MICROECONOMICS II.

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MICROECONOMICS II.

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ELTE Faculty of Social Sciences, Department of Economics

Microeconomics II.

week 6

THE ECONOMICS OF RISK AND INFORMATION, PART 2 Author: Gergely K®hegyi

Supervised by Gergely K®hegyi

February 2011

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week 6 Gergely K®hegyi

Information problems Information asymmetry Human resource management Auction markets

Prepared by: Gergely K®hegyi, using Jack Hirshleifer, Amihai Glazer és David Hirshleifer (2009) Mikroökonómia. Budapest:

Osiris Kiadó, ELTECON-könyvek (henceforth: HGH), and Kertesi Gábor (ed.) (2004) Mikroökonómia el®adásvázlatok.

http://econ.core.hu/ kertesi/kertesimikro/ (henceforth: KG).

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Outline

1 Information problems

2 Information asymmetry

3 Human resource management

4 Auction markets

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Why is information limited?

It is costly to collect information.

Only a limited amount of information can be recorded and recalled.

Information processing are usually imperfect and costly.

Distrust: information is usually inaccurate and quickly gets outdated.

Information process based on simple rules often leads to more ecient decisions (e.g. theory of bounded rationality. Simon), thus full information is unnecessary (not optimal).

Note

Which factor dominates? This depends on the industry and on the actor.

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Why is information limited? (cont.)

Note

Dealing with information within economic theory is rather problematic, since it can hardly be included in any of the simple models. It is debated that the interesting cases are the ones, where it cannot be included. Information sometimes is not a scarce good, but an abundant. Problems can be caused by too much of it.

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Value of information

Suppose you see an ad for a computer at a special price today of

$800. The sale is for one day only. If you wait for tomorrow, you are unsure what the price then will be. Let's say you estimate that the price will rise to $950, but a one-third chance the price will decline to $700. Let's assume we are risk neutral.

Expected price: (1/3)×700 dollar+(2/3)×950 dollar

=866,67 dollar

If our reservation price: Pd =810 dollar, then consumer surplus: CS=810-800=10 dollar, if we buy it today; but if we wait, then the expected consumer surplus

E[CS] = (1/3)×110 dollar +(2/3)×0 dollar=36,67 dollar.

It is worth to wait, in spite of that the expected price is greater tomorrow than today.

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Value of information (cont.)

Let's assume that our reservation price is greater than $950 and we can subscribe to a marketing service, which forecasts tomorrow's price perfectly. Then the expected consumer surplus: CS =Pd−800 dollar, if we do not subscribe, and E[CS] = (1/3)(Pd−700) + (2/3)(Pd−800) =Pd−766,67 dollar if we do subscribe.

Thus we would pay a maximum of 800−766,67=33,33 dollar, for this marketing service.

Note

Postponing the decision we provide ourselves an option to decide after tomorrow's information is available (see forward markets).

The utility of information is in this option. We only want to know more, if we change our decisions due to additional information.

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Value of information (cont.)

Possible outcomes (states of world): s₁;s₂

Probability of a change in these outcomes: f,(1−f) Possible alternatives (actions): a1,a2

Lets assume that in 1st state of the world a1is a better choice, while a2is better in the second.

Consumer surplus CS^o can be gained without additional information.

With additional information. the expected consumer surplus is CS⁰

CS^o=fCS(a₁|s₁) + (1−f)CS(a₁|s₂) CS⁰=fCS(a₁|s₁) + (1−f)CS(a₂|s₂)

The dierence between the two consumer surpluses gives the value of the information. That is the maximum price that we are willing to pay for a marketing service (for instance).

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Corrected supposition

Decision under information problem: the actor does not know the value of some parameter only its probability distribution. But before the decision s/he gains some additional information and modies the knowledge about the probability distribution accordingly (corrected supposition).

E.g.: Heads or tails with a nicked coin. (Source: Gömöri András (2001): Információ és interakció. Bp: Typotex)

Three types of coins: (head/head) (head/tail) (tail/tail) If you guess right, you get 30 Ft (Π=30); if now loose 50 Ft (Π=30)

Under uncertainty, if you guess "head": E(Π) =

(1/3)×(−50)+(1/3)×30+(1/3)×(0,5×30−0,5×50) =−10 Under information problem, if you can look at one side of the coin, (has "head" on it) and you guess "head" (corrected supposition):

E(Π) = 2

3×30+1 3 1

2×30+1 3 1

2 ×(−50) +0×(−50) =50 3

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Corrected supposition (cont.)

Making interactional decisions in case of information problems:

If actors do not have perfect information, but their information is identical: Symmetric information problem.

If actors do not have perfect information, neither identical:

Asymmetric information problem.

Two types:

Limited information of price

Limited information of quality (attributes of product, attributes of consumer, type of company, etc.)

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Search model

If we don't know the dierent prices of the desired (homogenous) product sold in numerous shops (information problem), how many shops is it worth to visit before buying the good? (source: Gábor Kertesi Ádám Rei: Az információs közgazdaságtana)

(www.econ.core.hu/kertesi/kertesimikro) n: number of visited shops

pn: price of the product in the n^th shop MC: marginal cost of visiting another shop Decision algorithm:

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Search model (cont.)

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Expected benet and marginal benet

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Expected benet and marginal benet (cont.)

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Search optimum

For example, if marginal cost of searching is MC1, then it is worth to visit two shops, but not three.

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Search optimum (cont.)

Factors inuencing the extent of optimal searching:

Price-center of the product ('its value') Dispersion of supply-prices

Preference and income of the consumer Geographic features of the market

In-time correlations of shops' supply-prices

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Tourist-trap model

Assumptions:

Every rm (souvenir-shop) sells the same product and faces the same costs.

Demand-curves of the consumers are identical.

Limited information of price: probability distribution of prices is known (how many shops ask a given price).

The cost of visiting another shop for the tourist is: c.

In case of a xed (n) number of companies

Competitive equilibrium in case of perfect information: pc. Competitive equilibrium is broken: p^∗<pc+εis more favourable.

The new 'competitive' equilibrium is a monopolistic price: pm. The reduction of searching costs doesn't inuence

equilibrium.

If higher than the consumers' reservation price, then market does not exist.

In case of free entry and exit

The reduction of the number of rms can increase welfare!

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Market for Lemons and adverse selection

G. Akerlof (1970): Market for Lemons

Two dierent quality (high/low) cars are to be sold (quality is known only by owners).

Consumers know only that half of the cars supplied is high-quality and the other half is low-quality (they know the probability distribution of quality).

Reservation prices of sellers: in case of high-quality: 1 M HUF; in case of low-quality: 0.5 M HUF.

Reservation prices of buyers: in case of high-quality: 1.2 M HUF; in case of low-quality: 0.6 M HUF.

Change: The buyer oers a price which is either accepted by the the seller or not.

All of this is common knowledge.

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Market for Lemons and adverse selection (cont.)

Equilibrium

If the consumer oers the "average" price (0,5×1.2+0.5×0.6=0.9).

He can get only a low-quality car at this price.

Therefore he oers only 0.5 M HUF.

Only low-quality cars are exchanged on the market.

High-quality cars cannot be sold.

Denition

When low-quality goods or services (lemons) destroy the market for high-quality goods (peaches) we talk about Adverse selection.

Modications:

If the reservation price of sellers of high-quality cars is 0.9 M HUF, then the quality of the car exchanged is uncertain.

If consumers don't pay for the low-quality car, then the market collapses.

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Market for Lemons and adverse selection (cont.)

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Reducing adverse selection

Examples for adverse selection: rare antiques, building industry, electricians, painters, masons, restaurants, life-insurers, health service, education, sub-urbanization, poisoned shares, etc.

Reducing adverse selection:

Signing: Action of the well-informed participant Warranty or guarantee

Reputation

Screening: Action of badly-informed participant Product-liability laws

Professionals

Standards and certicates

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Reducing adverse selection (cont.)

Conveying Quality through Reputation Case 1 Case 2

quality low high low high

price 4 13 4 7

cost of production 4 5 4 6

Source: Hirshleifer et al, 2009, 419.

Consequence

Even in the face of initial consumer ignorance, market forces can support production of high-quality products. Depending upon the specic demand and cost conditions, it may pay a high-quality rm to accept a temporary loss while building a reputation, thereby gaining future business. But in other circumstances it would be unprotable for a rm to incur the extra costs of establishing a reputation for high quality.

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Reducing adverse selection (cont.)

Signals

The eects of grade cards on restaurant hygiene score in Los Angeles. As of December 1997 restaurants were required, in a number of cities within the county, to publicly display grade reports rating their hygiene as A, B, or C. (Average scores are shown in the second column.)

Quarter Hygene score

1996/1 75.62

1996/2 75.37

1996/3 75.03

1996/4 75.27

1997/1 75.81

1997/2 75.31

1997/3 83.99

1997/4 81.82

1998/1 86.69

1998/2 90.26

1998/3 89.85

1998/4 90.30

Source: Hirshleifer et al, 2009, 421.

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Conveying quality through prices

A monopoly produces either high quality goods (MC =2), or low quality goods (MC =1)

The quality of the good is NOT a decision variable, it is given for the monopoly.

The reservation price of consumers (they buy either 1 portion or nothing): in case of high quality equals 10; in case of low quality 0.

Consumers know the probability distribution of quality:

P(high) =x, P(low) =1−x.

2 periods

In the rst period the consumer observes the quality of the product.

If quality is low then he doesn't consume in the second period; if quality is high he will consume in the second period.

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Conveying quality through prices (cont.)

Pricing: p₂=10

E(CS) =x(10−p1) + (1−x)(0−p1) +x(10−10) =0 10x−p₁=˙0

10x=p1

Π_j = (p₁−2) + (p₂−2) = (10x−2) + (10−2) Π_r =p₁−1=10x−1

Pooling equilibrium: If x=0.7;p1=7; Π_j=13; Π_r =6 Separating equilibrium: If

x =0.05;p1=0.5; Π_j =6.5; Π_r =−0.5

Every p1<1 price is appropriate as a separating equilibrium, but pooling equilibrium only exists if x>0.1.

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Labour market signals

On the labor market there are two types of workers:

high-ability and low-ability workers.

The marginal product of the high-ability worker is aH. The marginal product of the low-ability worker is a_L. aL <aH.

h is the ratio of high-ability workers.

Wages equal to the marginal product of the workers.

Employers are risk-neutrals.

w_P = (1−h)a_L+ha_H <a_H is the payment if the employer isn't familiar with the ability-level of the workers.

For the high-ability worker it is worth to sign his high-ability.

Therefore he studies, his degree will be a signal.

Unit cost of studying in case of the two workers: c_L>c_H. The high-ability worker will study eH units, if

wH−wL=aH−aL>cHeH

wH−wL=aH−aL<cLeH.

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Labour market signals (cont.)

Separating equilibrium:

a_H−a_L

cL <eh< a_H−a_L cH

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The Principal-Agent Problem

Moral hazard

E.g.: The eort that an employee ('the agent') devotes to the job can be only imperfectly monitored by the rm ('the principal'). A taxi driver, working out of sight of his supervisors, would be tempted to shirk if paid a straight hourly wage. Compensating him by a fraction of the amount shown on the meter, as is typically the case in current practice, reduces but does not eliminate the incentive to shirk. True, tips also reward diligence, and on the negative side there is the fear of being red. Still, unless the driver receives the full marginal dollar paid by the rider, an incentive problem remains.

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The Principal-Agent Problem (cont.)

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The Principal-Agent Problem (cont.)

Time-rate vs.

piece-rate payment

The worker with the greater aversion to eort prefers the time-rate scheme. The other worker prefers the piece-rate scheme, allowing her to attain point C^∗.

Compensation at Safelite between 19941995 Hourly wage Piece rate Units per worker per day 2.70 3.24

Actual pay (dollar) 2228 2283

Cost per unit (dollar) 44.83 35.24 Source: Hirshleifer et al., 2009, 509.

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The Principal-Agent Problem (cont.)

The principal pays (w) wage for the agent to do the job and gains (Π) amount of prot.

The principal cannot observe the eorts taken by the agent, only the outcome, which depends on external conditions too.

If the agent 'works', then he sacrices h>0 utility, if he is a 'slacker' then h=0.

Utility function of the agent: U(w,h)(w: wage).

Reservation wage and utility of the agent:

w₀,U(w₀,h=0), (U⁰>0,U⁰⁰<0)

If the agent works, then the principal realizes Π₂ high prot with probability x, if he is a 'slacker', then with probability y;

otherwise the agent realizesΠ₁ low prot(0<y <x <1). Question: What kind of(Π₁,w1); (Π₂,w2)contract menu should be oered by the principal?

Quantity sold in case of high prot: y₂. Participation constraint:

xU(w2,h) + (1−x)U(w1,h)>U(w0,h=0)

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The Principal-Agent Problem (cont.)

Incentive constraint:

xU(w₂,h) + (1−x)U(w₁,h)>U(w₀,h=0)>

yU(w2,h=0) + (1−y)U(w1,h=0) Expected prot (target function):

x(Π₂−w₂) + (1−x)(Π₁−w₁)→ max

w1,w2

Expected prot-function is diminishing in both wages, therefore constraints must be realized as equal.

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The Principal-Agent Problem (cont.)

Example (vacuum cleaner agent):

Output of the company: y, price of its product: p_y =1 (assumption: the company is a 'price-taker' on the market of its product).

Wage of a single employee: w.

Utility-function of the employee: U =√

w−a, where h=0, if he is a slacker and h=2, if he is hard-working.

Utility of leisure as an alternative activity: U₀=15.

If the agent is a slacker (h=0), then output will be high y_M =400 with probability y =1/3.

If the agent is a slacker (h=0), then output will be low yA=100 with probability 1−y =2/3.

If the agent is hard-working (h=2), then output will be high yM =400 with probability x=2/3.

If the agent is hard-working (h=2), then output will be low yM =400 with probability 1−y=1/3.

What kind of incentive wage-scheme should the employer oer?

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The Principal-Agent Problem (cont.)

Solution:

Target function: 2/3wM+1/3wA→minwM,wA

Participation constraint: 2√

w_M+√

w_A≥51 Incentive constraint: √

wM−√ wA≥6

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The Principal-Agent Problem (cont.)

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Types of auctions

Assumption

A relatively unique product, a single seller facing several potential buyers, whose 'reservation values' are unknown.

In terms of the bidding procedure, auctions fall into two main categories:

English (ascending-price) auction. This is the familiar system of open public bids. The person making the highest oer wins the item being sold, and must pay the amount bid.

Dutch (descending-price) auction. In the famous ower auctions at Aalsmeer in Holland, a clock visible to all participants is started at a high price. The price drops in steps until one of the potential buyers makes a bid by pushing a button. The winner pays the amount bid, as shown on the clock.

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Types of auctions (cont.)

In the sealed-bid method, all oers are submitted in sealed envelopes to be opened simultaneously. The highest bid naturally wins. But there are two types of sealed-bid auctions, corresponding to the amount that the winning bidder pays:

Sealed-bid rst-price auction. The winner pays the amount bid.

Sealed-bid second-price auction. Here the sale price, although paid by the winner, is only the amount oered by the runner-up the second-highest bid.

Variations

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Types of auctions (cont.)

Statement

Equivalence theorems

The equilibrium of the sealed-bid second-price auction is equivalent to the English open-outcry auction (truth-saying is the protmaximizing and equilibrium strategy).

The equilibrium of the sealed-bid rst-price auction is equivalent to the Dutch auction (revealing half of the reservation values is an equilibrium strategy in certain conditions).