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					Managerial Economics: Topic 9
Commitments and their effect on
   short-run competition
Commitments that change the game from
   Bertrand to …
Soft commitments in Bertrand
Tough commitments in Cournot
The Bigger Game
    We viewed the process of reaching a price through
     bargaining as part of a bigger game
                                        Bargaining
    Firm 1 makes    Firm 2 makes
    commitment      commitment          Bargaining

                                        Bargaining


    Now: view the process of reaching a price in competition
     as part of a bigger game
                                       Price/Quantity Competition
                    Firm 2 makes
    Firm 1 makes
                    commitment         Price/Quantity Competition
    commitment
                    or takes action
                                       Price/Quantity Competition
    Bertrand competition = price war!
   Extreme result: P = MC, even with only 2
    competitors.
   Competitors are likely to try and change the game:


     Limit their capacity = part A
     Differentiate their products = part B
     Merge (then they’d earn monopoly profits)
     Collude (illegal) or tacitly collude = ethically
      dubious, Topic 10!
A. Commitments that change the
   game from Bertrand to …

    1.   Limited stock
    2.   Limited capacity
What if firms have limited capacity to
meet demand? = a credible commitment
1. Limited stock:
 Shell and Mobil have pumped oil & shipped it to market.
 Galleria and Travelite are competing in the market for
    (identical) Melbourne souvenir Tee-shirts. There is limited
    stock in the store on any given day.

2. Limited productive capacity:
 Brunetti’s and the MBS coffee-shop have 1 espresso
    machine each  there is a limit to how many coffees they
    can produce in an hour (as we know!)
 Turbine generators: they can be ordered before they’re
    produced, but there is a backlog--only so many in a month.
Case 1. Limited stock
   Galleria and Travelite are competing in the market for
    sheepskin coats; the coats are identical, from the point of
    view of a tourist.
   The demand curve is Q=1000 – P per day

       Both companies face a marginal cost of $200 to produce the
        coats
       Once the coats are produced, they can be sold on the secondary
        market for $200

What happens today if Galleria stocks 400 coats and
 Travelite stocks 200 coats? (no re-stocking today)
Case 1. Limited stock
          Price         If the firms charged
                        P=MC=$200,
         $1000          customers would
                        demand 800 coats
                        = more than stock!
          $700




          $400
                                                Q
      MC= $200


                  300      600    800    1000
The game with limited stock:
   Galleria stocks 400 coats and Travelite stocks 200 coats
    today.
   Suppose the firms are currently charging $700, and selling
    150 each: is that a Nash equilibrium?
     No, each firm has a incentive to undercut the price and
       thereby sell more
     Price falls lower
   Suppose the market price falls to $400:
     Each firm could sell 300, if they had the stock
     In fact, Travelite doesn’t have the stock  some of its
       customers go to Galleria
     Travelite sells 200 and Galleria sells the rest (400)
   Is $400 a Nash equilibrium? Or does price fall to $200? Does
    the price fall lower?
 The new game with limited stock:
When the total stock is 600 = 400 + 200
 The price will not fall below $400, because at $400
  there is no incentive for either firm to cut its price
  further
 Cutting price at that point doesn’t increase your sales,
  it just lowers the price paid by customers



   Firms set the price to clear all the stock: P = $400
   $400 is the Nash equilibrium price
    Q: How do they decide how much to stock?
    Galleria is trying to choose the amount that it will stock, while Travelite is
     simultaneously choosing the amount that it will stock
    If their total quantity is above 800, the amount they stock is the amount
     they will sell, at the price that clears their shelves
    They sell their whole stock, at the market-clearing price
    Does this sound familiar?

  It’s the Cournot game! Choose how much to supply to the market, at the
   same time as your competitor is choosing how much to supply.
 your stock = the quantity you will supply to the market


  This explains why you end up in Cournot competition, if you have to
   choose your output before getting to market:
 Galleria & Travelite stock the Cournot quantity.
    Application: in-class exercise
Donnini’s and Ginevra’s both sell identical fresh pasta products on Lygon St
  They produce pasta early in the morning.
  Demand for fresh pasta is Q=80 - P per day (where quantities are
   measured in pounds)
  Marginal cost of each firm is $20
  Pasta is perishable, so they cannot sell it the following day. But they can
   sell any leftovers to an (undiscriminating) restaurant wholesaler that
   night, for $10 per pound.

1) What price do they charge?
2) Suppose that this Monday, after they produced, they realise that demand
    is unusually low: based on the first hour, they determine demand will be
    Q=55 - P that day. What price do they charge?
3) What about if the unusually low demand were Q=45 - P?
What is the relevant Marginal Cost?
Once they’re in the market, the amount they spent to make
  the pasta is irrelevant
  = it’s a sunk cost.
   the $20 per pound to make the pasta does not affect
  market behaviour.

But they will never price below $10 a pound. Why not?
 If they were selling for $8 a pound, they would be
   making an economic loss
 They’re worse off than if they sold to the wholesaler.

 $10 per pound is the relevant marginal cost.
 Case 2. Limited productive capacity
   Suppose there are only two coffee shops in Parkville, and they are
    next door to each other on Royal Parade:
        Grinders’ and Trilussa.
   They face a daily demand curve for coffees of Q=1000 – 250P
   Marginal cost of each firm (the cost of coffee, milk, and labour) is
    $0.80

Suppose
  Grinders’ has one espresso machine, which can produce 200
   coffees per day
  Trilussa has two espresso machines, and so can produce 400
   coffees per day

What is the equilibrium price?
Case 2. Limited productive capacity
        Price         If the firms charged
                      P=MC=$0.80,
          $4          customers would
                      demand 800 coffees
                      a day.

        $2.80




        $1.60

    MC= $0.80


                300     600    800    1000   Q
The new capacity game:
   Grinders’ has capacity of 200, Trilussa has capacity 400
   Suppose the firms are currently charging $2.80, and
    selling 150 each: is that a Nash equilibrium?
     No, each firm has a incentive to undercut the price and thereby
      sell more
     Price falls lower

   Suppose the market price falls to $1.60:
     Each firm could sell 300, if they had the capacity
     In fact, Trilussa doesn’t have the capacity
     Trilussa sells 200 and Grinders’ sells the rest (400)
   Is $2.80 a Nash equilibrium? Or does price fall to $1.60?
    Does the price fall lower?
The new capacity game:

   The price will not fall below $1.60, because at $1.60
    there is no incentive for either firm to cut its price further
   They price to use up their full capacity

   Now suppose total capacity is more than 800
     (800 is the quantity demanded when P=MC)
   Then it’s Bertrand equilibrium, again.
 The new capacity game:
If total capacity is less than demand at P=MC:

    Firms will produce up to full capacity, and charge the
     market-clearing price
    = no incentive to under-cut each other, if they cannot sell
     more by doing so

    They want to restrict capacity
    Remaining question: how do they choose their
     capacities?
Summary:
What is the source of “Cournot” competition?

Case 1. Quantity decisions have to be made a long time before sale
           Firms choose the quantity they want to produce without
            knowledge of others’ choices
           (or, equivalently, firms choose the amount they stock without
            knowledge of others’ choices of stock levels; all stock is sold)
           They will choose to produce/stock the Cournot quantity, and
            price so that both firms sell their whole stock.
(Case 2. Production on demand but limited capacities)
        = closely related situation, not identical
           Once they see each others’ capacities, they each charge the price
            at which they’re producing to full capacity.
 NO SELF CONTROL!
If firms are focused on maximising short term profits:
When they get to the market, they behave as if they have no self-
     control.
They can’t resist under-cutting each other to steal customers.
     = Bertrand behaviour
 ALL MARKETS are inherently Bertrand
 The only thing that stops the undercutting if is there is no way to steal
   any more customers:
Firms keep undercutting until
  Capacity of both firms completely used up (otherwise the one with
   extra capacity would undercut, and the other would be wary)
or
  Stock of both firms completely used up (otherwise the one with extra
   capacity would undercut, and the other would be wary)
or
  The firm has hit P=MC in its process of undercutting  stops.
Win-win commitments
 Both firms are aware that once they get to the market,
  their behaviour will be Bertrand.
 Both make commitments that (taken together) restrict
  their ability to undercut:
   Limit stock
   Limit capacity

    Galleria commits
    before the market:
    brings 267 coats               Higher profits in the market,
                                   even though market
                                   behaviour is Bertrand
    Travelite commits
    before the market:
    brings 267 coats
B. More win-win commitments:
   Soft commitments in Bertrand


   No maths in this section!
 Product differentiation
   Another way firms avoid the P = MC price war of Bertrand
    = differentiating their products—adding different features, etc.
      ex: Breakfast cereal!
   Extremely unusual for firms to sell exactly the same product!
Differentiating your product:
 eases competition, because some customers prefer your
    product to the other one, even if it’s a little more expensive
 creates more surplus, because now there’s more chance that a
    product corresponds to what a customer wants: if she doesn’t
    like product A, there’s always product B!
   How do we represent the effect of product differentiation?
West Milk Bar            Central Milk Bar                 East Milk Bar
$2.00                    $2.20                            $2.00



   Suppose your town has just one street with shops and residences.
   You want to buy milk, but some shops are closer to you than
    others. There are three milk bars, each two blocks apart. You live
    halfway between the Central and East Milk bars.
   You only care about price and distance from where you live 
    you go to the East Milk Bar.
   If everyone has a disutility of walking of $0.20 per block:
    People that are half a block from Central Milk Bar go there; the
    rest go to West or East.

West Milk Bar            Central                        East Milk Bar
$2.00                    $2.20                          $2.00
    Product differentiation, graphically
   Imagine a one-dimensional product characteristic distributed along a
    line (you could have more dimensions):
      Example: Breakfast cereals, going from less sweet to very sweet
   Imagine customers distributed along the same line: a line—every point
    on the line is someone’s ideal product
            Think of yourself as “residing” at your ideal product
            If you’re under 10, you probably prefer sweeter cereal
            this isn’t differentiation in quality (like horsepower in a car): no one direction is
             better for everyone
   A product that is not your ideal gives you less utility  your WTP is
    higher, the closer a product is to your ideal.
    (one way to think of it is as a “transportation cost”)

“Grape-Nuts”                        “Just Right”                           “Captain Crunch”

less sweet                                                                        very sweet
   For a given set of prices, there will be an allocation of the customers
    across the different products:



                          “Just Right” $4               “Captain Crunch” $4.50

 less sweet                                                    very sweet




       If all other products have chosen their price, you know how many
        customers you would get for each price you choose
       You can work out your best response curve
  Interesting difference from Cournot: best response curves are upward-
   sloping in differentiated Bertrand.
= if Captain Crunch cuts its price by $1, Just Right will probably cut its
   price too, but by less than $1, because it has some loyal customers (to
   the left), who are not swayed by the price of Captain Crunch.
Nash equilibrium = the stable outcome
       Just Right’s
       price.               Captn Crunch’s best
                            response

                                                  Just Right’s best
                                                  response




                                                        Captn Crunch’s
   “Best response” for each is graphed.                price.

   The intersection is a stable point (a Nash eq.).
   Product differentiation, graphically
    Differentiating your product from your competitor’s = moving it
     further away on the line from your competitor
    Disadvantage:
     = you are further away from your competitor’s customers, so
     you’re less attractive
    Advantage 1:
     = you’re closer to more remote customers, so their WTP goes up
    Advantage 2:
     = you compete much less intensely with your competitor.
   The shape of the best response curves is critical for differentiation to
     be profitable.
                            “Just Right”                   “Captain Crunch”

less sweet                                                       very sweet
Differentiation = a Soft commitment
                                Capn’ Crunch’s
     Just Right’s
     price.                     best response

                                                         Just Right’s
                                           B
                                                         best response

                                    A

                                                        Capn’ Crunch’s
                                                        price.

   A “soft” commitment means that Just Right wants to price higher, for
    every price of Capn’ Crunch
    (= a weaker position, but both benefit).
Tradeoff: Current profits vs. possible entry
We won’t discuss entry much in this class, but it’s obvious how
  you keep an entrant out in this market:
  = don’t leave enough “space” for her!
  = the reason for proliferation of varieties in cereal
                             ?




   “Leaving space” between you and your competitor eases
    competition
   But it might make it easier for a new competitor to enter!
    = that’s the tradeoff.
       That’s why new entrants often enter on the edges (with very weird
        products): sometimes incumbents don’t realise how far out demand
        extends…
 C. The Role of Tough
Commitments in Cournot
     competition
 Quantity Pre-commitments
In Cournot, reaction curves are downward sloping
 The more Shell expects Mobil competitor to produce, the less
    Shell wants to produce
 Mobil should pre-commit to producing more than it would
    otherwise want to (e.g. invest in mass-production equipment)
 Such pre-commitments cause rivals to back off and
    “accommodate” by producing less
 Numerical Example: Suppose that Mobil buys new
    equipment that reduces its marginal cost: MC falls from 200
    to 100.
      Now its best response curve is QM = 450 – ½QS (check this yourself,
       for practice!)
       (before it was QM = 400 – ½QS)
      Best response curve shifted up!
Tough quantity competition

  Mobil’s
  output

      450
            B
      400
                       Mobil’s best
            A          response
                  50


                            Shell’s output
Pre-commitments
   The commitment moves the equilibrium from A to B: at
    B, Shell is producing less than at A.
   CAREFUL! The commitment is only worth it if the firm
    earns more at B (after paying for the commitment)
       some commitments are too strong (you commit to producing way
        too much) or too expensive.
       you have to check that the commitment is worth it.
   When are quantity increases credible commitments?
       Reputation for high quantity
       Large supply or purchase contracts
       Cost leadership: investments in lower unit production costs
       Irreversible capacity investments
Pre-Emption
   Commitments change the game: now one or the
    other will try to commit

 Either firm may commit...
 But what happens if you can commit first?

 Other firm observes your action before choosing
  their own:
You gain a first-mover advantage
Case: Memory Chips
   Early 1980s: market dominated by US firms
   mid 1980s: Japanese firms (Toshiba, NEC) increased
    their investment in new capacity (while US firms
    didn’t)
   late 1980s: 80% of market controlled by Japanese firms
   1990s: massive investments by South Korean firms
    (Samsung, Hyundai) while the Japanese firms have not
    invested

 These investments are preceding market demand!
Stocking games versus capacity games
 Q = Why are capacity games “not exactly Cournot”?

    No long-term commitments available, in stocking games
        Amount of stock I bring in is a commitment “for the day”, but no
         more: if I brought in more stock today, that doesn’t change the
         game tomorrow
    But capacity = a one-time choice that lasts = a commitment
        If I’m stuck with the amount of capacity I build today
         (irreversible commitment), if you choose your capacity
         subsequently, you’ll choose a capacity that is a best response to
         mine.
  Firms will choose to make tough commitments in capacity (as
   in the memory chip industry)
NO TRADEOFF:
Current profits vs. possible entry
 Tough commitments are profitable against existing
  entrants, in Cournot (as long as you’re first, and they’re not
  too tough!)
 BUT tough commitments also keep entrants out

  (Why?)
 Interestingly, there is no tradeoff to make, in Cournot
  competition:
   tough commitments to improve current position
   tough commitments deter entry
 Only downside is that there can be a race to be the first to
  make a tough commitment.

				
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