L03 04 Theoretical foundations of C&B

Question 1

What are the 5 characteristics of a competitive labor market?

Answer 1

1. People are homogeneous and thus interchangeable: No person-specific skills
   2) Pay rates reflect all costs associated with employment: Base, incentives, bonus, …
   3) Markets are competitive: No advantage for a single firm to pay above or below the market
   4) Perfect information: all firms and workers have perfect information about jobs, skills and wages
   5) ‘Equilibrium’ wage and employment level: In the equilibrium workers are hired by all firms.

Question 2

What is measured by the labor demand and how is it influenced by 2 aspects?

Answer 2

It’s a measure of marginal productivity of labor (additional output of adding one unit of labor)

1) More human capital -> higher marginal productivity -> higher demand and wages
2) Labor is scarce (abundant) -> high (low) marginal productivity -> high (low) demand and wages

Question 3

What is measured by labor supply and how do wages influence it?

Answer 3

It’s a measure of people’s willingness to work at a given wage
Wages are low (high) -> few (many) people will want to work: concept of reservation wage

Question 4

What is the equilibrium wage?

Answer 4

… Wage level at which labor demand (#workers demanded) = labor supply (#workers willing to work)

Question 5

Sketch the labor market equilibrium.

Answer 5

Question 6

What is the reservation wage?

Answer 6

Job seekers have a reservation wage level below which they will not accept a job offer.

Question 7

Why do wages differ? (4 reasons)

Answer 7

1) Institutions
2) Compensating wage differential
3) Information asymmetry
4) Moral hazard

Question 8

Why wages differ: What is the role of institutions?

Answer 8

Institutions distort the equilibrium via legal, political and social arrangements by

1) Controlling demand (e.g. minimum wage above equilibrium->some willing workers and firms are not able to transact)->unemployment
2) Controlling supply (e.g. migration restrictions, unions)

Question 9

Why wages differ: What is the role of compensating wage differential?

Answer 9

Employers must offer higher wages for negative job features:
Equally-skilled jobs may vary in other aspects that need to be compensated for (e.g. pleasantness, risk, prestige).

Question 10

Why wages differ: What is the role of information asymmetries?

Answer 10

• *Firms cannot observe the productivity of potential workers**
• > Workers signal their productivity by acquiring education
• > Firms screen workers for their productivity using interviews, assessments, probation periods,…
• *Implication**: Firms with better (less good) screening hire more (less) productive workers and pay more (less)

Question 11

Why wages differ: What is the role of moral hazard (Assumptions, Problem, Solution)?

Answer 11

• Assumptions: Worker max. utility (work as little as possible) and firm max. profits (wants the worker to work as hard as possible)
• Problem: Worker’s effort is typically not perfectly observed
• Solution: Use of incentives to align interests

Question 12

Incentives: the basics. What is the logic behind effort, output and wage? What problem arises?

Answer 12

Higher effort => higher output

Worker: Effort is costly and must be rewarded with higher wage

Firm: Limited observability of effort, thus needs proxies for effort.

Question 13

Incentives: What can firms do if they don’t observe the effort level?

Answer 13

Proxy 1: Detect shirking while monitoring => ‘efficiency wage’

Proxy 2: Use actual performance due to the logic that higher effort leads to better performance => higher ‘performance-based pay’

Question 14

What is the efficiency wage?

Answer 14

… the wage that keeps workers just from shirking.

It is always above the equilibrium wage level.

Question 15

Efficiency wage: State the no-shirking condition.

Answer 15

The worker will work if:
w-c ≥ pw₀ + (1-p)w
<=> p(w-w₀) ≥ c

Question 16

Efficiency wage: Explain the variables used as well as their impact on the level of the efficiency wage.

Answer 16

w: fixed wage

c(+): effort costs

p(-): probability that shirking is detected

w₀(+): equilibrium wage

Question 17

Efficiency wage: What is the trade-off to meet the no-shirking condition?

Answer 17

Pay higher w and thereby reduce monitoring costs for same p

vs.

Intensify monitoring to yield higher p and thereby can afford to pay lower w

=> Firms choose (p,w) such that the no-shirking condition just holds: p(w-w₀) = c

Question 18

Efficiency wage: What is the implication of screening on w?

Answer 18

Implication:
Selection/screening may decrease w as high-ability workers have lower c.
Be careful: Better selection/screening requires higher recruitment and screening costs.

Question 19

Utility analysis of selection: State the utility function u from job applicant selection and explain the variables as well as their impact on u.

Answer 19

u = r x SD x Z - C/SR

r(+): correlation between assessment result and future performance (how accurate assessment is)

SD(+): standard deviation of the value in performance (how much difference in value is created by a one-SD difference in performance)

C(-): recruitment and assessment costs per applicant

SR(+/-): selection rate 0 < r < 1. Higher SR leads to higher Z(+), because of more applicants, but also higher C/SR(-)

Z(+): mean standard performance score of those hired (by how many SDs of performance those hired exceed the rest). For Z look into N(0,1) distribution table @SR.

Question 20

Utility analysis of selection: Give an example of tougher selection.

Answer 20

Assume r=0.4; SD=$50,000; C=$200; SR=0.5; Z=0.8

Mechanism: Pay higher wage of $10,000 for a given vacancy leads to lower SR=0.05 due to more applicants.

u(before) = 0.4 x 50,000 x 0.8 x 200/0.5 = 15,600 per hire
u(after) = 0.4 x 50,000 x 2.06 - 200/0.05 = 37,200 per hire
=> utility gain from tougher selection = u(after) - u(before) - additional wage = 37,200-15,600-10,000 = $11,500 per hire

Not taken into account:
Turnover would increase and thus SD as the time horizon rises. Additionally, monitoring costs decrease due to higher wage

Question 21

Utility analysis of selection: Give an example of a more accurate assessment.

Answer 21

Assume r=0.4; SD=$50,000; C=$200; SR=0.5; Z=0.8

Mechanism: Better screening technology leads to r=0.8 and C=$300.

u(before) = 15,600 per hire
u(after) = 0.8 x 50,000 x 0.8 - 300/0.5 = 31,400 per hire
=> Utility gain from more accurate assessment = 31,400-15,600 = $15,800 per hire

Additionally, monitoring costs decrease due to higher average quality of hired applicants.

Question 22

Model of performance-related pay: Assumptions (5)

Answer 22

1) No intrinsic motivation, only money motivates
2: A’s effort e is not observable
3) A produces output y = e + η with E(η)=0
4) A max. w = a + b * y
5) P max. π = y - w

Question 23

Model of performance-related pay: State the agent’s participation constraint and derive his optimal choice of effort level?

Answer 23

PC: u = E(w=a+by) - δe²/2 - λvar(w|e) ≥ ū

δe²/2: effort cost
λ: dislike of earnings’ uncertainty (=risk-aversion)
ū: reservation utility

max. u wrt. e yields optimal effort level e*=b/δ

Question 24

Model of performance-related pay: What are the principal’s actions, what a chooses P?

Answer 24

P anticipates A’s effort choice e*= b/δ

P max. π = b/δ - a - b²/δ

P chooses a = ū - b²/2δ + λb²σ² to just satisfy A’s PC

Thus, π = b/δ - ū - b²/2δ - λb²σ²

Question 25

Model of performance-related pay: What are the results (b*,a*,e*, π, u)?

Answer 25

Question 26

Model of performance-related pay: What is the incentive effect?

Answer 26

If b=0, e=0

If introducing incentive pay (b > 0), e↑ (incentive effect)

Workers with lower δ (hard-working workers) and/or lower λ (less risk-averse): e↑↑

Sum of individual outputs ↑

Question 27

Model of performance-related pay: What is the sorting effect?

Answer 27

Assumption: Free workers on the labor market

After the introduction of incentive pay:
Low-δ and low-λ workers will come and high-δ and high-λ will leave (sorting effect)

Sum of individual outputs ↑ and π ↑

Question 28

5 Factors affecting the design of an incentive pay scheme

Answer 28

1) Firm size: Smaller firms can monitor easier and thus need incentive pay less.
2) Risk/loss aversion: Reduces the effect of incentive pay since there are extra costs of risk beared by employees.
3) Uncertainty of output σ: The higher σ, the lower the optimal strength of incentives, the less effect has incentive pay.
4) Dysfunctional behavioral responses (e.g. credit sold to not creditworthy customer): Reduce applicability of incentive pay and/or call for reappraisal of performance criteria.
5) Individual/team-based incentives: Individual incentives discourages cooperation, team-based incentives may invite free-riding. Reputation and peer pressure are important for the success of incentive pay.

Question 29

Is incentive pay the first-best compensation scheme?

Answer 29

Under first-best scheme, the risk is borne by the party with highest risk attitude.

A bears some risk through b and bearing risk is more expensive than for P.
=> Incentive pay implies efficiency loss when A is risk-averse
=> Under first-best, P would pay A based on effort e - Due to unobservability unfeasible
=> Incentive pay is second-best scheme

Question 30

6 variants of incentive pay

Answer 30

1) Residual claimant schemes: e.g. taxi driver A pays fee to owner of the car P and takes all the revenue (only for risk-neutral A)
2) Fixed wage a + payment per unit of output produced
3) Fixed wage + target bonus as a fraction of wage or output
4) Stock options given to employees, that often can only be converted into cash after some years.
5) Deferred compensation: Pay less than productivity early in career, pay more than productivity later on. Incentive: stay on the job long enough.
6) Bonus or promotion for winning a tournament: In tournaments, relative performance counts - great way when output is hard to measure.