Economics of Management Strategy
BEE3027
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.
Vertically Integrated Production
• 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.
Vertically Integrated Production
• 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).
Vertically Integrated Production
• 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.
Principal-Agent Problem
• 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.
Principal-Agent Problem
• 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?
Principal-Agent Problem
• 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
Principal-Agent Problem
• 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
Principal-Agent Problem
• 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.
Principal-Agent Problem
• 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)?
Principal-Agent Problem
• 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.
Principal-Agent Problem
• 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
Principal-Agent Problem
• 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
Principal-Agent Problem
• How much does it cost to implement this type of
contract?
• Expected cost to entrepreneur is:
– 0.8*13+0.2*8 = 12
• Under symmetric information and certainty:
– Wh = 12, Wl=10.
• Hence, the contract does away with the need to
monitor worker.
Principal-Agent Problem
• 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
Principal-Agent Problem
• The worker will now have a different expected wage
than the owner for any Wh, Wl:
EWO  0.8 *Wh  0.2Wl  0.7 *Wh  0.3 *Wl  EWw
• 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
Principal-Agent Problem
• 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
Principal-Agent Problem
• 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.
Alternative contractual solutions
• 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.
Alternative contractual solutions
• 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 (relative to the loser), then the
unique Nash equilibrium is for both players to
submit high effort.
Alternative contractual solutions
• 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).
Alternative contractual solutions
• 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).
Bandiera et al. (2006)
• 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).
Bandiera et al. (2006)
• 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.
Alternative contractual solutions
• 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.
Alternative contractual solutions
• 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.
Alternative contractual solutions
• 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 solutions
Overview
• 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
7
130
110
90
70
50
30
10
6
-
120
100
80
60
40
20
Your
5
number
4
-
-
110
90
70
50
30
-
-
-
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 – 5.188
Dufwenberg & 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.