Chapter 3 Managing 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 3. 3.1. Selection of employees 3.2. Motivation of employees
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Chapter 3Managing 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 3 • 3.1. Selection of employees • 3.2. Motivation of employees • 3.3. The Psychology of incentives • 3.4. Teamwork and cooperation
3.1. Selection of employeesNeoclassical theory • The labor demand is derived from maximizing firms profits. Marginal Income of Labor = Marginal Cost of Labor (Price of Labor) MaxpQ - C(Q) Maxpf(K,L) - rK – wL p(∂f / ∂L) = w & p(∂f / ∂L) = r
3.1. Selection of employeesLimits of the Neoclassical theory • 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 employeesSearch costs and work mobility • Data on workers’ mobility and turnover. • The rate of mobility between EU countries is 0.1% a year whereas it is 4% in the US. • 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 employeesSearch costs and work mobility Why workers’ mobility is so low? • Few opportunities, imperfect competition (Hypothesis A does not hold). • Search costs, limited rationality (Hypothesis B1 does not hold). • Social preferences (Hypothesis B2 does not hold). • Imperfect information about jobs (Hypothesis C does not hold).
3.1. Selection of employeesAsymmetric information • Hypothesis C’: Asymmetric information. We consider in section 3.1 about personnel selection the case asymmetric informationexante (before the contract is signed).
Akerlof, Nobel 2001 3.1. Selection of employeesAdverse selection • Example: Consider the following distribution of abilities of workers and outside options.
Akerlof, Nobel 2001 3.1. Selection of employeesAdverse 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 3.1. Selection of employeesAdverse selection • Examples: the role of reputation and standardization. - Market for insurance. - Market for credit. - Retail stores. - Restaurants.
Spence, Nobel 2001 3.1. Selection of employeesSignaling • 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 employeesSignaling • 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 3.1. Selection of employeesSignaling • The following conditions allow the organization to identify high-ability workers, that is they allow for the existence of a separating equilibrium. • 100 - cL < 40 so that cL > 60 (low-ability workers do not go to college.) • 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 .
Akerlof, Nobel 2001 3.1. Selection of employeesAdverse selection • 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.
Spence, Nobel 2001 3.1. Selection of employeesSignaling • 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.
3.1. Selection of employeesScreening • 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 employeesScreening • 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.
3.1. Selection of employeesScreening • Example I (Toy industry). - Density function: ηi ~ U(0,10). f(x)=1/10 0 5 10
3.1. Selection of employeesScreening • Example I (Toy industry). - 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.
3.1. Selection of employeesScreening • Example I (Toy industry). a)Which types of workers will apply for a job in firm A? And which types will apply for a job in firm B?
3.1. Selection of employeesScreening • Example I (Toy industry). b)Can firm B stay in the toy business?
3.1. Selection of employeesScreening • Example I (Toy industry). c) Is there any level of fixed wage such that firm B could stay in the toy business?
3.1. Selection of employeesScreening • Example I (Toy industry). d) Could you give any reasons why high-productivity workers may be interested in working for the firm offering fixed wages? • Risk aversion. • Measurement errors. • Equity.
3.1. Selection of employeesScreening • 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 2types: • 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 €.
3.1. Selection of employeesScreening • Example II (franchising). 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? • 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%.
3.1. Selection of employeesScreening • Example II (franchising). 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?
Spence, Nobel 2001 3.1. Selection of employeesScreening example • 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?
3.1. Selection of employeesScreening • 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.
3.1. Selection of employeesScreening • Exercise: probation period. - There exists 2types 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 2types 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.
3.1. Selection of employeesScreening • 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.
3.1. Selection of employeesScreening • Screening high-ability workers. • 2000W1+ 2000 × 19W2 ≥ 20×2000WH • 2000W1+p2000×19W2+(1-p)2000×19WL ≤ 20×2000WL • Solution. • W2= WL+ 20×(WH- WL)/19×(1-p)
3.1. Selection of employeesEmpirical evidence • 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. • Very productive subjects are more likely to choose a variable wage. • Risk averse workers are more likely to choose a fixed wage. • Women are less likely to choose a variable wage. This is mainly due to higher risk aversion.
Structure of chapter 3 • 3.1. Selection of employees • 3.2. Motivation of employees • 3.3. The Psychology of incentives • 3.4. Teamwork and cooperation
3.2. Motivation of employeesOptimal contracts • We consider an agency relationship between an individual called agent (employee) that acts on the behalf of an individual called principal (manager). • The principal hires an agent a task that is costly to the agent C(e). • The principal does not always possess information on the level of effort exerted by the agent.
3.2. Motivation of employeesOptimal 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 Wage: w Agent Effort: e Action
3.2. Motivation of employeesOptimal contracts (risk attitudes) • 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 employeesOptimal 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.
3.2. Motivation of employeesOptimal contracts (risk attitudes) • 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?
3.2. Motivation of employeesOptimal contracts (risk attitudes) v(100) v(50) E(v)=5 CE = 25€ 50€ 0 100€ Wages
3.2. Motivation of employeesOptimal contracts (risk attitudes) • 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)
3.2. Motivation of employeesfirst-best contracts (risk attitudes) • 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 costC(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 employeesfirst-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 employeesfirst-best contracts: observable effort • 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 employeesfirst-best contracts: observable 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 employeesExample:first-best contract • 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 employeesExample:first-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]
3.2. Motivation of employeesExample:first-best contract • As a result, the firs-best contract is given by: - If e* < 250 then w = 0 - Ife* = 250then w = 1250 + v0
3.2. Motivation of employeesProblems to implement thefirst-best contract • 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: • Observability and measurement problems • Moral hazard and risk sharing
3.2. Motivation of employeesProblems to implement thefirst-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.