Chapter 3 Managing the firm School of Economics and Business Administration Universidad de Navarra.

Chapter 3Chapter 3 Managing the firmManaging the firm

School of Economics and Business Administration

Universidad de Navarra

Theories of the firm

Neoclassical Theory

Contractual Theory

Agency Theory

Behavioral Theory

Structure of chapter 3Structure of chapter 3

3.1. Selection of employees3.1. Selection of employees

3.2. Motivation of employees

3.3. The Psychology of incentives

3.4. Teamwork and cooperation

The labor demand is derived from maximizing firms profits.

Marginal Income of Labor=

Marginal Cost of Labor (Price of Labor)

3.1. Selection of employees3.1. Selection of employeesNeoclassical theoryNeoclassical theory

Max pQ - C(Q) Max pf(K,L) - rK – wL

p(∂f / ∂L) = w & p(∂f / ∂L) = r

Assumption A (Perfect Competition)A market exists for each good or service, and markets participants (consumers and producers) are in large number so that they do not affect the market outcomes.

Assumption B (Full Rationality)B1) Agents have unlimited computational abilities.

B2) Agents are self-interested and maximize an objective function referred to as a utility function.

Assumption C (Perfect Information)Agents have perfect information on prices and other agents' preferences (consumers) and technologies (producers).

3.1. Selection of employees3.1. Selection of employeesLimits of the Neoclassical theoryLimits of the Neoclassical theory

Data on workers’ mobility and turnover.

1. The rate of mobility between EU countries is 0.1% a year whereas it is 4% in the US.

2. Workers’ turnover and mobility is also low inside EU countries.

- In a 10 years horizon, 40% of the workers stay in the same job.

- Inside the mobility rate between provinces is around 7%.

3.1. Selection of employees3.1. Selection of employeesSearch costs and work mobilitySearch costs and work mobility

Why workers’ mobility is so low?

1. Few opportunities, imperfect competition (Hypothesis A does not hold).

2. Search costs, limited rationality (Hypothesis B1 does not hold).

3. Social preferences (Hypothesis B2 does not hold).

4. Imperfect information about jobs (Hypothesis C does not hold).

3.1. Selection of employees3.1. Selection of employeesSearch costs and work mobilitySearch costs and work mobility

Hypothesis C’Hypothesis C’: Asymmetric information.: Asymmetric information.

We consider in section 3.1 about personnel selection the case asymmetric information exante (before the contract is signed).

3.1. Selection of employees3.1. Selection of employeesAsymmetric informationAsymmetric information

Example: Consider the following distribution of abilities of workers and outside options.

% MI wR (outside option)

30 100€ 40€

70 40€ 100€

Akerlof, Nobel 2001

3.1. Selection of employees3.1. Selection of employeesAdverse selectionAdverse selection

In this case, the average productivity of a worker in the population is given by: 0.3×100 + 0.7×40 = 58€.

The firm faces a problem of adverse selection (Akerlof 1970: used cars markets) since only low-productivity workers will apply for the job.

Adverse selection: high-quality products or services cannot be sold in the market because of asymmetric information between buyers and sellers that renders impossible the identification of these products or services.

Akerlof, Nobel 2001

Examples: the role of reputation and standardization.

- Market for insurance.

- Market for credit.

- Retail stores.

- Restaurants.

Akerlof, Nobel 2001

To select employees with adequate levels of productivity, the firm may require a certain level of education acting as a signal in a context in which the information about candidates is scarce (Spence 1973, 1974).

A signal has to be costly such that only high-ability workers will be able to release the signal (e.g. College education) .

Spence, Nobel 2001

3.1. Selection of employees3.1. Selection of employeesSignalingSignaling

For a signal (e.g. College education) to be effective only high-ability workers should have the incentives to go to college (separating equilibrium: different types of individuals play different actions).

It is crucial that the cost of the education signal is higher for individuals with high levels of abilities (cH) than for individuals with low levels of abilities (cL > cH).

Spence, Nobel 2001

The following conditions allow the organization to identify high-ability workers, that is they allow for the existence of a separating equilibrium.

1. 100 - cL < 40 so that cL > 60 (low-ability workers do not go to college.)

2. 100 - cH > 40 so that cH < 60 (high-ability workers go to college.)

- The education system as a signaling mechanism: empirical evidence with “academias” with their unique objective of obtaining the pass of their clients .

Spence, Nobel 2001

Exercise: Given the following distribution of abilities of workers applying and given the following costs of the education signal: CH = 35 y CL = 65€.

Determine the optima job offer of the firm.

% MI wR (outside option) Coste C

30 100€ 40€ CH = 35€

70 40€ 100€ CL = 65€

Akerlof, Nobel 2001

Spence, Nobel 2001

Working into the night

Job market signaling does not end when one is hired. This is especially true for workers in knowledge-based fields such as engineering, computer programming, finance, law, management, and consulting.

Given this asymmetric information, what policy should employers use to determine promotions and salary increases?

Workers can often signal talent and productivity by working harder and longer hours.

Employers rely increasingly on the signaling value of long hours as rapid technological change makes it harder for them to find other ways of assessing workers’ skills and productivity.

Compensation also has an effect on the type of individuals applying for a job.

The influence of the compensation contract offered by the organization on the type of workers applying for a job is called screening. (Example: salesman paid a fixed wage).

3.1. Selection of employees3.1. Selection of employeesScreeningScreening

Example I (Toy industry).

- There exists a large set of workers with different levels of productivity measured by the number of toys produced per day. The productivity of worker i (ηi) follows a uniform distribution between 0 and 10, that is ηi ~ U(0,10).

- Productivity is private information.

Example I (Toy industry). - Density function: ηi ~ U(0,10).

f(x)=1/10

- Firm A pays a variable wage of 20€ per toy produced by the worker.

- Firm B pays a fixed wage of 100€ per day.

- The two firms sell their product at a price p equal to 30€ per unit.

- We assume that workers are risk neutral.

a) Which types of workers will apply for a job in firm A? And which types will apply for a job in firm B?

b) Can firm B stay in the toy business?

c) Is there any level of fixed wage such that firm B could stay in the toy business?

d) Could you give any reasons why high-productivity workers may be interested in working for the firm offering fixed wages?

1. Risk aversion.

2. Measurement errors.

3. Equity.

Example II (franchising).

- for its Spanish franchises, the fast food company McRey requires a payment by franchisees equal to a proportion α over the sales of the restaurant (i.e. “royalties”).

- Population of managers of 2 types: Good managers generate expected sales of 120 000€ a

month. Bad managers generate expected sales of 120 000€ a

month.

- Total costs are the same for the 2 types of managers:

50 000 €.

a) Assume that entrepreneurs of both types are currently earning 3000€ per month. That is, entrepreneurs’ outside option is 3000€. If McRey wants to attract only Good entrepreneurs, what should be the value of α?

1. πG ≥ 3000

120000 - α(120000) - 50000 ≥ 3000

α < 55.8%.

2. πB < 3000 implies that:

90000 - α(90000) – 50000 < 3000 so that α > 41.1%.

b) We consider now that the different types of entrepreneurs are currently earning different wages. Good entrepreneurs earn 5000 € a month whereas Bad entrepreneurs make 3000 € a month. In this case, what should be the value of α to attract only good entrepreneurs?

Banks usually give their clients the opportunity to pay mortgages with fixed rates or variable rates.

Do you believe banks are using a screening-mechanism? Why?

Spence, Nobel 2001

3.1. Selection of employees3.1. Selection of employeesScreening exampleScreening example

Other examples of screening mechanisms.

Selection process. Probation period.

- Establish an initial trial period, for example one year, an at the end of the year, the firm may decide whether to offer a lifetime contract.- The probation period allows managers to detect, with a certain probability, high-ability workers.- Pay a low salary in the probation period as a mechanism of screening.

Exercise: probation period.

- There exists 2 types characterized by a low level of ability (L) or a high level of ability (H).

- They produce respectively 4 and 6 units a day.

- Alternative options for the 2 types of workers:

WL = 16€ and WH = 20€ per day.

- Each employee will work 2000 hours a year and will be working for 20 years.

- The firm introduces a probation period of 1 year after which it decides whether to offer a contract for the next 19 years.

The firm decides wages for the probation period (W1) as well as the level of wages for the period following the trial period (W2) with the objective of attracting only high-ability workers.

A worker with a high level of ability will always be identified at the end of the trial period whereas a low-ability workers may mistakenly be identified as good with probability 0 < p < 1.

The conditions that have been satisfied to attract only high-ability workers are derived below.

Screening high-ability workers.

1. 2000W1+ 2000 × 19W2 ≥ 20×2000WH

2. 2000W1+p2000×19W2+(1-p)2000×19WL ≤ 20×2000WL

Solution.

W2= WL + 20×(WH - WL)/19×(1-p)

Dohmen and Falk (2006) ran an experiment in which 240 subjects undertake a real task. Subjects could decide the mode of payment before starting the task (fixed or variable).

Results.

1. Very productive subjects are more likely to choose a variable wage.

2. Risk averse workers are more likely to choose a fixed wage.

3. Women are less likely to choose a variable wage. This is mainly due to higher risk aversion.

3.1. Selection of employees3.1. Selection of employeesEmpirical evidenceEmpirical evidence

3.1. Selection of employees

3.2. Motivation of employees3.2. Motivation of employees

1. We consider an agency relationship between an individual called agent (employee) that acts on the behalf of an individual called principal (manager).

2. The principal hires an agent a task that is costly to the agent C(e).

3. The principal does not always possess information on the level of effort exerted by the agent.

3.2. Motivation of employees3.2. Motivation of employeesOptimal contractsOptimal contracts

We consider that there is an agency relationship when an individual, called the agent, acts on behalf of another individual, called the principal. The principal and the agent have diverging goals and different information.

Principal

Action

Wage: w

Effort: e

3.2. Motivation of employees3.2. Motivation of employeesOptimal contractsOptimal contracts

The principal is risk neutral, whereas the agent is risk averse.

Principal’s utility function (u) is linear in income: u(y) = y.

Whereas agent’s utility function (v) is concave: v(w) = √w.

3.2. Motivation of employees3.2. Motivation of employeesOptimal contracts (risk attitudes)Optimal contracts (risk attitudes)

As a result, we know that:

- For a risk neutral individual the CE of a lottery is equal to the expected value of the lottery.

- For a risk averse individual the CE of a lottery is lower than the expected value of the lottery.

- For a risk lover individual the CE of a lottery is higher than the expected value of the lottery.

Lottery L:

- You get 200€ with probability 50%.

- You get 0€ with probability 50%.

What is the CE of this lottery for the principal?

What is the CE of this lottery for the agent?

Wages0 100€

v(100)v(50)

E(v)=5

50€CE = 25€

Approximation used for the CE:

Then we can compute the risk premium:

Where r = - U’’ / U’

Compute the risk premium for the agent for lottery L.

CE = E(L) – 0.5×r×var(L)

RP = E(L) - CE =0.5×r×var(L)

Then, maximizing the expected utility of the agent consists in maximizing the certainty equivalent of the lottery associated to his income: w - C(e).

That is, the agent receives a salary w (that can be stochastic) and pays a cost C(e) to undertake the task required by the principal, where C’(e) > 0 y C’’(e) < 0 .

CE[w - C(e)] = E(w - C(e)) – 0.5×r×var(w)

3.2. Motivation of employees3.2. Motivation of employeesfirst-best contracts (risk attitudes)first-best contracts (risk attitudes)

Risk arises because the outcome of the action of the agent, z, depends on effort e and other random factors x:

z = e + x The wage contract w offered by the principal links pay

to the final outcome z, that is w(z). The certainty equivalent of the agent is:

ECa = E[w(z) - C(e)] – 0.5×r×var[w(z)] The certainty equivalent of the principal is:

ECp = P(z) – w(z)

3.2. Motivation of employees3.2. Motivation of employeesfirst-best contracts (risk attitudes)first-best contracts (risk attitudes)

The first-best contract implements the efficient level of effort as follows:Max E[P(z) - w(z)]

s.a. E[w(z) - C(e)] - 0.5r×var[w(z)] > v0

Substituting the restriction in the objective function of the principal:

Max E[P(z)] - C(e) - 0.5r×var[w(z)] - v0

3.2. Motivation of employees3.2. Motivation of employeesfirst-best contracts: first-best contracts: observable effortobservable effort

There is 2 important characteristics of the first-best contract:

P’(e) = C’ (e) (Give incentives to the agent)

Var (w) = 0 (Protect the agent against risk)

3.2. Motivation of employees3.2. Motivation of employeesfirst-best contracts: first-best contracts: observable effortobservable effort

For example, i P(z) = 10z, with z = e + x where:

x ~ N(0,σ²) , C(e) = e² / 50

The efficient level of effort is given by:

Max E[10z - w(z)]

s.a. E[w(z) - e² / 50 - 0.5r×var[w(z)] > v0

3.2. Motivation of employees3.2. Motivation of employeesExample:Example: first-best contractfirst-best contract

The maximization problem is equivalent to:

Then, the efficient level of effort is such that:

10 = e / 25 so that e* = 250. The first-best contract is such that the variance

of wages w is zero.

Max 10e – [e² / 50 + 0.5r×var[w(z)] + v0]

As a result, the firs-best contract is given by:

- If e* < 250 then w = 0

- If e* = 250 then w = 1250 + v0

The efficient level of effort is obtained by maximizing the aggregate welfare of the agent and the principal.

However, the level of effort is not always observable so that the following problems can arise:

1. Observability and measurement problems

2. Moral hazard and risk sharing

3.2. Motivation of employees3.2. Motivation of employeesProblems to implement theProblems to implement the first-best contractfirst-best contract

Hypothesis C’: the principal cannot observe the agent’s effort, he cannot write a contract that links pay with effort.

The only feasible contracts are those linking w with observable variables, in our case z.

Since x is random, the wage w is not perfectly correlated with the effort of the agent e.

In the case of asymmetric information there exists a conflict between incentives and risk sharing:

- A contract that minimized the risk premium would pay a fixed wage, independent of z

- However, this contract would lead the agent not to exert any effort e = 0.

If the principal wants to induce the agent to exert an effort, he needs to pay w as a function of z.

However, the more the wage w depends on z, the higher level of risk is supported by the agent, and the higher is the risk premium that the principal should pay.

The principal should find a balance between giving proper incentives to the agent and protecting him against risk.

We will study the design of contract when the effort of the agent is not observable. We will focus on linear contracts that are composed of a fixed part and a variable part:

w(z) = α + βz The principal’s problem consists in choosing a fixed

payment α a variable payment β, taking into account the conflict between incentives and risk sharing.

3.2. Motivation of employees3.2. Motivation of employees Unobservable effortUnobservable effort and linear contracts and linear contracts

Consider the following stages:1. The principal proposes a contract (α,β) 2. The agent accepts or rejects the offer

3. If the agent accepts, he chooses his level of effort, e4. The principal observes z, and pays the agent a wage w(z) = α + βz.

In stage 4., once z has been realized, the wage received by the agent is: w(z) = α + βz

In stage 3., the agent will choose his level of effort as follows:

Max α + βe - C(e) - 0.5rβ² ×var[x]

Max E[w(z)] - C(e) - 0.5r×var[w(z)]

The optimal level of effort exerted by the agent is such that: β = C’(e)

This restriction has to be taken into account by the principal to select the contract (Incentives Constraint: IC).

The principal has also to take into account that agent should be willing to accept the contract (Participation Constraint: PC).

The participation constraint (PC) is:

α + βe - C(e) - 0.5rβ² ×var[x] > v0 The problem of the principal consists in

choosing a contract (α , β) so that:

Max P(e) – (α + βe)

s.a. β = C’(e) (IC)

s.a. α + βe - C(e) - 0.5rβ² ×var[x] > v0 (PC)

Plugging these restrictions into the principal’s problem we get:

Max P(e) – (v0 + C(e) + 0.5r(C’(e))² ×var[x] )That is, it is as if the principal chooses the effort level.

The optimal level of effort is given by:P’(e) = C’(e) + rC’(e)×var[x]×C’’(e)

C’(e) = P’(e) / (1 + r var[x] ×C’’(e) )

And the value of β is:

β = C’(e) = P’(e) / (1 + r var[x] ×C’’(e) ) If C(e) is convex, the level of effort chosen by

the agent will be inferior to the efficient level of effort, except if r = 0 or if var(x) = 0.

C’(e) = P’(e) / (1 + r var[x] ×C’’(e) )

< P’(e) Efficient level of effort: C’(e) = P’(e)

If C(e) is convex, the level of effort is inferior to the efficient level.

P’(e), C’(e)

P’(e)

C’(e)e*

C(e) = e²

P(e) = a×e

If C(e) is convex, the level of effort is inferior to the efficient level.

P’(e), C’(e)

P’(e)

C’(e)e*

P’(e) / (1 + r.v[x]C’’(e) )

The value of α is given by the participation constraint (RP), as follows:

α = v0 - βe + C(e) + 0.5rβ² ×var[x]

For example, if P(z) = 10z, con z = e + x where:

x ~ N(0,σ²) , C(e) = e² / 50 The principal is risk neutral and the agent is

risk adverse with an absolute risk aversion coefficient r.

The level of effort e is not observable. Consider linear contracts: w(z) = α + βz.

3.2. Motivation of employees3.2. Motivation of employees Example I: Example I: linear contracts linear contracts

a) Determine the incentive compatibility constraint (IC) and the participation constraint (PC), given that v0 is the best outside option for the agent.

b) Determine the contract offered by the principal, that is the couple (α , β).

c) Compare the level of effort that principal implements in part b) with the efficient level of effort.

Lazear (2000) studies fixed pay versus variable pay in the Safelite Glass Corporation.

“We recognize and reward results” An increase of 36% in production: incentives effect

and screening effect. This study confirms the positive effect of variable

pay on incentives.

3.2. Motivation of employees3.2. Motivation of employees Examples of incentives contractsExamples of incentives contracts

Ledford et al. (1995) in Fortune 1000: between 1981 and 1990, the proportion of salesmen receiving a fixed pay decreased from 21% to 7% in the US.

Wood (1996) in UK is increasing every year since 1986 and has reached a proportion of 50% in 1990.

Table. % of companies offering Performance-related pay

EFILWC, IWD No. 47, 23 November 2000

Country % firms that pay for performance

France 51%

UK 28%

Sweden 12%

Germany 12%

Spain 6%

Italy 3%

3.2. Motivation of employees3.2. Motivation of employees Fixed wagesFixed wages

Why to pay FIXED WAGES?

Allen and Lueck (1992) consider a total of 3423 contracts between farmers and land owners in Nebraska and South Dakota.

71% of the contracts involve share cropping between farmers and land owners.

3.2. Motivation of employees3.2. Motivation of employees Example: share croppingExample: share cropping

a) Why farmers do not pay a fixed rent to the owner of the land?

b) What are the possible issues associated with crop-sharing?

3.3. The Psychology of incentives3.3. The Psychology of incentives

Assumptions Neoclassical theoryAssumptions Neoclassical theory

B2) Agents are self-interested and maximize an objective function referred to as a utility function.

Assumption C (Perfect Information)Agents have perfect information on prices and other agents' preferences (consumers) and technologies (producers).

B2) Agents do not only care about their own material payoffs but also

about others’ payoffs and actions. Assumption C (Perfect Information)

Agents have perfect information on prices and other agents' preferences (consumers) and technologies (producers).

Behavioral theoryBehavioral theory

3.3.1. Non-monetary incentives3.3.1. Non-monetary incentives

Characteristics of a job. (Maslow pyramid, Alderfer, Herzberg sixties). The following elements matter. Challenging job. Perspectives. Responsibility and control. Status. Social relations. Work conditions. Firm policy. Job security. Wages.

Abraham MaslowAbraham Maslow

Characteristics of a job. (Maslow pyramid, Alderfer, Herzberg sixties). The following elements matter. Challenging job. Perspectives. Responsibility and control. Status. Social relations. Work conditions. Firm policy. Job security. Wages.

Need for self-Need for self-acutalizationacutalization

Esteem needEsteem need

Belonging needsBelonging needs

Security needSecurity need

Phisiological needsPhisiological needs

Abraham MaslowAbraham Maslow

Example: The firm SAS in South Carolina has been growing lately at 25%.

Rather than emphasizing pay, SAS has achieved an unbelievably low turnover rate below 4% (industry around 20%) by offering intellectually engaging work, a family-friendly environment that features exceptional benefits and the opportunity to work with fun, interesting people using state-of-the art equipment.

3.3.1. Intrinsic motivation3.3.1. Intrinsic motivation

Intrinsic motivation: the individual’s desire to perform an activity for its own sake.

“The labor-of-love aspect is important. The most successful scientists often are not the most talented but the ones who are just impelled by curiosity. They’ve got to know what the answer is.”

Nobel laureate in Physics in 1981 Arthur Schawlow

Schawlow, 1981Schawlow, 1981

Example: The Tandem Computer company would not even tell you your salary before expecting you to accept a job. If you asked, you would be told that Tandem paid good, competitive salaries.

The company had a simple philosophy that if you came for money, you would leave for money

Emphasizing pay as the primary reward encourages people to come and to stay for the wrong reasons.

TANDEM TANDEM COMPUTERCOMPUTER

Example: intrinsic motivation versus extrinsic motivation. College students were asked to work on an interesting puzzle. Deci considered two treatments, one in which participants were paid to undertake the task and another in which they were doing it for free. When students were asked to return to the laboratory to work on another puzzle without rewards, subjects that were not paid in the initial task spent more time on that second puzzle that subjects that were rewarded in the initial task.

Example: Trust and distrust in GE and HP.- At the end of the thirties, GE was being very cautious about guarding its tools and parts bins to make sure that employees would not steal anything. - Employees responded to this evidence of distrust from their employer by actually stealing tools and parts whenever possible.- David Packard decided to avoid such distrust when leading the company Hewlett-Packard by letting storerooms and parts bins open.

Example: Trust and distrust in GE and HP. “... the open bins and storerooms were a symbol of trust that is central to the way HP does business.”

ActivityActivity

Stage 1. Subject M decides between:

(I) Imposing a minimum level e equal to 10 such that in stage 2 subject D decides e in [10,120].

(N) Let subject D free to choose the value e in [10,120].

- Subject A’ s payoffs are such that PM = 2e.

Stage 2.

If subject M let him free to choose e then subject D decides e in [0,120]. If subject M forces him to choose e at least equal to 10 then subject D decides e in [10,120].

- Subject D’ s payoffs are such that : 120 – e.

ActivityActivity

D chooses e in (10,120)

D chooses e in (0,120)

M chooses I or N

ActivityActivity

M chooses

Impose

M chooses

Do not impose

Median Effort 13.5 25***

Payoffs player M 50 27

Payoffs player D 110 108

ActivityActivityResultsResults

ActivityActivityResults Falk & Kosfeld (2006)Results Falk & Kosfeld (2006)

M chooses

Impose

M chooses

Do not impose

Median Effort 10 20***

Fairness model (Fehr y Schmidt 1999)

-Inequity aversion in a two players context.

- Monetary payments wi. The utility of player i is determined as follows,

where αi ≥ 0, βi ≥ 0 y αi ≥ βi.

Ui (x) = wi – αi ×(wj - wi) si wj ≥ wi (Envy)

Ui (x) = wi - βi ×(wi - wj) si wi ≥ wj (Guilt)

3.3.2. Optimal contracts 3.3.2. Optimal contracts with social preferences (with social preferences (Equity)Equity)

Fehr and Schmidt, 1999Fehr and Schmidt, 1999

% of the population

30% 0 0

30% 0.5 0.25

30% 1 0.25

10% 4 0.6

% of the population

30% 0 0

30% 0.5 0.25

30% 1 0.25

10% 4 0.6

Neoclassical theory

Envy & Guilt

Example: the firm Whole Foods Market is a world leader in the distribution of organic food.

The firm does not pay any employee more than 8 times the average wage.

The result is a firm with a volume of sales of 1 million $ a year with a CEO paid less than 200 000$ a year.

“Everybody kows that Makelele does not feel respected and valued in the club. More and more players are paid 5 times more than him. He actually said after a training session:

‘I run like four players at the same time but I am paid for half of it’ ”

Madrid, 14th of August 2003 in el País

“Florentino Pérez resigned as president of Real Madrid and recognizes the failure of his strategy”

Madrid, the 27th of February 2006 in el País

As a consequence of reciprocity, if an agent perceives the action of the principal as kind he will behave positively and value the payoffs obtained by the principal.

In that context, one can justify the use of fixed wages as a signal of trust.

3.3.2. Optimal contracts with social preferences 3.3.2. Optimal contracts with social preferences ((ReciprocityReciprocity))

We consider that there is an agency relationship when an individual, called the agent, acts on behalf of another individual, called the principal. The principal and the agent have diverging goals and different information.

Principal

Output (zz)

Wage: ww

Effort: ee

3.3.2. Optimal contracts with social preferences 3.3.2. Optimal contracts with social preferences Reciprocity in the Agency GameReciprocity in the Agency Game

Agency Game.

Stage 1- A subject (principal) makes a contract offer (ww, ee*) where ww in {0,1,2,...,100} is the fixed wage offered to the other subject (employee or agent) and ee* is the level of effort desired by the principal. Stage 2- If the agent accepts the contract he chooses his actual level of effort ee at a cost C(e)C(e) that strictly increases in ee.

The payoffs of the game are as follows. - Principal’s payoff: π{P} = 100e - wπ{P} = 100e - w. - Agent’s payoff: π{A} = w - C(e)π{A} = w - C(e).

ee 0.001 0.008 0.027 0.064 0.1 0.2 0.3 0.4 ... 1

C(e)C(e) 0 1 2 3 5 7 9 11 ... 20

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0.20.30.4

0.60.7

0.80.9

Tree Planting in British Columbia (2007)Tree Planting in British Columbia (2007)

Firm managers told a crew of tree planters they would receive a pay raise of 80$ for one day as a result of a surplus not attributable to past planting productivity.

2.2. The Psychology of incentivesOptimal contracts with Reciprocity (Field Experiment)

Number of planters

Average Daily Pay Bonus

Average Productivity

Productivity

With Gift

18 $200 $80 987.8 trees 1082.8 trees

9.7%9.7%

Documento Acrobat

Tree Planting in British Columbia (2007)Tree Planting in British Columbia (2007)

Relationship between reciprocity and tenureRelationship between reciprocity and tenure

Example I:

Efficiency wages: Efficiency wages: FordFord..

“Ford announced his $5-per-day program on January 5, 1914. The revolutionary program called for a raise in minimum daily pay from $2.34 to $5 for qualifying workers. It also set a new, reduced workweek.”

- Huge decrease in turnover!

Example II:

Varszegi Hungarian business man: pay Varszegi Hungarian business man: pay workers 4 times the market wage (1990).workers 4 times the market wage (1990).

- The idea was to save on monitoring and supervision of employees.

3.3.2. Optimal contracts with social preferences ((ReciprocityReciprocity))

3.4. Teamwork and cooperation3.4. Teamwork and cooperation

Teamwork has become increasingly popular in organizations since the beginning of the nineties.

1.1. Rising complexity of tasks.Rising complexity of tasks.

2.2. Improvement of information technology.Improvement of information technology.

3.3. Managerial TrendManagerial Trend

Teamwork is crucial to the success of organizations.

“Coming together is a beginning; keeping together is progress; working together is success.”

Henry FordHenry Ford

Moral hazard and teamwork(Holmstrom 1982).

Individual effort not observable. Pay depends on team output. Team member incurs the full cost of effort

whereas they only receive a proportion of the marginal product of effort.

“Free rider”.

Examples…

Moral hazard and teamwork x is the team output x ≡ e1 + e2 where eL = 0 and eH = 1 C (eL) = 0 and C (eH) = c > 0.

Timing of the model.- Stage 1, each member of the team exerts an

effort ei.- Stage 2, workers observe the team outcome x and are paid w = x / 2.

Moral hazard and teamwork

Efficient equilibrium is such that e1 = e2 = eH.Notice that if the individual levels of effort were verifiable then such an equilibrium could be obtained by paying each worker according to the benefits of his effort, that is, w1 = e1 y w2 = e2.

Efficient equilibrium.

Utility of worker 1 if he exerts an effort given that worker 2 exerts an effort> Utility of worker 1 if he does not exert an effort given that worker 2 exerts an effort

It means that c < 1/2.

A member of the French Olympic committee willing to avoid free riding in teams decides the following:

If a team obtains the gold medal in the Olympics, the million-euro bonus will be shared among teammates according to their individual contributions.

To implement this system the individual contributions will be measured by a statistical model that takes into account passes, goals, time of play, fouls…

2.3. Teamwork and cooperation2.3. Teamwork and cooperationIncentives in the OlympicsIncentives in the Olympics

As a member of the Olympic committee Would you support this proposal? Why?

2.3. Teamwork and cooperation2.3. Teamwork and cooperationIncentives in the OlympicsIncentives in the Olympics

Moral hazard and teamwork x is the team outcome. x ≡ e1 + e2 where eL = 0 y eH = 1 C (eL) = 0 and C (eH) = c =0.6 > 0.

a) Can the efficient equilibrium be implemented?

2.3. Teamwork and cooperation2.3. Teamwork and cooperationAltruismAltruism

Consider now that individuals are altruistic so that the utility of a worker is a weighted average of the payoffs obtained by himself and his teammate.

Utility of worker i = 2/3 × (Utility of worker i) + 1/3 × (Utility of worker j)

b) In the presence of altruism can the efficient equilibrium be implemented?

2.3. Teamwork and cooperation2.3. Teamwork and cooperationAltruismAltruism

Other psychological factors have been considered so as to understand the extensive use of team incentives.

Kandel y Lazear (1992): peer pressure. Falk y Ichino (2006). Experiment: subjects had to

undertake a task that consists of filling envelopes with letters.

When seating subjects by pairs, the individual with low performances on the task tends to work harder so as to reach the productivity of the high performer.

2.3. Teamwork and cooperation2.3. Teamwork and cooperationPeer pressurePeer pressure

Peer pressure: an important element is negative reciprocity of the hard-working team members.

2.3. Teamwork and cooperation2.3. Teamwork and cooperationPeer pressurePeer pressure

Stages 1&2: subjects randomly grouped by pairs at the entrance.

Random matching

Inefficient Team FormationInefficient Team FormationExperimental designExperimental design

Stages 1&2: subjects undertake task 1.

Task 1

You have 10 minutes to find as many numbers as you can, satisfying the following conditions:

It has 3 or 4 digits. If you sum its digits the result is equal to 10. If you multiply its digits the result is strictly larger than 23.

- For each correct number that you find you will be rewarded with 40 centimes of euros.

Stage 3: subjects are isolated and take decisions separately about the allocation of the future team outcome.

A2Subjects are isolated

Stages 4&5: depending on their decisions in stage 3, subjects are re-matched with the same partner or undertake the task alone.

Subjects are re-matched or not

Institutions Proportion of efficient

Proportion of efficient teams possibly formed

Proportion of inefficient teams possibly formed

Navarra (Spain)

1/10 1/1 56%

Burgundy (France)

5.6% 91% 78%

Osaka (Japan)

0% - 100%

Average 5.2% 95% 78%

ENDEND

Chapter 3 Managing the firm School of Economics and Business Administration Universidad de Navarra.

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