i chooses qm is
  sufficient for e to make a profit (Fig 12.4),
  blockading entry by producing monopoly quantity
  is not possible
• but i can impede entry by producing a quantity
  qLgtqm that shifts residual demand further down
  such that it is tangent to es average cost curve
  and hence e cannot make profit (Fig 12.5)
• hence e will not enter
• qL is called limit quantity and the associated pL
  limit price
• qL is the smallest quantity and pL the highest
  price that impede entry

5

• 12.3 Criticisms of the Bain, Modigliani,
  Sylos-Labini Model Subgame Perfection
• game first stage (period 0) i chooses quantity,
  second stage (period 1) e decides whether to
  enter if e enters, third stage (period 1) i
  decides whether to stick to quantity from period
  0 (Fig 12.6)
• assumptions 5 and 6 say i threatens to stick to
  qL chosen in period 0 also in period 1
• but threat is not credible
• assume entrant will choose Cournot-equilibrium
  quantity if he enters
• by backward induction the only subgame-perfect
  equilibrium is qm in period 0, e enters, and
  then i changes quantity to Cournot-equilibrium
  quantity
• given that entry occurs, i should adapt level to
  best reply, hence it pays to enter, i maximizes
  in period 0
• how can incumbent commit to a quantity that
  deters entry?

6

• 12.4 Entry Prevention, Overinvestment, and the
  Dixit-Spence Model
• Consulting Report 12.2 overinvestiment in
  capacity makes threat of producing large quantity
  credible and entry deterrence subgame-perfect
  strategy
• model if firm has installed production capacity
  K, then marginal cost for quantity ltK is v, but
  for quantity gtK, marginal cost is vs.
• If a firm has excess capacity, i.e. more capital
  than needed, than for additional unit only
  additional variable inputs are needed, but if
  there is no excess capacity, then for each unit
  the capacity has to be extended (Fig 12.8)
• incumbent has capacity K, hence cost function is
• Ci(q,K)vqF for qltK, Ci(q,K)vqs(q-K)F for q ?
  K
• the entrant has not build capacity, hence cost
  function is
• Ce(q,K)(vs)qF, will enter only if fixed costs
  F can be covered

7

• due to fixed costs, reaction curve of e drops to
  0 at an output level of i that drives down prices
  far enough, call this quantity qL limit quantity
  (Fig 12.9)
• the reaction function of the incumbent depends on
  its capacity
• lower marginal cost implies a higher best
  response (because best response is quantity where
  MRMC)
• hence is reaction function Ri(0) for marginal
  cost vs (K0) is below Ri(Q(0)) for marginal
  cost v (K is large enough to satisfy whole demand
  at price 0)
• for intermediate capacity K, the reaction
  function Ri(K) is equal to Ri(Q(0)) for qltK and
  then drops down to Ri(0)
• game period 0 i chooses K, period 1 e decides
  whether to enter, period 2 quantities are chosen
  (simultaneously)
• if K0, outcome will be Cournot-equilibrium.
• But if K ?qL (and v is small enough), es best
  response would be to produce nothing and hence
  not to enter
• subgame perfect, because i chooses optimally
  after entry
• i builds capacity higher than monopoly quantity
  for MC vs

8

• 12.5 Perfect Competition as the Limit of
  Successful Entry When Entry Prevention Fails
• assume incumbent cannot prevent entry and there
  are eventually n firms
• output of firm 1 q1, etc, total output is Q
  q1... qn
• inverse demand p(Q)
• in case of monopoly the price is p MC/1-
  1/?(Q)
• now for firm i the marginal revenue is
  MRip(Q)(dp/dQ)qi
• rewrite MRip(Q) 1 (dp/dQ) (Q/p(Q)) (qi/Q)
• denote by qi/Q si firm is market share, then
• MRip(Q) 1- si / ?(Q)
• a profit maximizing oligopolist will choose qi
  such that MRiMCi, and hence p(Q) MCi / 1- si
  / ?(Q)
• thus the price markup will be smaller than in
  monopoly and is decreasing in si and hence in
  the number of firms price converges to marginal
  cost as number of firms goes to ?

9

• The Characteristics of Perfectly Competitive
  Markets
• as number of firm grows, price converges to
  marginal costs and hence to the
  welfare-maximizing outcome
• for a large number of firms, the demand a firm
  faces is essentially flat (infinitely elastic)
  it cannot influence the price and only decide how
  much to produce at a given price
• firms act as price takers, industry of
  price-taking firms constitutes a perfectly
  competitive market,
• characteristics of perfectly competitive markets
  
• many firms with insubstantial market shares
• free entry, no barriers to entry
• homogenous product, i.e. all firms produce the
  same
• perfect factor mobility, can move to and from
  other industries
• perfect information, all participants know price
  and potential profits

10

• Appendix Incomplete Information and Entry
  Prevention
• Milgrom-Roberts Model there are two possible
  technologies and hence two different possible
  marginal costs
• game period 0 nature determines the level of
  marginal cost for incumbent, only i is informed
  about his marginal cost
• period 1 incumbent acts as monopolist, selects
  quantity and earns profit
• period 2 entrant decides whether to enter (has
  fixed cost K) if yes, e learns is marginal
  costs they play Cournot-game
• assume e would not like to enter if i has low
  cost, but would like to enter if i has high cost
• then high cost incumbent would like to pretend to
  have low cost

11

• if es expected payoff against probability
  distribution of high and low is negative, there
  is pooling equilibrium both types of i produce
  low cost monopoly quantity, e does not enter
• if es expected payoff against probability
  distribution of high and low is positive, there
  is separating equilibrium low cost type produces
  high quantity (this may be larger than the low
  cost monopoly quantity) such that high cost type
  is better off with high cost monopoly and then
  entry, e enters if i chooses low quantity (i.e.
  monopoly quantity of the high cost incumbent) in
  period 1

12
13. Perfectly Competitive Markets

• If a monopolist cannot prevent market entry,
  firms will enter as long as this pays
• if entry pays for many firms, this will
  eventually lead to a perfectly competitive
  market, with a large number of firms, free entry,
  a homogeneous product, factor mobility and
  complete information
• 13.1 Competitive Markets in the Short Run
• Quantity Decision of a Competitive Firm in the
  Short Run
• In the short run, there is no further entry and
  firms have at least one fixed factor, call this
  capital, hence average total cost differs from
  average variable cost (in long run all costs are
  variable) (Fig 13.1)
• in perfectly competitive market a firm has no
  influence on the price, so MRp and hence the
  firm will choose a quantity such that pMC if
  p?AVC, and q0 if pltAVC
• the price need not cover the ATC because fixed
  cost are sunk

13

• Supply Function of a Competitive Firm in the
  Short Run
• supply function specifies how much a firm would
  be willing to sell at each possible price
• this quantity is the one where pMC unless pltAVC,
  hence unless MCltAVC, i.e. unless q is smaller
  than the quantity q0 where AVC is minimal or p is
  smaller than p0MC(q0)
• thus supply curve coincides with MC curve above
  (p0,q0) and is 0 below p0 (Fig 13.2)
• The Market Supply Curve
• like market demand curve, market supply curve or
  aggregate supply curve is obtained by
  horizontally adding the individual firms supply
  curves the result is the aggregate short-run
  marginal cost of supplying each unit (Fig 13.3)

14

• Price Determination and the Definition of a
  Short-Run Equilibrium in a Competitive Market
• a short-run equilibrium for a competitive market
  is price-quantity combination such that
• no firm wishes to change the quantity it supplies
• no consumer wishes to change the quantity he
  demands
• the aggregate supply equals the aggregate demand
• this means there is no force to change price or
  quantity
• equilibrium is at the intersection of supply and
  demand
• otherwise firms would offer lower prices (if SgtD)
  or consumers higher prices (if DgtS) (Fig 13.4)
• In short-run equilibrium firms can make positive
  profits, which may differ according to their
  individual cost structure (Fig 13.5)

15

• Policy Analysis in the Short Run Comparative
  Static Analysis
• Policy changes can be evaluated by comparative
  static analysis, i.e. comparing the static
  equilibria before and after the change (e.g. in
  terms of consumer surplus)
• in a dynamic analysis the path how the market
  moves from old to new equilibrium is examined
• Example 13.1 Market for Illegal Drugs
• increasing prosecution of trade of illegal drugs
  increases costs for dealers and users
• targeting the dealers will shift up the supply
  curve, leading to a smaller quantity and a higher
  price
• targeting the users will shift down the demand
  curve, leading to a smaller quantity and a lower
  price
• the most effective strategy depends on which side
  is more sensitive to punishments (Fig 13.7)

16

• Example 13.2 the Incidence of a Tax
• who is actually paying a tax, i.e. if a tax is
  levied on producers, will this simply lead to an
  increase in prices?
• the incidence of a tax, i.e. the ultimate
  distribution of the burden depends on the
  elasticity of demand (and supply)
• if demand is perfectly inelastic, the consumers
  carry the whole burden, if it is perfectly
  inelastic, the producers do, for intermediate
  levels both share the burden, with the share of
  the producers increasing in the elasticity of the
  demand (Fig 13.8)
• Tax Liability Side Equivalence it does not
  matter which side of the market a tax is levied
  on, i.e. for the economic incidence of the tax,
  the statutory (legal) incidence is irrelevant
• Experimental Evidence Borck et al. (SEJ, 2002)
  in posted-offer markets tax liability side
  equivalence is confirmed net prices do not
  differ between treatments where either buyers or
  sellers pay the tax

17
Figure 2 Summary of experimental results (?
SellerTax, ? BuyerTax)
18

• Example 13.3 Minimum Wage
• installing a minimum wage above the equilibrium
  wage will lead to lower employment but a higher
  wage for those employed (Fig 13.9)
• since unemployment might increase susceptibility
  for crime, abolishing minimum wage might appear
  an effective crime prevention strategy
• but low wages (as in equilibrium) may make crime
  appear an alternative option as well
• hence more effective might be to subsidize wages
  for low-skill workers, this leads to both higher
  wages and more employment (Fig 13.10)
• disadvantages can be quite costly and leads to
  inefficiencies the marginal workers are paid
  more than their marginal product

19

• 13.3 Competitive Markets in the Long Run
• The Long-Run Equilibrium for Identical Firms
• in a short-run equilibrium, firms can make
  extra-normal profits
• but this situation cannot continue in the long
  run as long as firms make extra-normal profits,
  this will attract entry
• long-run equilibrium is a price-quantity
  combination such that
• no firm wishes to change the amount it supplies
• no consumer wishes to change the amount he
  demands
• no firm in the market has an incentive to change
  the combination of inputs it uses or to exit the
  market
• no firm outside the market has an incentive to
  enter it
• the aggregate supply equals the aggregate demand
• extends short-run requirements by absence of
  incentives for entry and exit and capital
  expansion

20

• if a firm makes extra-normal profits at the price
  that is determined by the intersection of
  aggregate supply and aggregate demand, and its
  optimal long-run level of capital and its profit
  maximizing quantity (i.e. where p long-run
  marginal cost), this will attract other firms to
  enter, which will shift the supply curve to the
  right (Fig 13.20)
• the incentive for new firms to enter disappears
  when firms in the market do not make extra-normal
  profits, hence when the price equals the minimal
  long-run average cost (where they are equal to
  long-run marginal costs)
• thus in long-run equilibrium firms use amount of
  capital that allows them to produce at minimal
  long-run average cost
• The Long-Run Equilibrium for Heterogeneous Firms
• if a firm has a lower cost due to a special
  factor, it earns an economic rent. Since this
  factor could be sold, the price the firm could
  obtain is the opportunity cost of using the
  factor including this opportunity cost in the
  total cost, the firm does not make extra-normal
  profits

21

• Dynamic Changes in Market Equilibria
• in the short run an increase in demand leads to a
  higher price, because the short-run supply curve
  is upward sloping
• this implies firms in the market make
  extra-normal profits
• this attracts new firms, which shifts supply
  curve right
• if the industry has only a small share in the
  input markets, entry will not affect input prices
  (Fig 13.23)
• entry does not change costs of existing or new
  firms
• long-run supply curve is flat constant-cost
  industry
• if supplying more inputs is increasingly costly,
  entry has a pecuniary externality on the market,
  because it increases cost for existing firms
  increasing-cost industry
• long-run supply curve is upward sloping
• if the supplier of an input has increasing
  returns to scale, prices for inputs can decrease
  by entry decreasing-cost industry
• long-run supply curve is downward-sloping

22

• Why Are Long-Run Competitive Equilibria So Good?
• Welfare Proposition 1 Consumer and Producer
  Surplus Are Maximized
• at any smaller quantity there is a dead-weight
  loss, at any larger quantity marginal cost
  exceeds willingness to pay
• Welfare Proposition 2 Price Is Set at Marginal
  Cost
• In long-run equilibrium of competitive industry
  price is at intersection of supply and demand and
  supply equals MC
• Welfare Proposition 3 Goods Are Produced at the
  Lowest Possible Cost and in the Most Efficient
  Manner
• If firms do not produce with the level of capital
  that minimizes average cost, they earn
  extra-normal profits that attract entry
• Production is organized efficiently among firms
• output shares are allocated such that all firms
  have the same marginal cost if C(qi)gtC(qk),
  the same output could be obtained at lower cost
  by decreasing qi and increasing qk

23

• 13.2 Market Institutions and Market Equilibria
• the analysis so far has been institution-free,
  ignoring the specific rules that organize
  behavior in different markets
• does it depend on the rules that organize a
  market whether a market equilibrium is reached?
• this has been investigated in thousands of
  experiments (notably by Vernon Smith, Nobel Prize
  Laureate 2002)
• these experiments use induced demand and supply
  curves, i.e. buyers are paid by the experimenter
  a predetermined value for each (fictitious) unit
  purchased and sellers have to pay the
  experimenter a cost for each unit they sells
• buyers have incentive to buy for a price as low
  as possible, sellers have incentive to sell for a
  price as high as possible
• this allows the experimenter to compare
  experimentally different market institutions with
  exactly the same supply and demand schedules,
  hence isolating the effect of the market
  institution

24

• examples for market institutions
• double oral auction buyers and sellers shout
  bids and offers simultaneously and at any time
  each buyer or seller can accept the best standing
  offer or bid
• one-sided oral auction only the buyers (or the
  sellers) can make bids (or offers) the sellers
  (or buyers) can only accept the best standing bid
  (or offer)
• experimental results double oral auctions
  converge quickly to market equilibrium, one-sided
  oral auctions tend to favor the passive side
• Note with upward-sloping supply and
  downward-sloping demand, the competitive
  equilibrium does not maximize the number of units
  sold, but it does maximize the total surplus

25

• Other Auction Institutions
• an auction is a market institution to sell (or
  buy) an object where potential buyers make bids
  and the outcome (who obtains the good and who
  pays how much) depends only on the bids
• hence auctions are universal any object can be
  sold by any auction, and anonymous the result
  for a bidder does only depend on the bids, but
  not on his identity
• examples
• English auction bidders openly place increasing
  bids
• Dutch auction price starts at high level and
  decreases until one buyer accepts
• Sealed-bid auctions bidders submit written bids,
  highest wins
• First-price auction winner pays his bid
• Second-price auction winner pays second highest
  bid
• Dutch and first-price sealed-bid auctions are
  strategically equivalent they define the same
  game choose a number, the highest number wins
  and the winner pays his bid

26

• auctions can be differentiated into
• private value auctions each bidder has an
  independent value of the object, knows only his
  own value (e.g. works of art)
• (pure) common value auctions there is an
  objective value of the object, identical for all
  bidders value is unknown, but each bidder has
  some signal of this value (e.g. oil field)
• Private Value Auctions
• Outcomes in English and second-price auctions are
  identical in both it is a weakly dominant
  strategy to bid the own value hence the bidder
  with the highest value wins (thus they are
  efficient) and pays the second highest value
• standard auction the bidder who bids the highest
  amount wins the object
• Revenue Equivalence Theorem if bidders values
  are drawn independently from the same
  distribution and all bidders are risk-neutral,
  then all standard auctions generate the same
  expected revenue, which is identical to the
  expected second highest value

27

• Common Value Auctions and the Winners Curse
• winning a common value auction brings bad news,
  because it means that the other bidders had
  information that led them to a lower estimate of
  the value
• not taking this into account leads to the
  winners curse, the winner of the auction pays
  too much
• assume you are bidding with a thousand other
  people for a jar full of 20 CZK coins if
  everybody bids his or her estimate, then if you
  win, it is extremely probable that your estimate
  was too high and hence you make a loss
• note that the winners curse does not occur in
  equilibrium equilibrium bids take it properly
  into account, by bidding the estimate of the
  value conditional on the own signal being the
  highest