Chapter 21 Monopoly

1
Chapter 21Monopoly

1. Auctions and Monopoly
2. Prices and Quantities
3. Segmenting the Market

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1. Auctions and Monopoly
We begin this chapter by putting auctions in a
more general context to highlight the
similarities and differences between auctions and
monopolies. In this spirit we investigate the
sale of multiple units by auction, to see when
the selling mechanism affects the outcome, and
how. Within the context of a multiple unit
auction we derive our first result in finance,
the efficient markets hypothesis, that in its
simplest form, states prices of stocks follow a
random walk.
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Are auctions just like monopolies?

• Monopoly is defined by the phrase single
  seller, but that would seem to characterize an
  auctioneer too.
• Is there a difference, or can we apply everything
  we know about a monopolist to an auctioneer, and
  vice versa?
• We now begin to make the transition between
  auctions and markets by noting the similarities
  and differences.

4
Two main differences between most auction and
monopoly models

• The two main differences distinguishing models
  of monopoly from a auction models are related to
  the quantity of the good sold
• Monopolists typically sell multiple units, but
  most auction models analyze the sale of a single
  unit. In practice, though, auctioneers often sell
  multiple units of the same item.
• Monopolists choose the quantity to supply, but
  most models of auctions focus on the sale of a
  fixed number of units. But in reality the use of
  reservation prices in auctions endogenously
  determines the number the units sold.

5
Other differences between most auction and
monopoly models

1. Monopolists price discriminate through market
   segmentation, but auction rules do not make the
   winners payment depend on his type. However
   holding auctions with multiple rounds (for
   example restricting entry to qualified bidders in
   certain auctions) segments the market and thus
   enables price discrimination.
2. A firm with a monopoly in two or more markets can
   sometimes increase its value by bundling goods
   together rather than selling each one
   individually. While auction models do not
   typically explore these effects, auctioneers also
   bundle goods together into lots to be sold as
   indivisible units.

6
An agenda for the first portion ofour work on
monopoly

• We will focus on two issues
• How does a multiunit auction differ from a single
  unit auction?
• What can we learn about market behavior from
  multiunit auctions?

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Auctioning multiple units to single unit
demanders

• Suppose there are exactly Q identical units of a
  good up for auction, all of which must be sold.
• As before we shall suppose there are N bidders or
  potential demanders of the product and that N gt
  Q.
• Also following previous notation, denote their
  valuations by v1 through vN.
• We begin by considering situations where each
  buyer wishes to purchase at most one unit of the
  good.

8
Decisions for the seller to makein multiunit
auctions

• The seller must decide whether to sell the
  objects separately in multiple auctions or
  jointly in a single auction.
• The seller must choose among different auction
  formats.

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Open auctions for selling identical units

• Descending Dutch auction
• Suppose the auctioneer has five units for sale.
  As the price falls, the first five bidders to
  submit market orders purchase a unit of the good
  at the price the auctioneer offered to them.
• Ascending Japanese auction
• The auctioneer holds an ascending auction and
  awards the objects to the five highest bidders at
  the price the sixth bidder drop out.

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Multiunit Japanese auction

• In a Japanese auction, bidders drops out until
  there are only as many remaining bidders in the
  auction as there are items.
• The winning bidders pay the price at which the
  last bidder dropped out of the auction.
• In this auction it is easy to see that the
  bidders with the highest valuation win the
  auction.

11
Multiunit sealed bid auctions

• Sealed bid auctions for multiple units can be
  conducted by inviting bidders to submit limit
  order offers, and allocating the available units
  to the highest bidders.
• In discriminatory auctions the winning bidders
  pay different prices. For example they might pay
  at the respective prices they posted.
• In a uniform price auction the winners pay the
  same price, such as a kth price auction (where k
  could range from 1 to N.)

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Revenue equivalence revisited

• Suppose each bidder
• - knows her own valuation
• - only want one of the identical items up for
  auction
• - is risk neutral
• Consider two auctions which both award the
  auctioned items to the highest valuation bidders
  in equilibrium.
• Then the revenue equivalence theorem applies,
  implying that the mechanism chosen for trading is
  immaterial (unless the auctioneer is concerned
  about entry deterrence or collusive behavior).

13
Prices follow a random walk

• In repeated auctions that satisfy the revenue
  equivalence theorem, we can show that the price
  of successive units follows a random walk.
• Intuitively, each bidder is estimating the bid he
  must make to beat the demander with (Q1)st
  highest valuation, that is conditional on his own
  valuation being one of the Q highest.
• If the expected price from the qs1 item exceeds
  that of the qs item before either is auctioned,
  then we would expect this to cause more (less)
  aggressive bidding for qs item (qs1 item) to
  get a better deal, thus driving up (down) its
  price.

14
Multiunit Dutch auction

• To conduct a Dutch auction the auctioneer
  successively posts limit orders, reducing the
  limit order price of the good until all the units
  have been bought by bidders making market orders.
• Note that in a descending auction, objects for
  sale might not be identical. The bidder willing
  to pay the highest price chooses the object he
  ranks most highly, and the price continues to
  fall until all the objects are sold.

15
Clusters of trades

• As the price falls in a Dutch auction for Q
  units, no one adjusts her reservation bid, until
  it reaches the highest bid.
• At that point the chance of winning one of the
  remaining units falls. Players left in the
  auction reduce the amount of surplus they would
  obtain in the event of a win, and increase their
  reservation bids.
• Consequently the remaining successful bids are
  clustered (and trading is brisk) relative to the
  empirical probability distribution of the
  valuations themselves.
• Hence the Nash equilibrium solution to this
  auction creates the impression of a frenzied grab
  for the asset, as herd like instincts prevail.

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Why the Dutch auction does not satisfy the
conditions for revenue equivalence

• We found that the revenue equivalence theorem
  applies to multiunit auctions if each bidder only
  wants one item, providing the mechanism ensures
  the items are sold to the bidders who have the
  highest valuations.
• In contrast to a single unit auction, the
  multiunit Dutch auction does not meet the
  conditions for revenue equivalence, because of
  the possibility of rational herding.
• If there is herding we cannot guarantee the
  highest valuation bidders will be auction
  winners.

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Multiunit demanders

• By a multiunit demander we mean that each bidder
  might desire (and bid on) all Q units for
  himself. We now drop the assumption that N gt Q.
• Relaxing the assumption that each bidder demands
  one unit at most seriously compromises the
  applicability of the Revenue Equivalence theorem.
• Typically auctions will not yield the same
  resource allocation even if the usual conditions
  are met (private valuations, risk neutrality,
  lowest feasible expects no rent from
  participation).

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Example Two unit demanders in a third price
sealed bid auction

• Consider a third price sealed bid auction for two
  units where there are two bidders, each of whom
  wants two units. Thus N Q 2. Each bidder
  submits two prices.
• We suppose the first bidder has a valuation of
  v11 for his first unit and v12 for for his
  second, where v11 gt v12 say. Similarly the
  valuations of the second bidder are v21 and v22
  respectively, where v21 gt v22.

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Example continued

• The arguments given for single unit second price
  sealed bid auctions apply to the highest price of
  each bidder. One of his prices is highest
  valuation.
• There is some probability that each bidder will
  win one unit, and in this case the price paid by
  one of the bidders will be determined by his
  second highest bid. Recognizing this in advance,
  he shades his valuation on his second highest
  bid.

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Vickery auctions defined

• A Vickery auction is a sealed bid auction, and
  units are assigned according to the highest bids
  (as usual).
• Each bidder pays for the (sum of the) price(s)
  for the losing bid(s) his own bids displaced. By
  definition the losing bids he displaced would
  have been included within the winning set of bids
  if the bidder had not participated in the
  auction, and everybody else had submitted the
  same bids. In a single unit auction this
  corresponds to the second highest bidder.
• The total price a bidder pays in a Vickery
  auction for all the units he has won is the sum
  of the bids on the units he displaced.

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Vickery auctions are efficient

• A Vickery auction is the multiunit analogue to a
  second price auction, in that the unique solution
  (derived from weak dominance) is for each bidder
  to truthfully report his valuations.
• This implies that a Vickery auction allocates
  units efficiently, in contrast to many multiunit
  auction mechanisms.

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Summary

• This session compared auctions with monopoly, and
  thus established the close connections between
  them.
• We found the revenue equivalence theorem applies
  to multiunit auctions if each bidder only wants
  one item.
• Prices in first and second price sealed bid
  repeated multiunit auctions follow a random walk.
• When bidders demand more than one unit each, the
  revenue equivalence theorem breaks down.
• The Vickery auction is efficient, in contrast to
  many other auction mechanisms.

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2. Prices and Quantities

• This section of the chapter analyzes how the
  determination of quantity impacts on the
  monopolists optimization problem. We begin with
  a discussion of the reservation price in an
  auction, before moving on to monopoly supply.
  Although traditional arguments suggest that
  monopolists are inefficient, we argue the
  monopolist has an incentive to be as efficient as
  a competitive industry.

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Choosing quantity

• When analyzing monopoly, an important issue is
  the quantity the monopolist chooses to supply and
  sell.
• Regulators argue that compared to a competitively
  organized industry where there are many firms
  supplying the product, a monopolist restricts
  the supply of the good and charges higher prices
  to high valuation demanders in order to make
  rents out of his position of sole source.
• Is this true in practice?

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Reservation prices for auctions

• One reason for an auctioneer to set a reservation
  price is because of the value of the auctioned
  item to him if it is not sold. This value
  represents the opportunity cost of auctioning the
  item. For example he might sell it at another
  auction at some later time, and maybe use the
  item in the meantime.
• Should the auctioneer set a reservation above its
  opportunity cost?
• A related question is whether the auctioneer has
  the power to commit himself to setting a
  reservation price above its opportunity cost.

26
Auction Revenue

• What is the optimal reservation price in a
  private value, second price sealed bid auction,
  where bidders are risk neutral and their
  valuations are drawn from the same probability
  distribution function?
• Let r denote the reservation price, let v0 denote
  the opportunity cost, let F(v) denote the
  distribution of private values and N the number
  of bidders. Then the revenue from the auction is
  

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Solving for the optimal reservation price

• Differentiating with respect to r, we obtain the
  first order condition for optimality below, where
  r0 denotes the optimal reservation price.
• Note that the optimal reservation price does not
  depend on N.
• Intuitively the marginal cost of the top
  valuation falling below r, so that the auction
  only nets v0 instead of r0, equals the marginal
  benefit from extracting a little more from the
  top bidder when he is the only one to bidder to
  beat the reservation price.

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The uniform distribution

• When the valuations are distributed uniformly
  with
• then

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Designing a monopoly game with a quantity choice

• In the game below, the valuations of buyers are
  uniformly distributed between 10 and 20 for one
  unit, and have no desire to purchase multiple
  units.
• Each buyer is endowed with 20.
• The monopolists production capacity is 100 units
  of the good. The marginal cost of producing each
  unit up to capacity is constant at 10.
• What is the equilibrium quantity bought and sold?

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Eleven buyers and one seller
20 19 18 17 16 15 14 13 12 11 10
- - - - - - - - - - -
MC10


q
1 2 3 4 5 6 7 8 9
10 11
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Demand schedule
In this example the marginal cost is 10.

Price Quantity Revenue Marginal revenue Total costs Profit
20 1 20 10 10
19 2 38 20 18
18 3 54 30 24
17 4 68 40 28
16 5 80 50 30
15 6 90 60 30
14 7 98 70 28
13 8 104 80 24
12 9 108 90 18
11 10 110 100 10
10 11 110 110 0
18 16 14 12 10 8 6 4 2 0
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Static Solution to game

• There are two outputs that yield the maximum
  profit, which is 30.
• If the monopolist offers 6 units for sale, the
  market will clear at a price of 15.
• If the monopolist offers 5 units for sale, the
  market will clear at a price of 16.

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A differential approach

• The traditional argument can be framed as
  follows. Let c denote the cost per unit produced,
  and suppose consumers demand quantity q(p) when
  the price is p.
• Assume q(p) is differentiable and declining in p,
  and write p(q) as its inverse function. That is
• q(p(q)) q.
• The monopolist chooses q to maximize
• (p(q) c) q

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Marginal revenue equals marginal cost

• Let qm denote the profit maximizing quantity
  supplied by the monopolist. Then qm satisfies the
  first order condition for the optimization
  problem, which is
• p(qm) p(qm) qm c
• The two terms on the left side of the equation
  comprise the marginal revenue from increasing the
  quantity sold. When an additional unit is sold it
  fetches p(q) if we ignore any downward pressure
  on prices.
• The traditional argument is that the monopolist
  will only produce sell an extra unit if the
  marginal revenue from doing so exceeds the
  marginal cost.

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Uniform distribution

• In the uniform distribution example. if there is
  a large number of potential customers with mass
  of one unit
• q(p) 20 p (if 10 lt p lt 20)
• so p(q) 20 20q (if 0 lt q lt 1)
• and marginal revenue is 20 40q
• Setting marginal revenue equal to marginal cost
  yields the equation
• 20 40q 10q
• and solving we obtain q ¼ and p 15.

36
Intermediaries with market power

• We typically think of monopolies owning the
  property rights to a unique resource. Yet the
  institutional arrangements for trade may also be
  the source of monopoly power.
• If brokers could actively mediate all trades
  between buyers and sellers, then they could
  extract more of the gains from trade.
• How should a broker set the spread between the
  buy and sell price? A small spread encourages
  greater trading volume, but a larger spread nets
  him a higher profit per transaction.

37
Real estate agents

• Suppose real estate agencies jointly determined
  the fees paid by home owners selling their real
  estate to buyers.
• How should the cartel set a uniform price that
  maximizes the net revenue for intermediating
  between buyers and sellers?
• We denote the inverse supply curve for houses by
  fs(q) and the inverse demand curve for houses by
  fd(q).
• Writing price p fs(q) means that if the price
  were p then suppliers would be willing to sell q
  houses. Similarly if p fd(q), then at price p
  demanders would be willing to purchase q houses.

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Optimization by a real estate cartel

• By convention the seller is nominally responsible
  for the real estate fees. Let t denote real
  estate fees and q the quantity of housing stock
  traded. The cartel maximizes tq subject to the
  constraint that t fd(q) - fs(q), or chooses q
  to maximize
• fd(q) - fs(q)q
• The interior first order condition is
• fd(q) fd(q)q fs(q) fs(q)q
• The marginal revenue from a real estate agency
  selling another unit (selling more houses at a
  lower price) is equated with the marginal cost of
  acquiring another house (and thus driving up the
  price of all houses being sold).

39
NYSE dealers

• In the NYSE dealers see the orders entering their
  own books, in contrast to the brokers and
  investors who place limit orders.
• The exchange forbids dealers from intervening in
  the market by not respecting the timing
  priorities of the orders from brokers and
  investors as they arrive.
• However dealers are expected to use their
  informational advantage make the market by
  placing a limit order in the limit order books if
  it is empty.

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The gains from more information

• If dealers do not mediate trades, but merely
  place their own market orders, their ability to
  make rents is severely curtailed, but not
  eliminated. The trading game is characterized by
  differential information.
• The order flow is uncertain, everyone sees past
  transaction prices and volume but only the dealer
  sees the existing limit orders, so the dealer is
  in a stronger position than brokers to forecast
  future transaction prices.
• If valuations are affiliated then the broker is
  also more informed about the valuations of
  investors and brokers placing future orders.

41
Perfect price discrimination

• Suppose the monopolist knows the valuation each
  consumer places on a unit of the item or service
  and there is no possibility of re-trade amongst
  consumers.
• In that case, legal issues aside, the monopolist
  should offer the item to each consumer who values
  it at more than the marginal production cost, at
  his or her valuation (or for a few cents less).
• The monopolists profit is then the integral of
  demand up to the point where the demand crosses
  the marginal cost curve, less total costs, which
  clearly exceeds the profit from charging a
  uniform price.

42
Comparison with competitive equilibrium

• Note that the and the production level of a
  perfectly discriminating monopolist is the
  competitive equilibrium level, where price equals
  marginal cost.
• The basic difference is that a price
  discriminating monopolist extracts all the gains
  from trade, whereas a in a competitive
  equilibrium, all the gains from trade go to the
  consumers in the case where marginal costs are
  constant.
• In the example with 11 consumers, the perfectly
  discriminating monopolist garners profits of 55,
  a uniform price monopolist 30, and a
  competitively organized industry nothing.

43
Laws against price discrimination

• The 1936 Robinson-Patman Act of updated the
  earlier 1914 Clayton Act instituting laws against
  price discrimination. The Federal Trade
  Commission (FTC) is charged with the oversight of
  these laws.
• The fact that different consumers pay different
  prices is not sufficient to prove illegal price
  discrimination has occurred.
• A firm cannot be found guilty of engaging in
  illegal price discrimination unless there are ill
  effects on competition, meaning competition is
  reduced, or a monopoly is sustained, or a
  monopoly is created.

44
How important are these legal issues?

• Economists are skeptical about how much
  competition has been fostered by laws against
  price discrimination.
• More than half the firms prosecuted for breaking
  price discrimination laws are relatively small
  (local) monopolies.
• Perhaps the most important reason we observe less
  price discrimination than the simple static model
  analysis predicts, is that the monopolist
  typically does not know how each consumer values
  his goods and services.

45
Summary

• Monopolists are said to create inefficiencies,
  restricting supply by trading off higher prices
  with less demand.
• Intermediaries can also sometimes exploit their
  monopolistic position by creating a wedge between
  their buy and sell prices.
• If monopolists price discriminate they produce
  where the lowest price consumer pays the marginal
  cost of production, an efficient outcome.
• Laws against price discrimination are directed
  against anticompetitive practices that limit
  entry, and are not primarily concerned with how
  trading surplus is divided between consumers and
  producers.

46
3. Segmenting the Market

• Perfect price discrimination is often hard to
  impose directly. However quantity discounting,
  product bundling and dynamic pricing strategies
  sometimes provide the means for achieving its
  objective of value maximization.

47
Segmenting the market

• To profitably engage in explicit price
  discrimination, the monopolist must be able to
• 1. Identify the individual reservation prices
  by his clientele for his goods
• 2. Prevent resale from customers with low
  reservation prices to potential customers
  with high reservation prices.
• 3. Be free of incrimination from laws of
  price discrimination.
• When the monopolist knows the distribution of
  demand but not the characteristics of individual
  demanders, or alternatively is subject to laws
  against price discrimination, it can sometimes
  segment the market to increase its profits.

48
Quantity discounting

• We first consider a geographically isolated
  retail market monopolized by a firm selling
  kitchen and laundry detergents or bathroom
  toiletries to two types of consumers, large
  volume commercial buyers and small volume
  households.
• The commercial demanders are willing to search
  over a wider area for suppliers, and consider a
  greater range of close substitutes (paper towels
  versus blow dry).
• Households have less incentive to search for
  these low cost items, rarely consider substitute
  products, and limited space to store these items
  household rental rates for inventory storage are
  typically greater commercial property rates (per
  cubic foot).

49
A parameterization

• Suppose the reservation value of a commercial
  demander is vc and the reservation price of a
  household is vh where vc lt vh.
• We also assume a commercial demander would buy k
  units if the price is less than its reservation
  value, whereas a household would only buy one
  unit.
• Commercial and household demanders are
  distributed in proportion p and (1 p)
  respectively throughout the local market
  catchment area.
• Unit (wholesale) costs for the monopolist are c,
  where c lt vc.

50
Solution to the parameterization

• If the firm adopts a uniform pricing policy, then
  the maximum monopoly profits are found by
  charging a high price and only serving
  households, or charging a low price to capture
  all the local demand
• maxp(vc c) (1 - p)k(vc p), p(vh c)
• If the firm charges a high price for single units
  and a discount price for bulk orders of k units
  then the maximum monopoly profits are
• p(vh c) (1 - p)k(vc p)
• Comparing the net profits of the two, we see that
  discounting bulk orders is profitable.

51
When can perfect price discrimination be achieved
through quantity discounting?

• Here perfect price discrimination is achieved
  without resort to charging households and
  commercial demanders different prices!
• Note that if vc gt vh then segmenting the market
  in this way cannot be achieved unless the
  monopolist can restrict the number of individual
  units purchased separately (which is typically
  infeasible).
• This result on segmentation can be extended to
  monopoly markets with several consumer types. We
  only assume that the consumer types demanding
  more units have lower reservation values. The
  same logic applies.

52
Product bundling

• Consider now another related method for
  segmenting market demand to extract greater
  economic rent.
• The firm exploits the idea that customers who
  demand several of the firms products might
  exhibit more elastic demands (be more price
  sensitive) than customers who only wish to
  purchase a smaller subset of the firms products.
• Indeed the monopoly offer a bundle of goods and
  services that includes its monopoly product as
  well as a product that is available separately at
  a competitive price elsewhere.

53
Ski resort

• Enthusiastic skiers bring their own equipment to
  the resort, while casual skiers rent.
  Enthusiastic skiers are willing to pay up to ve
  for a ski ticket, but casual skiers are only
  willing to pay vc where ve gt ve.
• Resort employees at the ticket booth cannot
  distinguish between a casual skier versus an
  enthusiastic skier, because enthusiastic skiers
  have lots of experience watching and listening to
  casual skiers.
• There is, however, a competitive market for
  rental skis. The price of renting skis, poles and
  boots is p, and this reflects the cost of running
  a rental firm.
• How does the resort maximize its value?

54
Solution to the ski resorts problem

• If the resort charges ve for ski tickets, and
  does not offer any other services, only the
  enthusiastic skiers will visit. If the resort
  only charges vc for ski tickets, then not all the
  rent is extracted from enthusiastic skiers
• Suppose the ski resort sells its tickets for ve
  but offer its rentals for
• p (ve - vc)
• In that case enthusiastic skiers pay their
  reservation price for skiing, while casual skiers
  pay their reservation price for the package of
  skiing and renting, and after cross subsidization
  from the ticket office, the resort breaks even on
  its rental operation.

55
Principles for product bundling

• More generally the solution to this problem is
  found by identifying a product that the lower
  valuation customers demand but the high valuation
  customers do not want, and offering a package
  deal on the bundle.
• The package is typically marketed as a bargain.
• Note that we have said nothing about the costs of
  doing business. If the ski resort has high fixed
  costs from running its lifts or preparing its
  runs, then it might not be profitable to operate
  unless it can engage in this form of price
  discrimination.

56
Other examples

1. Firms sell assembled goods such as cars to new
   car buyers, and also meet demand from previous
   buyers for plus replacement parts arising from
   collision damage or wear and tear.
2. Restaurants sometimes offer complete dinners with
   a limited range of items on the menu, and also
   offer portions a la carte to those willing to
   spend more.
3. Travel agencies offer all inclusive vacation
   packages for travel and lodging as well as sell
   tickets for individual items.

57
The static solution revisited
Price in dollars
20
inverse demand curve
Uniform price solution
unit cost
9
marginal revenue curve
quantity
0
Uniform quantity solution
58
Residual demand
Price
New vertical axis for origin of residual inverse
demand
20
Uniform price solution
Unit cost
9
New marginal revenue curve
Quantity
0
59
A dynamic inconsistency?

• After selling the original demanders the item at
  price p(qm) the monopolist would have an
  incentive to sell the item to the remaining
  consumers at a lower price.
• If the original consumers knew that the product
  would go on sale later they might delay their
  purchase. Does that undermine our prediction that
  qm will be bought if the price is p(qm)?
• One possibility is that the monopolist commit to
  a uniform price policy by promising everyone the
  lowest price he offers to anyone.
• These issues cannot be fully resolved within the
  context of a static model.

60
Dynamic considerations

• There are several ways to model the dynamics of
  price setting and the service flow from the good
  over time.
• If all trading must occur before customers take
  delivery of their purchases, we can separate
  considerations of price dynamics from those of
  the service flow.
• Another approach is that the game lasts a fixed
  amount of time and that consumers receive service
  flows from the good as soon as they buy it. This
  approach provides a natural way of modeling
  durable goods.
• In both case we assume that agreements to trade
  occur instantaneously, meaning transactions can
  be conducted in infinitesimal amounts of time.

61
Dynamic pricing policy in a closed time interval

• Suppose that all trading must take place in a
  closed interval of time, say 0,1, and customers
  receive the good after trading closes.
• This corresponds to a situation where the market
  closes at a give fixed time.
• At time t 1 consumers recognize that the
  monopolist will solve the static problem.
  Therefore no consumer will buy above that price.
• By a backwards induction argument we conclude
  that the monopolist cannot charge more than the
  uniform price in that case.

62
Dynamic pricing policy in an open time interval

• Suppose that all trading must take place in a
  (half) open interval of time, say 0,1), and as
  before customers receive the good at time t 1.
• This corresponds to the case where the monopolist
  is open ended about when trading will end.
• Suppose the monopolist refuses to lower his price
  until everyone with a higher reservation price
  than the current price has purchased his product.
  In that case consumers are sequentially presented
  with all or nothing offers that are subgame
  perfect.
• The monopolist reaps the full benefits of price
  discrimination.

63
Durable goods

• Now consider what happens in a closed trading
  interval 0,1 when the good yields a service
  flow over the portion of the interval that a
  consumer owns it.
• For example if the consumer buys the good at t
  ½ then she receives a service flow between times
  t ½ and 1, and her total benefit is half her
  valuation.
• In this case there are no consumer benefits from
  trading at t 1.
• A simple adaptation of our arguments in the open
  interval case proves that the monopolist can
  extract all the benefits of discriminating by
  sequentially reducing prices at the beginning of
  the game from highest reservation value to the
  lowest.

64
Summary

• In the traditional view, monopolists maximize
  their value by setting price where marginal
  revenue equals marginal cost and restricting
  trade, that is compared to competitive
  equilibrium where price equals marginal cost.
• We showed that the monopolist has an incentive to
  price discriminate, extracting more of the gains
  from trade, and raising output to the efficient
  outcome achieved in competitive equilibrium.
• When the conditions for perfect price
  discrimination are absent, quantity discounting,
  product bundling and dynamic pricing policies may
  provide the means to the same end.