economics of management strategy bee3027 lecture 2

Economics of Management StrategyBEE3027

Lecture 2

Recap

• Last week we covered the basic arguments for why production may be organised within the firm vis-à-vis outsourcing production.

• We looked at the neo-classical view of the firm and the scale & scope advantages of size.

• We looked at how resorting to spot markets or long-term contracts on product-specific inputs may result in the hold up problem.

Vertically Integrated Production

• We now focus our attention to the firm.

• The more specific the transaction, the greater the incentive to produce in-house, rather than to outsource.

• There are several reasons why firms may want to vertically integrate.


• There are two important differences to vertically integrated production vis-à-vis outsourcing:– Different ownership structure;– Difference governance structure.

• Ownership of an asset is crucial in a world of incomplete contracts.

• It determines residual controls rights over the asset.


• In other words, in an unforeseen event, the owner determines the use of the asset.– This solves (part of) the hold-up problem.

• Differences in the governance are also important, especially from a legal perspective:– Legal obligations of employees are different than

those of a supplier;– Contractual disagreements are solved internally

rather than in court (lower costs).


• The owner of the firm has rights:– To be the residual claimant;

– To hire/purchase production inputs (i.e. labour & capital);

– To monitor/oversee factors of production;

– To change the factors of production;

– To sell these rights.

Principal-Agent Problem

• Take the example of a manager who hires a worker to perform a given task.

• The manager naturally wants the worker to work as hard as possible to raise revenue;

• The worker, however dislikes working and will shirk if possible.


• Suppose for simplicity, that our worker can either work hard or not work at all.– Worker effort, e, is either equal to 2 or 0.

• U = w – e if worker takes the job

• U = 10 if he works somewhere else.


• Firm profits are a function of how hard the worker works.

• Π = H – w if e = 2

• Π = L – w if e = 0

• What contract should the owner offer the worker in order to maximise profit?


• Since the owner cannot observe effort, he must set the wage based on revenues (H or L).– Wh is the wage when revenue is H– Wl is the wage when revenue is L

• There are two constraints the owner must consider when setting wages:– It must be worth for the worker to take the contract– The contract must provide the incentive to work

hard


• Since the worker can make at least 10 if he goes somewhere else:– Wh – 2 ≥ 10 – participation constraint

• The contract must be done in such a way as for the worker to have higher utility by working hard:– Wh – 2 ≥ Wl – 0 – incentive constraint


• Therefore, the optimal contract is Wh = 12 and Wl = 10.

• This means profits for the owner are:– H – 12 if e = 2– L – 10 if e = 0.– This means that in order for the contract to be

optimal for the owner:– H – 12 ≥ L – 10 <=> H ≥ L + 2.


• This is a rather easy way to solve a very complicated problem…

• It is simple because worker effort can be directly inferred from revenues.– In a sense, owner can directly monitor worker

• What happens when worker productivity is uncertain (and monitoring is imperfect)?


• Profits, Π(e) are given by:– Π(2) = H – w with prob = 0.8– Π(2) = L – w with prob = 0.2– Π(0) = H – w with prob = 0.4– Π(0) = L – w with prob = 0.6

• Now, working hard only increases the likelihood of higher revenue.


• Worker’s utility is given by:– U = EW – e if worker takes the job– U = 10 if he works somewhere else.

– EW = 0.8*Wh + 0.2*Wl when e = 2– EW = 0.4*Wh + 0.6*Wl when e = 0


• The uncertainty has an impact in both participation and incentive constraints:– PC: 0.8*Wh + 0.2*Wl – 2 ≥ 10

– IC: 0.8*Wh + 0.2*Wl – 2 ≥ 0.4*Wh + 0.6*Wl – 0

• PC implies Wl = 60 – 4*Wh

• IC implies Wl = Wh – 5.

• Solving two equations gives Wh = 13, Wl = 8


• How much does it cost to implement this type of contract?

• Expected cost to entrepreneur is:– 0.8*13+0.8*8 = 12

• Under symmetric information, Wh = 12, Wl=10.

• Hence, the contract does away with the need to monitor worker.


• Let’s introduce a further twist in this story. Let’s suppose that the worker is more skeptical about the likelihood of H occurring if e =2.

• In particular, the worker assigns a different probability to H occurring if he sets e=2, s.t.:– Π(2) = H – w with prob = 0.7– Π(2) = L – w with prob = 0.3


• The worker will now have a different expected wage than the owner for any Wh, Wl:

• PC is now given by:– 0.7*Wh + 0.3*Wl - 2 ≥ 10 =>Wh = (12 - 0.3*Wl)/0.7

• IC is now given by:– 0.7*Wh + 0.3*Wl - 2 ≥ 0.4*Wh + 0.6*Wl – 0

<=> Wh = 2/0.3 + Wl

w

W

O

WEWlWhWlWhE *3.0*7.02.0*8.0


• The owner will choose a contract which minimises his wage costs = 0.8Wh+0.2Wl– (remember that the owner has different subject

probs over the different states of the world)

• In equilibrium, Wh = 14, Wl = 22/3

• Expected wage bill is equal to:– 0.8*14+0.2*22/3=12.66 > 12


• The expected wage in equilibrium is higher than the worker’s reservation wage plus effort level.

• The rationale behind this result is that the worker must be compensated for taking a random-wage contract.– The difference is a “risk-aversion” premium.

Alternative contractual solutions

• Performance-related pay.– Piece rates. In other words, workers get w for each

unit (q) they produce.

– This type of contract goes back to Taylor in the XIX century; it is still widely used in the agricultural sector.

– Individuals will work until MC(q) = w.


• However, how does one set w?

• If w is set based on previous performance, there is a moral hazard problem: workers have an incentive to underperform.

• Also, the applicability of piece rates is limited to agricultural or industrial contexts.


• Another alternative is to pay workers based on their relative performance:– Promotion Tournaments.

• These contracts work much like sports competitions:– The individual who is more productive wins either a

bonus or a promotion.– A variant of this type of contract was in place at GE

under their former CEO, Jack Welsh. Every year, the bottom 10% managers would be sacked!

Tournaments

• Consider a firm with 2 workers.

• Their probability of success depends on both workers’ effort, which is costly– High effort has a cost of 1.

• Table outlines the probability of success for each player as a function of effort.

High effort

Low effort

High effort

1/2,1/2 3/4,1/4

Low effort

1/4,3/4 1/2,1/2

Tournaments

• If both players are paid the same, then the Nash equilibrium of this game is for both players to submit zero effort – (why? This is a homework question.)

• However, if the winner of the tournament is paid sufficiently highly, then the unique Nash equilibrium is for both players to submit high effort.


• Another possibility is to set a fixed target to a team.– If achieved, bonus is shared by the group.– If not, each group member is paid a basic wage,

which is typically low (unless you are an investment banker).

• Target-based schemes are very popular in the services industry (e.g. retail, inv. banking).


• How do these types of contracts compare?

• Bandiera et al. (2006) compare piece rates to a productivity-based compensation contract.– Wage = βK, where K is amount of fruit picked by

worker and β = w/y.– w = minimum wage + constant, – y = mean daily productivity of group.

Bandiera et al. (2006)

• Under this contract, working hard implies (all else constant):– Higher earnings (K ↑);– Increases average effort, thus increasing average

productivity (y ↑), which in turn lowers earnings for everyone else.

– This contract has a PG game aspect to it, since it contrasts the individual gain vs. the detrimental effect to other group members.

• The relative performance contract was introduced to control for productivity shocks (e.g. weather conditions).


• Paper looks at worker productivity under piece rates and relative performance scheme.

• Farm workers were temporary workers from outside the UK.

• Productivity under piece rates was 50% higher than under relative performance scheme.

• The reason is that social norms are created among co-workers, promoting cooperation (i.e. lower effort).


• Given heterogeneity in backgrounds, they find that individuals who have higher piece rates work harder.– Although piece rate is equal across workers, the

value in local currency of each worker will be different.

– The larger the value of the piece rate as a function of average salary in home country, the higher the productivity of the worker.


• Bull, Schotter and Weigelt (1987) compare tournaments to piece rates in controlled experiments.

• They find that, on average, subjects’ effort is close to what theory would predict.

• However, they find that behaviour in tournaments is much more variable.


• Nalbantian and Schotter (1997) compare a number of group incentive institutions:– Tournaments;– Revenue sharing;– Target-based schemes.

• They find that:– Relative performance schemes more effective than

target based schemes;– Monitoring is effective but very costly.


• Müller and Schotter (2003) study tournaments where they manipulate individual subject ability.

• They find that:– High ability subjects work harder than predicted;– Low ability subjects simply drop out.

• So, relative performance mechanisms may lead to dropout/workaholic behaviour.

• Even if total output is higher, it is unclear whether it is desirable to have such a corporate culture.

Alternative contractual solutionsOverview

• Piece rates appear to be useful tools to boost productivity.

• However, their applicability is limited.

• While tournaments can be useful alternatives, they lead to high variability in worker behaviour.

Team production

Smallest Number in Your Group

7 6 5 4 3 2 1

Your

number

7 130 110 90 70 50 30 10

6 - 120 100 80 60 40 20

5 - - 110 90 70 50 30

4 - - - 100 80 60 40

3 - - - - 90 70 50

2 - - - - - 80 60

1 - - - - - - 70

Minimum-effort game

• The game we just played is called the minimum-effort game.

• In certain activities, the productivity of a given worker or department depends on the productivity of the worker/department in the previous step of the production process.

• It captures two key ideas in team production:– Public good problem;

– Coordination problem.

Minimum-effort game

• This game has a very large number of equilibria in pure strategies

• In all equilibria, all players choose the same level of effort.

• Although theoretically, individuals should be able to coordinate on the maximum amount, they often don’t.

Minimum-effort game

• The reason is that the equilibrium where all players choose 7 is very risky.

• If by chance, one player decides not to play 7, all players can lose up to 110 points, while that player will only lose up to 50!

• On the other hand, the equilibrium where all choose 1 is quite safe: there is no way you can lose money.

Minimum-effort game

• This problem increases the larger the group size:

Studies Group size Country Average e

Van Huyck et al. (1990). 2 USA 6.250

Weber et al. (2004); Knez & Camerer (1994, 2000). 3 USA 3.074 – 5.188Dufwenberg & Gneezy

(2005); Knez & Camerer (1994)

6 ISR, USA 5.357

Bornstein et al. (2002) 7 SP 1.667

Van Huyck et al. (1990). 14-16 USA 1

Summary

• Property-rights motivation for existence of firms;

• Team production;

• Compensation schemes;

• Coordination problem in production

• Next week:– Managerial compensation.– Pricing and marketing strategies.

economics of management strategy bee3027 lecture 2

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