Cartel and asymmetric information
Varian: Intermediate Microeconomics,
chapters 27.10–11, 28.4–6, 37.1–6
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In this lecture you will learn
• what cartels do, when they are stable and when not
• what moral hazard and adverse selection are
• how signalization can solve the problem of adverse selection
• what function might have a school not teaching anything useful
• how incentives under complete and asymmetric information work
• what incentives have real-estate agents
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Cartel
Cartel – firms are trying to maximize the sum of their profits.
The cartel behaves as a monopoly with more production plants.
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Cartel
Cartel – firms are trying to maximize the sum of their profits.
The cartel behaves as a monopoly with more production plants.
Cartel is illegal.
In the US – personal
responsibility of
managers.
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Profit maximization of a cartel with two firms
Inverse market demand: p(y), where y = y1 + y2 (identical product)
Total revenue of cartel: r(y) = p(y)y
Cost functions of firms: c1(y1) and c2(y2)
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Profit maximization of a cartel with two firms
Inverse market demand: p(y), where y = y1 + y2 (identical product)
Total revenue of cartel: r(y) = p(y)y
Cost functions of firms: c1(y1) and c2(y2)
Cartel chooses quantity y1 and y2 in order to maximize profit:
max
y1,y2
π(y1, y2) = r(y) − c1(y1) − c2(y2)
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Profit maximization of a cartel with two firms
Inverse market demand: p(y), where y = y1 + y2 (identical product)
Total revenue of cartel: r(y) = p(y)y
Cost functions of firms: c1(y1) and c2(y2)
Cartel chooses quantity y1 and y2 in order to maximize profit:
max
y1,y2
π(y1, y2) = r(y) − c1(y1) − c2(y2)
First-order conditions:
∂π(y1, y2)
∂y1
=
dr(y)
dy
dy
dy1
−
dc1(y1)
dy1
= MR(y) − MC1(y1) = 0
∂π(y1, y2)
∂y2
=
dr(y)
dy
dy
dy2
−
dc2(y2)
dy2
= MR(y) − MC2(y2) = 0
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Profit maximization of a cartel with two firms (graph)
First-order conditions: MR(y∗) = MC1(y∗
1 ) and MR(y∗) = MC2(y∗
2 )
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Profit maximization of a cartel with two firms (graph)
First-order conditions: MR(y∗) = MC1(y∗
1 ) and MR(y∗) = MC2(y∗
2 )
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Cartel is unstable in an one-shot game – example
Inverse demand: p = 11 − y
Costs: c1(y1) = 3y1; c2(y2) = 3y2; MC1 = MC2 = 3
Cartel’s quantities, price and profit, if each firm produces half the output?
How does the result change if firm 1 maximizes its own profit?
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Cartel is unstable in an one-shot game – example
Inverse demand: p = 11 − y
Costs: c1(y1) = 3y1; c2(y2) = 3y2; MC1 = MC2 = 3
Cartel’s quantities, price and profit, if each firm produces half the output?
How does the result change if firm 1 maximizes its own profit?
• Cartel:
max
y1,y2
π(y1, y2) = (11 − y)y − 3y1 − 3y2
The same first order conditions for both firms: 11 − 2y = 3
Result: y = 4, y1 = y2 = 2, p = 7, π1 = π2 = 8
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Cartel is unstable in an one-shot game – example
Inverse demand: p = 11 − y
Costs: c1(y1) = 3y1; c2(y2) = 3y2; MC1 = MC2 = 3
Cartel’s quantities, price and profit, if each firm produces half the output?
How does the result change if firm 1 maximizes its own profit?
• Cartel:
max
y1,y2
π(y1, y2) = (11 − y)y − 3y1 − 3y2
The same first order conditions for both firms: 11 − 2y = 3
Result: y = 4, y1 = y2 = 2, p = 7, π1 = π2 = 8
• Firm 1:
max
y1
π(y1, 2) = (9 − y1)y1 − 3y1
First-order condition: 9 − 2ˆy1 = 3
Result: ˆy1 = 3, y2 = 2, y = 5, p = 6, π1 = 9, π2 = 6
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Cartel is unstable in an one-shot game (graph)
Result cartel: y = 4, y1 = y2 = 2, p = 7, π1 = π2 = 8
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Cartel is unstable in an one-shot game (graph)
Result cartel: y = 4, y1 = y2 = 2, p = 7, π1 = π2 = 8
Result firm 1: D1 : p = 9 − y1, MR1 = 9 − 2y1, ˆy1 = 3
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
Nash equilibrium and equilibrium in dominant strategies is CC.
Is this equilibrium Pareto efficient?
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Prisoner’s dilemma
The situation of a cartel corresponds to a game prisoner’s dilemma
= a simultaneous game in which
• there are 2 players – player A and B,
• each player has 2 actions – confess C and deny D,
• preferences of both payers are CD DD CC DC.
Nash equilibrium and equilibrium in dominant strategies is CC.
Is this equilibrium Pareto efficient? No. Both players are better off in DD.
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Prisoner’s dilemma – a cartel with two firms
Simultaneous game:
• two firms 1 and 2
• each firm has two actions:
– cartel quantity qm
i
– competitive (Cournot) quantity qc
i
• preferences given by profits of firms:
πd
i (default) > πm
i (monopoly) > πc
i (competition) > πs
i (sucker)
Payoff matrix of the game – the same structure as prisoner’s dilemma:
firm 2
qc
2 qm
2
firm 1
qc
1 πc
1; πc
2 πd
1 ; πs
2
qm
1 πs
1; πd
2 πm
1 ; πm
2
Nash equilibrium and equilibrium in dominant strategies (qc
1, qc
2) is not
Pareto efficient – both firms better off in (qm
1 , qm
2 ).
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Repeated prisoner’s dilemma
In the repeated prisoner’s dilemma, the players may keep (qm
1 , qm
2 ),
because it is possible to punish the player who chooses qc in future rounds.
Example of a punishment strategy = grim trigger if one of the firm
defaults, the other firm chooses qc
i for the rest of the game
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Repeated prisoner’s dilemma
In the repeated prisoner’s dilemma, the players may keep (qm
1 , qm
2 ),
because it is possible to punish the player who chooses qc in future rounds.
Example of a punishment strategy = grim trigger if one of the firm
defaults, the other firm chooses qc
i for the rest of the game
Cartel in a finitely repeated game is not stable.
Why? Let us assume that the cartel game has 10 rounds:
• Both firms choose qc
i in the 10th round (the dominant strategy).
• Firms’ actions in the 9th round cannot be punished.
=⇒ Both firms choose qc
i in the 9th round.
• . . .
• Firms’ actions in the 1st round cannot be punished.
=⇒ Both firms choose qc
i in the first round.
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Repeated prisoner’s dilemma
In the repeated prisoner’s dilemma, the players may keep (qm
1 , qm
2 ),
because it is possible to punish the player who chooses qc in future rounds.
Example of a punishment strategy = grim trigger if one of the firm
defaults, the other firm chooses qc
i for the rest of the game
Cartel in a finitely repeated game is not stable.
Why? Let us assume that the cartel game has 10 rounds:
• Both firms choose qc
i in the 10th round (the dominant strategy).
• Firms’ actions in the 9th round cannot be punished.
=⇒ Both firms choose qc
i in the 9th round.
• . . .
• Firms’ actions in the 1st round cannot be punished.
=⇒ Both firms choose qc
i in the first round.
In an infinitely repeated game, the punishment strategy can be successful.
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Cartel stability in an infinitely repeated game
Under what conditions does grim trigger make the cartel stable?
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Cartel stability in an infinitely repeated game
Under what conditions does grim trigger make the cartel stable?
Firm i chooses:
1 stay in cartel – net present value of profits:
πm
i +
πm
i
r
• πm
i = cartel profit in this round
• πm
i /r = discounted future cartel profit (r = interest rate)
2 default – net present value:
πd
i +
πc
i
r
• πd
i = a higher profit from defaulting in this round
• πc
i /r = a lower discounted future competitive profit
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Cartel stability in an infinitely repeated game (cont’d)
The cartel will be stable if
πm
i +
πm
i
r
> πd
i +
πc
i
r
r <
πm
i − πc
i
πd
i − πm
i
Because πd
i > πm
i and πm
i > πc
i ,
πm
i − πc
i
πd
i − πm
i
> 0.
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Cartel stability in an infinitely repeated game (cont’d)
The cartel will be stable if
πm
i +
πm
i
r
> πd
i +
πc
i
r
r <
πm
i − πc
i
πd
i − πm
i
Because πd
i > πm
i and πm
i > πc
i ,
πm
i − πc
i
πd
i − πm
i
> 0.
Conclusion:
The cartel is stable if the firms are sufficiently patient (r is low).
If r is low, the loss of future profits πm
i /r − πc
i /r outweights the increase
of current profits πd
i − πm
i .
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Example – cartel stability in an infinitely repeated game
The same instructions as in the previous example:
Cartel profit πm
i = 8
Cournot profit π
c(C)
i = 64/9 = 7,¯1
Profit from default: πd
i = 9
What is the threshold interest rate that makes the cartel stable?
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Example – cartel stability in an infinitely repeated game
The same instructions as in the previous example:
Cartel profit πm
i = 8
Cournot profit π
c(C)
i = 64/9 = 7,¯1
Profit from default: πd
i = 9
What is the threshold interest rate that makes the cartel stable?
Cournot:
r <
πm
i − πc
i
πd
i − πm
i
=
8 − 7,¯1
1
= 0,¯8
Cartel is stable if the interest rate is below 89%.
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CASE: Indianapolis concrete cartel
2006 and 2007: the DOJ busted up a long-lived cartel with concrete.
How did the cartel work?
• regular meetings at local hotels – agreement on prices
• monitoring – directors anonymously gathered price quotes
• threats or an emergency meeting when the agreement was violated
Cartel had a lot of problems, but occasionally increased prices by 17%.
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CASE: Indianapolis concrete cartel
2006 and 2007: the DOJ busted up a long-lived cartel with concrete.
How did the cartel work?
• regular meetings at local hotels – agreement on prices
• monitoring – directors anonymously gathered price quotes
• threats or an emergency meeting when the agreement was violated
Cartel had a lot of problems, but occasionally increased prices by 17%.
Why did the cartel fall apart?
1 problem: a noncooperative manager from a firm outside of the cartel
2 repeated attempts to persuade the manager to join the scheme
3 complaints about his performance to his corporate boss
4 manager went to the FBI and informed them of the cartel’s operations
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EXAMPLE: OPEC
• legal cartel
• 12 members
• is not a monopoly – half of production from non-OPEC countries
Problems with overproduction – example (2011):
OPEC-11 = OPEC without Iraq that did not have a quota (transition phase)
Libya – not reaching its quota for technical reasons (Arab spring)
Source: http://seekingalpha.com/article/314086-who-is-cheating-on-their-opec-production-quota
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Asymmetric information
Up to now we assumed complete information = consumers and firms
know quality of goods sold and purchased.
Market with asymmetric information = one side of the market has
better information than the other side of the market.
Examples:
• health sector – the MD is better informed than the patient
• insurance – the client has better information than the insurer
• used cars – the seller has better information than the buyer
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Asymmetric information
Up to now we assumed complete information = consumers and firms
know quality of goods sold and purchased.
Market with asymmetric information = one side of the market has
better information than the other side of the market.
Examples:
• health sector – the MD is better informed than the patient
• insurance – the client has better information than the insurer
• used cars – the seller has better information than the buyer
Asymmetric information =⇒ quantity traded can be inefficiently low.
There are private solutions of the problem of asymmetric information.
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Asymmetric information (cont’d)
We will deal with 2 types of asymmetric information...
• adverse selection – a situation, in which one side of the market does
not observe the type/quality of the good on the other side
• moral hazard – a situation, in which one side of the market does not
observe the behavior of the other side of the market
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Asymmetric information (cont’d)
We will deal with 2 types of asymmetric information...
• adverse selection – a situation, in which one side of the market does
not observe the type/quality of the good on the other side
• moral hazard – a situation, in which one side of the market does not
observe the behavior of the other side of the market
a 2 possible solutions of asymmetric-information problems.
• signalization – agents might want to invest in signals that will
differentiate them from other agents
• incentives – using contract conditions to solve moral hazard
in labor markets
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Example of adverse selection – the market for “lemons”
Market for used cars: good cars G and bad cars B
Suppy:
• 100 sellers offering 50 G and 50 B
• willingness to sell G for $2,000 and B for $1,000
Demand:
• a large quantity of risk-neutral buyers
• each knows that 50 cars are G and 50 cars are B
• willingness to purchase G for $2,400 and B for $1,200
What cars do sell and for what price if
buyers can tell G from B?
Is the market for used cars efficient?
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Example of adverse selection – the market for “lemons”
Market for used cars: good cars G and bad cars B
Suppy:
• 100 sellers offering 50 G and 50 B
• willingness to sell G for $2,000 and B for $1,000
Demand:
• a large quantity of risk-neutral buyers
• each knows that 50 cars are G and 50 cars are B
• willingness to purchase G for $2,400 and B for $1,200
If the buyers can tell G from B,
all good cars G sell for $2,400
and all bad cars B sell for $1,200.
The market for used cars is efficient.
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Example of adverse selection – the market for “lemons”
What cars sell and for what price if the buyers can’t tell G from B?
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Example of adverse selection – the market for “lemons”
What cars sell and for what price if the buyers can’t tell G from B?
If buyers can’t tell G from B, their willingness to pay is
1/2 × 1,200 + 1/2 × 2,400 = $1,800.
Who is willing to sell at the price? Only the owners B.
The buyer is willing to pay only
1 × 1,200 = $1,200.
Result: Only B will be traded in equilibrium for $1,200.
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Example of adverse selection – the market for “lemons”
What cars sell and for what price if the buyers can’t tell G from B?
If buyers can’t tell G from B, their willingness to pay is
1/2 × 1,200 + 1/2 × 2,400 = $1,800.
Who is willing to sell at the price? Only the owners B.
The buyer is willing to pay only
1 × 1,200 = $1,200.
Result: Only B will be traded in equilibrium for $1,200.
Conclusion: The quantity sold in the market is inefficiently low.
Reason: The presence of B reduces the willingness to pay for G
(externality due to adverse selection)
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Example of signalization – the market for “lemons”
Sellers of G can signal that they have good cars.
E.g. they can spend $100 for a certificate of quality.
If sellers of B can’t get the certificate, customers can use the certificate to
tell G from B – the certificate signals quality.
Certificates solve the adverse-selection problem:
• The market is efficient. Cars B and G are sold.
• The welfare in the market increases by
50 × (2,400 − 2,000 − 100) = $15,000.
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Model of signalization – labor market in a town
Labor supply:
10,000 able workers A:
• value of product: aA = 16M
• year of study costs: cA = 0.2M
10,000 unable workers U:
• value of product: aU = 14M
• year of study costs: cU = 1M
All workers are willing to work for a minimum wage wmin = 5
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Model of signalization – labor market in a town
Labor supply:
10,000 able workers A:
• value of product: aA = 16M
• year of study costs: cA = 0.2M
10,000 unable workers U:
• value of product: aU = 14M
• year of study costs: cU = 1M
All workers are willing to work for a minimum wage wmin = 5
Demand for labor:
Perfect competition: many risk-neutral firms
Each firm has a production function: aALA + aULU
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Model of signalization – labor market in a town
Labor supply:
10,000 able workers A:
• value of product: aA = 16M
• year of study costs: cA = 0.2M
10,000 unable workers U:
• value of product: aU = 14M
• year of study costs: cU = 1M
All workers are willing to work for a minimum wage wmin = 5
Demand for labor:
Perfect competition: many risk-neutral firms
Each firm has a production function: aALA + aULU
Endogenous variables:
• the number of workers: LA and LU
• lifetime wage of workers: wA and wU
• the number of years at the university: eA and eU
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Model of signalization – labor market in a town (cont’d)
The town has no universities – no one has education (eU = eA = 0)
Who works and for what wages? Is the labor market efficient?
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Model of signalization – labor market in a town (cont’d)
The town has no universities – no one has education (eU = eA = 0)
Who works and for what wages? Is the labor market efficient?
The result depends on whether firms can tell A from U.
• Complete information – firms can tell A from U:
Demand for labor as in perfect competition – w = value MPL:
• wA = aA = 16
• wU = aU = 14
Wages higher than wmin =⇒ everyone works =⇒ efficient market
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Model of signalization – labor market in a town (cont’d)
The town has no universities – no one has education (eU = eA = 0)
Who works and for what wages? Is the labor market efficient?
The result depends on whether firms can tell A from U.
• Complete information – firms can tell A from U:
Demand for labor as in perfect competition – w = value MPL:
• wA = aA = 16
• wU = aU = 14
Wages higher than wmin =⇒ everyone works =⇒ efficient market
• Asymmetric information – firms cannot tell A from U:
Firms willing to pay an average value of MPL:
wA = wU = aA/2 + aU/2 = 15
Wages higher than wmin =⇒ everyone works =⇒ efficient market
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Model of signalization – labor market in a town (cont’d)
Asymmetric information – firms cannot tell A from U.
Workers can study, but education does not increase their productivity.
Sequential game with two steps:
1 Workers have 2 choices:
• study program lasting e∗
years
• study program lasting 0 years
2 Firms choose the wages of workers wA and wU
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Model of signalization – labor market in a town (cont’d)
Asymmetric information – firms cannot tell A from U.
Workers can study, but education does not increase their productivity.
Sequential game with two steps:
1 Workers have 2 choices:
• study program lasting e∗
years
• study program lasting 0 years
2 Firms choose the wages of workers wA and wU
Two different sequential equilibria:
• pooling equilibrium – all workers make the same choice
=⇒ not possible to tell A from U
• separating equilibrium – A and U make a different choices
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Model of signalization – labor market in a town (cont’d)
Asymmetric information – firms cannot tell A from U.
Workers can study, but education does not increase their productivity.
Sequential game with two steps:
1 Workers have 2 choices:
• study program lasting e∗
years
• study program lasting 0 years
2 Firms choose the wages of workers wA and wU
Two different sequential equilibria:
• pooling equilibrium – all workers make the same choice
=⇒ not possible to tell A from U
• separating equilibrium – A and U make a different choices
When does the separating equilibrium arise?
Do education opportunities increase efficiency of markets and welfare?
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Model of signalization – labor market in a town (cont’d)
Looking for separating equilibrium, in which A study and U don’t.
In this separating equilibrium, firms believe that
• workers with education are A =⇒ they pay them wA = aA = 16
• workers without education are U =⇒ they pay them wU = aU = 14
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Model of signalization – labor market in a town (cont’d)
Looking for separating equilibrium, in which A study and U don’t.
In this separating equilibrium, firms believe that
• workers with education are A =⇒ they pay them wA = aA = 16
• workers without education are U =⇒ they pay them wU = aU = 14
If the duration of education e∗ is in a range
aA − aU
cU
< e∗
<
aA − aU
cA
2 < e∗
< 10,
the profile (eA, eU, wA, wU) = (e∗, 0, 16, 14) is separating equilibrium.
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Model of signalization – labor market in a town (cont’d)
Looking for separating equilibrium, in which A study and U don’t.
In this separating equilibrium, firms believe that
• workers with education are A =⇒ they pay them wA = aA = 16
• workers without education are U =⇒ they pay them wU = aU = 14
If the duration of education e∗ is in a range
aA − aU
cU
< e∗
<
aA − aU
cA
2 < e∗
< 10,
the profile (eA, eU, wA, wU) = (e∗, 0, 16, 14) is separating equilibrium.
It is an equilibrium – no incentive to change actions:
• firms maximize profit (workers A get aA and U get aU)
• U does not choose eU = e∗ because the education cost 1 × e∗ > 2
• A does not choose eA = 0 because wage increase 2 > 0.2e∗
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Model of signalization – labor market in a town (cont’d)
Do study possibilities increase welfare and efficiency of the market?
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Model of signalization – labor market in a town (cont’d)
Do study possibilities increase welfare and efficiency of the market?
No:
• Market efficiency stays the same – efficient even without education.
• Welfare is lower because workers A spent 0.2e∗ for education
(assuming that education does not create any value per se).
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Model of signalization – labor market in a town (cont’d)
Do study possibilities increase welfare and efficiency of the market?
No:
• Market efficiency stays the same – efficient even without education.
• Welfare is lower because workers A spent 0.2e∗ for education
(assuming that education does not create any value per se).
BONUS QUESTION:
Does the result change if A can also freelance for wf
A = af
A = 15.2?
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Model of signalization – labor market in a town (cont’d)
Do study possibilities increase welfare and efficiency of the market?
No:
• Market efficiency stays the same – efficient even without education.
• Welfare is lower because workers A spent 0.2e∗ for education
(assuming that education does not create any value per se).
BONUS QUESTION:
Does the result change if A can also freelance for wf
A = af
A = 15.2?
Yes:
If the education e∗ < 4, A are willing to study.
• Efficiency increases because A are more productive in firms: aA > aZ
S
• Welfare is higher because the cost of studying 0.2e∗ < aA − aZ
S = 0.8.
Education signals the quality of the worker.
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APPLICATION: The sheepskin effect
Difficult to measure the effect of diploma on wages – selection bias.
Clark and Martorell (JPE, 2014) – use regression discontinuity design.
No evidence of a sheepskip effect of a Texan high school diploma.
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CASE: Reputations in collectibles sales
List (JPE, 2006) studied the market for sports memorabilia.
Asymmetric information – sellers know the value of the items.
Natural experiment:
1 Seller:
”
I would like to buy a card, which has a value of $x.“
2 The buyers can offer a card of
• a corresponding value
• a lower value – but he may damage his reputation
3 the card is evaluated by an independent expert
Findings:
• local sellers cheat less (they are
more often in the market)
• everyone cheats with items that
cannot be evaluated by a third party
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Example of moral hazard – bicycle insurance
Theft probability depends on behavior (e.g. the number of locks).
If the insurance
• observes clients’ behavior, it can adjust insurance accordingly
• does not observe the behavior, the insured bikers do not have
incentives to take care of their bicycles = moral hazard
The insurance is not willing to provide full insurance (“deductible”).
The amount of insurance is inefficienty low due to moral hazard.
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CASE: Vehicle insurance
Probability of accident depends on many factors such as speed. =⇒
moral hazard occurs in this situation.
The insurance premium is usually based on driver’s history.
It is an imperfect solution of moral hazard.
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CASE: Vehicle insurance
Probability of accident depends on many factors such as speed. =⇒
moral hazard occurs in this situation.
The insurance premium is usually based on driver’s history.
It is an imperfect solution of moral hazard.
Solution: usage-based insurance (UBI) or pay as you drive (PAYD)
Payment for km may be based on data collected from the vehicle:
• type of driving (speed, braking)
• time-of-day information
• historic riskiness of the road
• distance or time traveled
• time/distance driven without a break
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What should you know?
• The prisoner’s dilemma is a particular
game in which the Pareto efficient
outcome is strategically dominated
by an inefficient outcome.
• A cartel is a group of firms that
maximize profit of the industry.
• If firms play a one-shot or a finitely
repeated game, the cartel is unstable.
• If they play an infinitely repeated game,
punishment ensures cartel’s stability if
firms are sufficienty patient (r is low).
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What should you know? (cont’d)
• Adverse selection is a situation, in which one
side of the market does not observe the
type/quality of the good on the other side
• Moral hazard a situation, in which one side of
the market does not observe the behavior of
the other side of the market.
• Signalization may solve the problem of
asymmetric information, but may also be
socially wasteful.
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