Part A-III (continued) Microeconomic Theory Review (continued)

1
Part A-III (continued) Microeconomic Theory
Review (continued)
2
Economics One-on-Onecontinued

• Cooperation/Non-cooperation
• Bargaining Theory
• Transaction Costs

3

• Co-operation/Non-cooperation

• We saw that the outcome of a game of strategy can
  be very different if the players cooperate or
  dont cooperate.
• Recall Mary and John
• PAYOFF MATRIX
• Marys decision
• SELL DONT SELL
• Johns decision
• SELL (-2, -2) ( 1, 0)
• DONT SELL ( 0, 1) ( 0, 0)

4

• We saw that if Mary and John decide to
  co-operative they can each do better (and society
  as whole will be better off in the sense that a
  Pareto Improvement will result - market failures
  sometimes we dont want them to co-operate??)
• This simple game represents a very common
  situation. So why dont agents always cooperate?
• They often do but they sometimes dont
• We are very interested in why cooperation might
  not occur and whether or not POLICY can foster
  more cooperation among agents

5
Recall, if Mary and John decide that one of them
will sell and one will not sell, together they
will make 1 in profit. BUT, they must also
decide how to split the profit (0.01/0.99 or
0.99/0.01 or 0.50/0.50 or whatever). Sounds
simple enough but it generally isnt.

• PAYOFF MATRIX
• Marys decision
• SELL DONT SELL
• Johns decision
• SELL (-2, -2) ( 1, 0)
• DONT SELL ( 0, 1) ( 0, 0)

6

• Remember Mary does not know Johns profit
  function (his payoffs under the various
  strategies) and John does not know Marys
  payoffs.
• Maybe a 50/50 split is fair but maybe not.
• What if John tells Mary that even if she sells he
  can still make a profit of 0.50 so if she wants
  him to cooperate she must give him 0.75 and
  accept only 0.25 for herself?

7
Or what if John is a slightly more profitable
firm. Now the optimal cooperative outcome is for
John to sell and Mary to not sell. (Note that
the non-cooperative solution remains (0,
0)) Together they will make 1.50 in profit.
Why should John agree to a 50/50 split? But why
should Mary reveal that she only stands to make
1.00 profit? She could tell John that if he
sits idle and she sells she could make 1.45.

• PAYOFF MATRIX
• Marys decision
• SELL DONT SELL
• Johns decision
• SELL (-2, -2) ( 1.50, 0)
• DONT SELL ( 0, 1) ( 0, 0)

8
The primary reason why players find it difficult
to cooperate is that each has a different
information set

• Mary knows
• Marys decision
• SELL DONT SELL
• Johns decision
• SELL (?, -2) (?, 0)
• DONT SELL (?, 1) (?, 0)
• John knows
• Marys decision
• SELL DONT SELL
• Johns decision
• SELL (-2, ?) (1, ?)
• DONT SELL ( 1, ?) (0, ?)

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Think of union/employer, investor/firm,
buyer/seller

• The first step towards cooperation is sharing
  information, for example
• Trade association generally questionable
  motives
• Union representation on company boards
• Russian military observers at NATO exercises

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Bargaining Theory

• We need a framework (theory) which will allow us
  to understand the structure of the process
  through which agents negotiate a cooperative
  solution. The process itself is somewhat
  mysterious.
• Elements of Bargaining theory
• Cooperative surplus (whats at stake)
• Reservation prices of each agent

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An example

• Jones has a cottage for sale. She values it at
  100,000. She offers it for sale.
• Smith has 200,000. He decides that he is
  interested in buying the Jones cottage. Smith
  decides that it is worth 110,000 to him.
• What will happen? Will a sale go through? What
  will the price be?

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We know

• the cottage is worth 10,000 more to Smith than
  it is to Jones
• the lowest price acceptable to the potential
  seller, Jones, is 100,000.
• the highest price acceptable to the potential
  buyer is 110,000.
• the problem is that they must agree on a price,
  and this agreement determines who gets what share
  of the increased well-being that results from the
  sale (the gains from the Pareto improving trade
  of cottage for money).

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• Cooperative Surplus - difference between the
  maximum buying price and the minimum selling
  price - the value created by reallocating
  resources between the agents (10,000 in our
  example)
• Reservation Price of the Buyer - the price above
  which the buyer will not buy (110,000 in our
  example) the walk-away price for the buyer
• Reservation Price of the Seller the price below
  which the seller will not sell (100,000 in our
  example) the walk-away price for the seller
• Reservation Prices are also known as Threat Values

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• The transaction price the price at which the
  trade takes place
• The transaction price determines the share of the
  cooperative surplus that each party will get
• If the agreed price is 105,000, then each will
  share equally (5,000) in the cooperative surplus
  
• If the agreed price is 102,000, then Jones gets
  20 (2,000/10,000) of the surplus and Smith
  gets 80 (8,000/10,000)

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Purpose of bargaining

• To allow the seller to try to determine the
  buyers true reservation price, while trying to
  convince the buyer that her reservation price is
  quite high.
• To allow the buyer to try to determine the
  sellers true reservation price while trying to
  convince the seller that he has a very low
  reservation price.
• The process of bargaining is intended to help
  each side develop a notion of the other sides
  reservation price. At the start, the buyer
  and/or seller might not even know if a trade is
  possible. The cooperative surplus might be zero.

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• Information revealed in the course of bargaining
  must be viewed as credible by the other side
• - prices of other cottages in the area
• - the physical state of the cottage
• - the fact that the buyers spouse would rather
  move to Florida
• - the fact that the buyer is having trouble
  arranging a mortgage
• - the fact that the cottage represents a lifetime
  of memories to the seller and she is having
  second thoughts about selling
• - etc., etc.

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• Bargaining makes it a cooperative game, as
  opposed to a non-cooperative game
• No guarantee that the bargainers will be able to
  agree on a price (a sharing of the surplus).
• Negotiations might break down and no trade
  result.
• (The Pareto improving transaction might not take
  place.)
• Negotiations might be impossible

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• Returning to Jones and Smith and the cottage
• Lets look at some possible outcomes and see how
  far bargaining theory can actually get us.
• Can we predict the selling price of the cottage?
• Cab we predict that a trade will take place?

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Jones dominates the bargaining process

• Player Non-cooperative Cooperative Cooperative
• solution solution surplus
• payoff payoff (Threat Values) (Jones
  dominates)
• Jones 100,000 cottage 109,999 money 9,999
• Smith 110,000 money 110,000 cottage
• for cottage
• 90,000 money 90,001 money 1
• Total
• wellbeing
• in society 300,000 310,000 10,000

20
Smith dominates the bargaining process

• Player Non-cooperative Cooperative Cooperative
• solution solution surplus
• payoff payoff (Threat Values) (Smith
  dominates)
• Jones 100,000 cottage 100,001 money 1
• Smith 110,000 money 110,000 cottage
• for cottage
• 90,000 money 99,999 money 9,999
• Total
• wellbeing
• in society 300,000 310,000 10,000

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Reasonable Solution bargaining outcome 50/50
split warning this is a purely theoretical
concept

• Player Non-cooperative Cooperative Cooperative
• solution solution surplus
• payoff payoff (Threat Values) (Jones
  dominates)
• Jones 100,000 cottage 105,000 money 5,000
• Smith 110,000 money 110,000 cottage
• for cottage
• 90,000 money 95,000 money 5,000
• Total
• wellbeing
• in society 300,000 310,000 10,000

22

• If a cooperative solution results (they agree on
  a price and a voluntary trade takes place) the
  total value of the cooperative solution will
  always be 310,000
• Bargaining is simply a process to determine if a
  cooperative solution is possible and who will get
  what share of the surplus
• If bargaining is successful (a trade is made)
  then an efficient Pareto improving trade occurs
  
• - who gets what is a matter of distribution of
  wellbeing

23
This bargaining game can tell us the value of the
cooperative surplus - it cannot tell us how the
surplus will actually be divided between the two
parties, or even if a trade will actually
occur. Rational self-interested behaviour on
the part of each agent is not enough to determine
what the price might end up being in such a model
Often we cannot even predict whether or not
bargaining will be successful
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When we face such situations in economic
modelling. We generally assume that a
reasonable as opposed to a rational price
results if bargaining is successful. The
reasonable solution will be the one for which
the buyer and seller divide the surplus evenly.
Economic theory provides no basis for assuming
that the reasonable distribution rule will
actually apply. The reasonable solution has
nothing to do with fairness (or rationality). It
is just a convenient assumption.
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Some variations on the cottage sale

• QUESTION Suppose Jones neighbour offers an
  identical cottage for sale at a price of
  103,000, while Jones is still bargaining with
  Smith. How would this change the threat values,
  the surplus from cooperation and the reasonable
  solution?
• ANSWER
• Jones threat value remains 100,000
• Smiths threat value falls to 103,000 since he
  now has an alternative offer of sale at that
  price
• Cooperative surplus (from a trade taking place
  between Jones and Smith) now falls to 3,000,
  since 103,000 is the most the Jones cottage is
  worth to Smith
• Reasonable solution is now a price of 101,500.

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Interpretation

• Parts of this response might appear
  counter-intuitive.
• We started with Smith valuing a cottage such as
  that offered for sale by Jones at 110,000.
• Presumably he still values such a cottage it at
  110,000.
• But Jones neighbour offered such a cottage for
  sale at 103,000 and thereby established a
  maximum price that Smith would be required to pay
  Jones.
• The action of Jones neighbour granted Smith
  7,000 in guaranteed consumers surplus,
  something he no longer has to bargain over or
  share with anyone.
• What remains for him is to bargain (with either
  Jones or her neighbour) over the remaining 3,000
  which represents the new lower cooperative
  surplus although we do not know the neighbours
  reservation price.

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• QUESTION Suppose Jones neighbour does not
  offer his cottage for sale but Jones receives an
  offer to purchase at a price of 105,000 from
  Wilson, while still negotiating with Smith. How
  would this change the threat values, the surplus
  from cooperation and the reasonable solution?
• QUESTION Suppose that Smith begins to feel that
  purchasing a mobile home might also be enjoyable
  and as a result, lowers his valuation of the
  cottage to 95,000. Jones still believes that
  the cottage is worth a minimum of 100,000. How
  would this change the threat values, the surplus
  from cooperation and the reasonable solution?
• QUESTION What if the government imposes a 10
  buyers fee on all cottage purchase? How would
  this change the original threat values, the
  surplus from cooperation and the reasonable
  solution? (Land Transfer Tax)

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Bargaining model - summary

• The bargaining model reduces the bargaining
  process to three basic elements
• 1 The threat values (reservation prices) of the
  buyer and seller.
• 2 The cooperative surplus.
• 3 Agreement on terms for distributing the
  surplus between the agents.
• But why does actual bargaining sometimes fail?
• Transaction Costs

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Transaction Costs

• Is bargaining free (does it have zero costs)?
• No, in the simplest setting the agents must take
  the time to meet and haggle.
• In more complicated settings, they might need to
  spend time carefully assessing each others
  threat value (hire accountants, engineers, etc.)
  hire bargaining agents (lawyers), etc.
• Bargaining can at times be very costly. These
  costs are referred to as transaction costs

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• Transaction costs are the costs of carrying out
  trade the resources required to bring about
  Pareto improving voluntary exchange.
• In well organized markets, these costs can be
  very low e.g. trading securities on the
  internet.
• At times they can be high relative to the value
  of what is being trade fine art and collectible
  auctions 30 or more.
• Sales and other trading taxes are also part of
  transaction costs.

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• Whatever they are, transaction costs cut into
  (detract from) the cooperative surplus.
• Consider Jones and Smith, if there is a 15 land
  transfer tax on the sale of cottages can a
  trade go through under any conditions?
• Individuals trade net of transactions costs and
  the general rule is
• The greater are the transaction costs
• the less trading will occur.
• (transaction costs are not a gain to either the
  buyer of seller)
• We need to understand the nature of transaction
  costs

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The elements of transaction costs

• Three components of transaction costs
• 1 search costs
• 2 bargaining costs
• 3 enforcement costs

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• Search costs
• Costs associated with locating a buyer or seller.
• These costs tend to be relatively high when
  trading in unique goods or services (a spare part
  for an vintage automobile) and low for
  standardized goods (most consumer goods).

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• Bargaining costs
• Costs associated with carrying out the
  negotiations.
• If each partys threat value and the cooperative
  surplus is known to all parties then bargaining
  costs will be relatively low.
• In general the more information concerning all
  aspects of the trade that is public to the
  parties, the easier it will be to reach a bargain
  - otherwise the bargaining process will have to
  make that information known.
• Bargaining will be more difficult (more costly)
  the greater is the number of parties the greater
  is the amount of primary uncertainty associated
  with the transaction (requiring agreement on
  contingencies) the greater is the extent of
  hostility between the bargainers the extent to
  which there is overreaching, on the part of one
  or both parties.

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• Enforcement costs
• Costs associated with monitoring the behaviour of
  the parties and punishing failure to fulfil
  agreements.
• If there is no time lag between the bargain being
  reached and being fulfilled, then there will be
  no enforcement costs.
• If there is a lapse of time between bargaining
  and fulfilment of the bargain conditions, then
  monitoring and enforcement costs will arise.
• Note that many apparently instantaneous
  transactions carry warranties or guarantees of
  one sort or another and therefore monitoring and
  enforcement costs exist.

36

• Consider the purchase of illicit drugs versus
  alcohol
• All three components of transaction costs are
  likely to be higher for illicit drugs search
  costs, bargaining costs and enforcement costs.
• This results mostly from the fact that
  recreational drugs are illegal.
• Would legalizing the sale of recreational drugs
  increase their use? It would certainly make the
  transaction costs fall, implying more successful
  bargaining.

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To summarize

• At times the cooperative solution to a potential
  conflict of interest will yield a Pareto
  improvement over the non cooperative solution
  there is a cooperative surplus, or gain from
  trade)
• However, the agents must cooperate successfully
  agree to bargain and eventually come to some
  agreement on the division of gains
• Since neither agent generally has perfect
  information this bargaining is costly (the
  information must be developed)
• This gives rise to transaction costs
• Bargaining will breakdown (fail) if the
  transaction costs exceed the cooperative surplus
  
• We are interested in situations in which the law
  can facilitate successful cooperation.