Transcript Lezioni di Economia e organizzazione industriale

Chapter 4: Coordinating plans and
actions
In many sectors of the economy,the visible
hand of management replaces what Adam
Smith referred to as the invisible hand of
market forces (A. Chandler).
• The goal of this Chapter is to examine the
characteristics of different sorts of
coordination problems and of the mechanisms
used to solve them.
EOM: Chapter 4 (P. Bertoletti)
1
Actions and Plans
• We saw in Chapter 3 that a decentralized system of
prices and markets can sometimes solve the
organizational problem by making use of a very
limited information transmission.
• However (as once noticed by M. Weitzman), formal
organizations make at most quite limited use of prices.
Managers usually formulate general strategies which
specify quantitative goals, and direct people to carry
out specific tasks using the resources they have been
allocated. Routines and administrative procedures are
used to guide activities, with plans, budgets, work
assignments and operational schedules, in a process
which rarely involves prices.
EOM: Chapter 4 (P. Bertoletti)
2
Command power and direct orders I
• Even in market economies, means of
coordination different from prices are
extensively used.
• Governments, in particular, favour giving
direct orders which specify particular actions,
and command resources directly (as in a
system of compulsory military services).
• Ex: public provision of roads, police services,
health care, food for the needy.
EOM: Chapter 4 (P. Bertoletti)
3
Command power and direct orders II
• Firms, too, often interact with “cooperative”
procedures which involve negotiations of
complex requirement contracts, information
sharing and joint plans, far away of simple
market transactions. Ex: alliances, joint
ventures, royalty agreements and franchise
contracts.
• Chapter 4 focuses on case in which, in
principle, there are no market failures, and
yet other mechanisms are actually employed.
EOM: Chapter 4 (P. Bertoletti)
4
Planning economic activity
• Planning never comes without specific costs
(offices, files, data banks, computing
communication equipments, labor time
devoted to fill out forms and complete
reports, errors).
• Actual economies use a loose mix of systems
to coordinate and manage: what determines
which system ought to be used? Why “the
price system as an allocator of resources does
not pass the market test”? (M. Weitzman)
EOM: Chapter 4 (P. Bertoletti)
5
Resource allocation problems
•
Particular attributes of resource allocation
problems determine which system of
coordination is especially effective.
• In problems with design attributes:
1. A great deal of a priori information about the
form of the optimal solution is available;
2. Failing to achieve the right relationship
among the variables is generally more costly
than other kind of errors.
EOM: Chapter 4 (P. Bertoletti)
6
Synchronization problems I
• An example of problems with design attributes are
the synchronization problems.
• An extreme example is the sport of crew, in which
it is crucially important that each rower make her
stroke at precisely the same moment (the rhythm is
determined by the coxswain, who calls out the
signal for each stroke). And the cost of not setting
quite the right pace are small compared to those of
failing to have everyone pulling in unison.
EOM: Chapter 4 (P. Bertoletti)
7
Synchronization problems II
• Interesting, one might think of the coxswain
using a “price system” (calling the prices), which
would have the same advantages in this
application as in the case of the highway safety
department.
• But it would be difficult for her getting the
relevant information, and too slow to
communicate the prices. Moreover, the crew may
respond inaccurately, and with even small errors
implying very high costs.
EOM: Chapter 4 (P. Bertoletti)
8
Assignment problems I
• In assignment problems there are one or more
tasks to accomplish and there is a need for just
one person or unit to do each.
• The coordination problem is to ensure that each
task is done without wasteful duplication of
effort.
• Ex: when someone is seriously injured in a car
accident, there is a need for one ambulance as
soon as possible. In practice, a central dispatcher
assigns a particular ambulance to drive to the site.
EOM: Chapter 4 (P. Bertoletti)
9
Assignment problems II
• Again, dispatchers may not have all the
relevant information, but to use a price system
would perform poorly because it would too
often lead (if prices were set incorrectly) to
unnecessary duplication or costly delay.
EOM: Chapter 4 (P. Bertoletti)
10
Design problems and organizational routines
• Notice that the crew and ambulance examples
combine: 1) a sense of urgency; 2) the dependence of
the optimal course on particular circumstances (who
is leading? where is the accident?); 3) substantial
knowledge about the form of the optimal decision.
• These features make central control an attractive
alternative.
• However, when similar problems arise repeatedly and
call for largely the same solution, it is unnecessary to
solve them centrally, and routines are established to
guide decentralized solutions.
EOM: Chapter 4 (P. Bertoletti)
11
Routines
• Once routines are established, for the most common
kinds of demands made on the organization no
managerial discretion need to be exercised, because
those who first become aware of the issue (e.g., “the
projector is not working”) know what to do and who
notify, and each part of the organization can rely on
the others to do their parts.
• Only when the organizational environment changes
new routines will need to be devised.
EOM: Chapter 4 (P. Bertoletti)
12
Innovation Attributes I
• Decentralized decision making will perform
poorly whenever the optimal allocation depends
on information not available to people at the
operating level of the organization.
• This innovation attribute is commonly present
when the organization is trying to do something
that is outside its experience, such as introducing
a new kind of product, entering a new market, or
adopting a new approach to manufacturing.
EOM: Chapter 4 (P. Bertoletti)
13
Innovation Attributes II
• When innovation attributes are present, solving
the coordination problem involves someone
gathering or developing the needed information
and communicating it to the decision makers in
the organization.
• This might or might not require that higher-than
operating-level decision makers get involved,
but a simple price system relying on the
responses of individuals using only local
knowledge cannot be trusted to achieve an
optimal plan in these circumstances.
EOM: Chapter 4 (P. Bertoletti)
14
Comparing Coordination Schemes I
•
The simple coordination problems we have
described, and their solutions, differ widely.
•
Some are extremely urgent, and leave little time to
process information. Others require close
synchronization with little tolerance for faults.
•
Some require only an effective use of information
that is already within the organization, whereas
others require the gathering of new information.
EOM: Chapter 4 (P. Bertoletti)
15
Comparing Coordination Schemes II
Coordination systems also vary, and fail in predictably
different ways.
• Certain centralized command system demand little
upward communication of local knowledge (but arrive
quickly at reasonable plans easy to communicate),
while others require more but are correspondingly
more responsive to it.
• Decentralized systems emphasize communicating
information to support local decisions, and may work
too slowly or lead to duplication.
EOM: Chapter 4 (P. Bertoletti)
16
Criteria for Comparing Systems
1. If all the required information were reported honestly
and accurately, and processed perfectly and costless,
could the system achieve efficiency?
2. How much information and communication does the
system require to achieve its purpose?
3. How brittle is the system? (i.e., if some information
is missing or inaccurate, how badly will its
performance deteriorate?)
EOM: Chapter 4 (P. Bertoletti)
17
Assessing Brittleness: Prices vs Quantities
•
To study the effectiveness of different
approaches to coordination, we reconsider a
standard economic problem of allocation,
comparing the use of a system of prices with a
system of centralized quantity. In particular:
1. Either the central coordinator simply specifies
the production units’ quantities;
2. Or the center attempts to guide units’
decisions via price signals.
EOM: Chapter 4 (P. Bertoletti)
18
Prices vs Quantities I
•
•
•
Since available information is fixed, we judge
performances on the basis of efficiency and
brittleness.
We assume that benefits accruing from any
level of output are accurately known to the
planner, but that she has to rely upon
estimates concerning production costs.
See Table 4.1, p. 95.
EOM: Chapter 4 (P. Bertoletti)
19
Example: Table 4.1, p. 95
Units
Total
Benefit
4
5
6
7
8
9
10
40
50
58
64
68
70
70
Marginal
Benefits
Total
Costs
10
8
6
4
2
0
5
12
20
29
39
50
62
Marginal
Costs
Net
Benefit
Total
Costs
7
8
9
10
11
12
35
38
38
35
29
20
8
17
20
24
29
35
42
50
Planner’ s Estimates
EOM: Chapter 4 (P. Bertoletti)
Marginal
Costs
Net
Benefit
3
4
5
6
7
8
23
30
34
35
33
28
20
Error Scenario
20
Prices vs Quantities II
•
In the previous example, to produce
either 5 or 6 is the efficient choice,
which leads to a total net benefit of 38.
•
The planner can achieve efficiency
either by directing the firm to produce 6
(or 5), or by setting a price equal to 8
for the firm (this is the price which
would clear a market based on marginal
benefits and marginal costs).
EOM: Chapter 4 (P. Bertoletti)
21
Prices vs Quantities III
•
To examine the the relative brittleness, suppose
now the estimates are wrong, and the true values
(known to the firm, which cannot communicate
them) are those given in the “Error scenario”: in
such a case the efficient quantity is 7, which
leads to a total benefit of 35.
•
Then if the planner chooses a quantity equal to 6
the total benefit is of 34, but it becomes of only
20 if she names a price of 8 and 10 got produced
(the firm might also choose to produce just 9,
generating a net benefit of 28).
EOM: Chapter 4 (P. Bertoletti)
22
Prices vs Quantities IV
•
•
•
In the previous example the quantity system
works better, but suppose that benefits are as
in the following Table 4.2, p. 96.
Then the marginal benefit is constant at 8,
the efficient quantity is 6 (or 5) under the
planner estimates, but equal to 8 (or 7) in the
error scenario.
Notice that the choice of 6 unit would deliver
only a net benefit of 34, while the efficient
net profit of 40 would be achieved by naming
8 as a price.
EOM: Chapter 4 (P. Bertoletti)
23
Example: Table 4.2, p. 96
Units
Total
Benefit
4
5
6
7
8
9
10
42
50
58
66
74
82
90
Marginal
Benefits
Total
Costs
8
8
8
8
8
8
5
12
20
29
39
50
62
Marginal
Costs
Net
Benefit
Total
Costs
7
8
9
10
11
12
37
38
38
37
35
32
28
17
20
24
29
35
42
50
Planner’ s Estimates
EOM: Chapter 4 (P. Bertoletti)
Marginal
Costs
Net
Benefit
3
4
5
6
7
8
25
30
34
37
39
40
40
Error Scenario
24
Prices vs Quantities V
•
•
•
Suppose now that marginal benefit is vertical
at the relevant point, as in Table 4.3, p. 97.
Then 6 is the efficient quantity, both under
the planner estimates (net benefit equal to
40), and in the error scenario (net benefit
equal to 36), and it can achieved by directing
the firm to that level of production.
However, by naming the price equal to 8 the
firm will be induced to produce either 10 or
9, with a net benefit of either just 10 or 18.
EOM: Chapter 4 (P. Bertoletti)
25
Example: Table 4.3, p. 97
Units
Total
Benefit
4
5
6
7
8
9
10
40
50
60
60
60
60
60
Marginal
Benefits
Total
Costs
10
10
0
0
0
0
5
12
20
29
39
50
62
Marginal
Costs
Net
Benefit
Total
Costs
7
8
9
10
11
12
35
38
40
31
21
10
-2
17
20
24
29
35
42
50
Planner’ s Estimates
EOM: Chapter 4 (P. Bertoletti)
Marginal
Costs
Net
Benefit
3
4
5
6
7
8
23
30
36
31
25
18
10
Error Scenario
26
Prices vs Quantities VI
•
•
The third example is close to the
ambulance story: you do not want to name
a price which might induce too many
ambulance (according to irrelevant
information you do not have) if you know
you need just one.
In the second example you know exactly
how worth is one unit, and if you can fix
that value as a price the market will
establish correctly the quantity.
EOM: Chapter 4 (P. Bertoletti)
27
A Mathematical Formulation I
•
•
•
•
Suppose that, as in our numerical
examples:
a) marginal benefit and costs are linear
function of the output;
b) the planner knows the slope of those
functions but she is unsure about the
intercept of the marginal cost;
c) measure “welfare” losses as differences
in net benefit between actual and correct
choices.
EOM: Chapter 4 (P. Bertoletti)
28
A Mathematical Formulation II
•
•
Suppose, finally, that we do not restrict to
integer amounts.
Then:
2
Price Control Loss
=
Quantity Control Loss
Marginal Benefit Slope
Marginal Cost Slope
Formula 4.1
EOM: Chapter 4 (P. Bertoletti)
29
A Mathematical Formulation III
•
Notice that the previous formula implies that a
price system will perform better than a regulated
quantity if and only if the slope of marginal
benefit is smaller that the slope of marginal cost
(as in our examples).
•
Also note that if a firm is acting in a competitive
market in which it takes the price as given, then
the slope of its marginal benefit curve is zero and
the performance of the unregulated market
cannot be improved.
EOM: Chapter 4 (P. Bertoletti)
30
A Mathematical Formulation IV
•
•
•
•
A graphical proof of the previous formula can be
grasped from the following picture (Fig. 4.1, p. 98).
As usual, the net benefit is the area between the
marginal benefit and the actual marginal cost.
Suppose that MC* is the marginal cost curve in the
error scenario, while MC is the marginal cost curve
overestimated by the planner.
Q* is the efficient output in the error scenario, while
Q would be directly chosen by the planner under
quantity regulation, and P is the price it would name,
which correspond to the quantity QP.
EOM: Chapter 4 (P. Bertoletti)
31
A graphical proof
tg = MC*’= MC’ = d/(QP - Q), tg  = |MB’ | = D/(QP - Q)
MC
MB
a
P


f

MC*
c
d
D
b

e
Q
Q*
EOM: Chapter 4 (P. Bertoletti)
QP

Q
32
A Mathematical Formulation V
•
•
Then the area of the trapezoid QacQ* is the
reduction of the total benefit if the planner
chooses Q, while the area QbcQ* is the total cost
corresponding reduction. It follows that the loss
associated to quantity regulation is given by the
area of the triangle abc.
On the contrary, the area Q*cfQP is the increase of
total cost if the planner names P (inducing QP),
while the area Q*ceQP is the associated total
benefit increase. It follows that the loss associated
to the use of price regulation is given by the area
of the triangle cfe.
EOM: Chapter 4 (P. Bertoletti)
33
A Mathematical Formulation VI
•
•
•
•
Notice that the area abc is given by (Q* Q)d/2, while the area cfe is given by (QP Q*)D/2.
Now notice that the triangles abc and cfe are
similar (angles at a and e and angles at b
and f are alternate interior angles).
Then it must be the case that (QP - Q*)/(Q*
- Q) = D/d.
Finally, notice that tg = d/(QP - Q), where
tg = D/(QP - Q).
EOM: Chapter 4 (P. Bertoletti)
34
A Mathematical Formulation VII
•
It follows that:
•
(tg)/(tg) = D/d,
and
•
[(QP - Q*)/(Q* - Q)] D/d = (D/d)2 =
[(tg)/(tg)]2,
which proves the result.
EOM: Chapter 4 (P. Bertoletti)
35
Intuition
•
•
The idea is that the planner should use the
quantity when she is relatively more sure about
the efficient output level, as when the marginal
benefit is vertical (in such a case Q* = Q), or the
marginal cost very flat.
She should instead use the price signal if having
a smaller uncertainty on the optimal price, as
when the marginal benefit is flat (in such a case
P* = P, where P* is the price that would induce
Q*), or the marginal cost very steep.
EOM: Chapter 4 (P. Bertoletti)
36
Exercise 1, p. 120
• Consider the problem of providing an input to a
firm division or to a plant in a planned
economy.
• Let the situation being represented by the
following picture (Fig. 4.4, p. 120), in which
there is a given increasing marginal cost curve
MC, but “the planner” is uncertain between two
scenario, a best estimate decreasing marginal
benefit curve MB and a “error scenario” MB*.
EOM: Chapter 4 (P. Bertoletti)
37
Exercise 1, p. 120
tg = MC’ = D/(QP - Q) , tg  = |MB’ |= |MB*’ | = d/(QP - Q).
MC
MB*
f
MB
a
c
D
d
e
b
P


Q Q*

QP
EOM: Chapter 4 (P. Bertoletti)
Q
38
Exercise 1: continuation
• The areas of triangles abc and cef are the
losses (with respect to the efficient quantity
Q*) associated respectively to the use of
quantity vs price controls in the error
scenario.They are given by (Q* - Q)d/2 and
(QP - Q*)D/2.
• Notice that triangles are once again similar,
and then (Q* - Q)/(QP - Q*) = d/D.
• Finally, tg  = d/(QP - Q) and tg = D/(QP Q), and thus (tg )/(tg) = d/D.
EOM: Chapter 4 (P. Bertoletti)
39
Exercise 1: conclusion
• It follows that:
• [(Q* - Q)d]/[(QP - Q*)D] = (d/D)2
• i.e.,
Quantity Control Loss
Price Control Loss
Marginal Benefit Slope
2
=
Marginal Cost Slope
• just the opposite than in Formula 4.1!
EOM: Chapter 4 (P. Bertoletti)
40
Exercise 1: conclusion
•
•
•
The previous result shows the relevance of the
source of uncertainty for the decision criterion.
Intuitively, again the planner should use the
quantity when she is relatively more sure about
it, as when marginal cost is vertical (in such a
case Q* = Q), or the marginal benefit very flat.
She should instead use the price signal if facing a
smaller uncertainty on the optimal price, as when
the marginal cost is flat (in such a case P* = P),
or the marginal benefit almost vertical.
EOM: Chapter 4 (P. Bertoletti)
41
Returns to Scale I
•
•
An increasing marginal cost implies that there
decreasing returns to scale, in which case it is
generally efficient to divide the production
among a number of small units. In this case,
not surprising, the decentralization advantages
are great.
Consider, instead, the case of increasing
returns to scale (decreasing average cost), in
which efficiency implies a division of
production among a few firms.
EOM: Chapter 4 (P. Bertoletti)
42
Returns to Scale II
•
•
In such a case, as we saw in the previous
chapter, market fails, and actually a given
price will never induce efficient production
since the firm would be willing to produce
an infinite amount (revenue grows linearly
with output while average cost declines).
Consider now constant return to scale
(CRS), in which marginal costs are constant
and equal to average costs. See Table 4.4, p.
99.
EOM: Chapter 4 (P. Bertoletti)
43
Example: Table 4.4, p. 99
Units
Total
Benefit
4
5
6
7
8
9
10
40
50
58
64
68
70
70
Marginal
Benefits
Total
Costs
10
8
6
4
2
0
32
40
48
56
64
72
80
Marginal
Costs
Net
Benefit
Total
Costs
8
8
8
8
8
8
8
10
10
8
4
-2
-10
28
35
42
49
56
63
70
Planner’ s Estimates
EOM: Chapter 4 (P. Bertoletti)
Marginal
Costs
Net
Benefit
7
7
7
7
7
7
12
15
16
15
12
7
0
Error Scenario
44
Returns to Scale III
• Notice that Formula 4.1 implies that, in such a
case, quantity regulation will always be the
best approach.
• In particular, the efficient quantity is 6 (or 5)
under the planner estimate (net benefit 10), and
6 also in the error scenario (net benefit 16).
• However, the use of the “equilibrium” price 8
will lead to the “maximum” production of 10
with a null net benefit in the error scenario,
and it would be no guide to choice for the firm
under correct planner estimates.
EOM: Chapter 4 (P. Bertoletti)
45
Returns to Scale IV
• The fundamental message here is that, with
CRS, producers’ responses to small price
change are too extreme to let price be an
effective instrument of controlling
production.
• This also illustrate a further limitation of the
FTWE: with CRS the price system does not
exactly determine the output level
(efficiency is achieved only if it happens
that demand equals supply).
EOM: Chapter 4 (P. Bertoletti)
46
Returns to Scale V
• Notice that if several firms exhibit CRS at different
cost levels a further problem of coordination arises:
efficiency would command that only the most
efficient firm does produce, with price adjusted to
its marginal cost and quantity accordingly adjusted.
• This is possibly achieved by competitive bidding,
which explains such a business practice (with
“requirements contracting” the seller agrees to
supply how many units are decided by the buyer at
the quoted price) and suggests is most used under
constant (or increasing) returns to scale.
EOM: Chapter 4 (P. Bertoletti)
47
The Cost of Information and Communication
• Gathering, organizing , storing, analyzing,
and communicating information in a form
that is useful for decision making does cost.
• As suggested in the previous chapter, a
system of prices is possibly a particularly
good way to economize on those costs.
• Consider the problem of minimizing total
cost of producing a given amount of total
output in a firm with several facilities (or in
an economy as a whole).
EOM: Chapter 4 (P. Bertoletti)
48
Economizing on Information I
•
•
A planned allocation centrally determined
and implemented with quantity controls
requires huge amounts of detailed
information about individual (marginal)
production costs (just to assess feasibility).
In contrast, the use of a price should induce
all facilities to produce at a common
marginal cost (the condition for efficient
production), without any communication of
local production conditions.
EOM: Chapter 4 (P. Bertoletti)
49
Economizing on Information II
•
•
•
•
Of course, the determination of the right price
requires to find which price will call forth the
desired total output.
And this requires to know the total supply
function, a task which nevertheless seems less
demanding.
In a market system, this is actually left to the
market forces, which adjust prices.
In a planned economy, one can think of rounds
of communication of tentative prices and
output levels (one per plant), up to equilibrium.
EOM: Chapter 4 (P. Bertoletti)
50
Economizing on Information III
•
•
Actually, a similar scheme could be used for
quantity planning, having output levels first
tentatively set and then adjusted up and
down as a function of communicated
marginal cost levels (the process stops when
all units communicate the same marginal
cost level).
But this requires the communication of
more information (with N plants, 2N
numbers instead of just N + 1 (the price)).
EOM: Chapter 4 (P. Bertoletti)
51
Informational Efficiency I
•
•
•
To measure and compare informational
requirements we adopt the so-called Hurwicz
Criterion (HC), by the polish Nobel Prize
winner Leonid Hurwicz.
The key idea is to consider how much
information it takes to determine whether a
particular plan is efficient.
Think of the planning system as based on
broadcasts (“communications available to
everybody”) of producers and consumers
plans, augmented with possibly additional
information to check the efficiency.
EOM: Chapter 4 (P. Bertoletti)
52
Informational Efficiency II
• Upon receiving the broadcast each
individual evaluates the plan using his local
information and replies with a message,
either “yes” or “no”.
• In terms of the previously described rounds
is as if the center were announcing both the
prices and the quantities, with a firm
replying yes if its marginal cost is equal, at
the given quantity, to the announced price.
EOM: Chapter 4 (P. Bertoletti)
53
Informational Efficiency III
• The system must be constructed so that if
everybody replies yes then the resulting plan is
an efficient one.
• The HC holds that one system operates with
less communication than another if the first
broadcasts fewer additional variables (besides
the plans themselves).
• A system is then informationally efficient if no
other system uses less extra information than it
does to verify that a given plan is efficient.
EOM: Chapter 4 (P. Bertoletti)
54
Informational Efficiency IV
• Notice that the HC is weak in that it does not
account for how quickly different systems
find an efficient allocation, nor for how much
information is communicated in the process.
• Nevertheless, it capture one essential feature
of the working of a price system, i.e., the
intuitive idea of its informational efficiency.
EOM: Chapter 4 (P. Bertoletti)
55
Informational Efficiency Theorem
• Consider the setting of the A-D model of a
private ownership economy, and suppose that
any information about consumer preferences
and feasible technology is private and located
with the corresponding consumer/firm.
• Then any system capable of supporting an
efficient resource allocation using augmented
plans must communicate, in addition to the
plans, at least one additional variable for each
commodity (minus one).
EOM: Chapter 4 (P. Bertoletti)
56
•
•
•
Informational Efficiency V
It follows that, when a competitive equilibrium
exists, the price system achieves economic
efficiency with minimal communication (i.e., it
is informationally efficient by the Hurwicz
criterion).
The intuition for this result is based on the fact
that to assess efficiency the production of each
firm must take place with a so-called marginal
rate of transformation of any input into any
output that must be the same in the whole
economy.
This necessary informational requirement is
sufficient as well in a competitive equilibrium.
EOM: Chapter 4 (P. Bertoletti)
57
Exercise 3, p. 120.
• One hundred families in a community must
decide how much land y to improve for
public parks (a case of “public good”).
• There are no wealth effects, so that family’s
n has utility Un(xn, y) = xn + vn(y), where x is
money, and vn(y) its willingness to pay for y.
• Suppose that a plan y with cost cy is
proposed, to be financed through lump-sum
taxes tn by family n.
EOM: Chapter 4 (P. Bertoletti)
58
Exercise 3: continuation
• What conditions must be checked to test the
efficiency of the plan?
• By using value maximization (ntn = cy), FOC is:
• nvn’(y*) = c.
• What is the minimal amount of communication
required to verify proposal efficiency?
• The “centre” has to communicate y* and families
need to report about the marginal willingness to
pay vn’(y*), i.e., 100 + 1 pieces of information.
EOM: Chapter 4 (P. Bertoletti)
59
Exercise 3: conclusion
• Last number suggests that, in principle, a
market-like system might also be used.
• This is actually what happens with the so-called
“Lindahl prices”, which require treating each yn
as a separate commodity, and asking each family
to pay pnyn for the amount yn he chooses, where
pn = vn’(y*).
• The “market clearing” condition (under
“competitive behaviour”) is then yn = y* for each
family n.
EOM: Chapter 4 (P. Bertoletti)
60
Exercise 3: conclusion
• Notice that efficiency of the equilibrium can
actually be verified by “broadcasting” 100 prices
and 1 quantity (and having all families to agree).
• However, the problem is how to determine the
equilibrium quantity y*, which requires to obtain
the information incorporated into the (individual
“demand”) schedules vn’(y).
• Indeed, a family should anticipate that the higher vn’
the larger the price pn that it will have to pay in the
equilibrium, and should then be unwilling to report
truthfully about his (marginal) willingness to pay
(the well known “free riding” problem).
EOM: Chapter 4 (P. Bertoletti)
61
Informational Efficiency VI
•
•
Of course, a market system works without
broadcasting plans, but it works in fact with the
amount of communication identified by the
Theorem (prices are “announced” and each
agent “responds” with the corresponding
amounts she wants to buy or sell).
Moreover, the previous setting and related
result applies to explicit production planning
problems, e.g. to coordination problems with
design attributes.
EOM: Chapter 4 (P. Bertoletti)
62
Planning with Design Attributes I
•
•
Notice that the hypothesis of the informational
efficiency theorem rules out problems with
design attributes, in which there is a priori
much information about the nature of the
efficient choice, and less information is
necessary to verify optimality.
Think of the coxswain guiding a crew of
rowers with much less communication than a
price system.
EOM: Chapter 4 (P. Bertoletti)
63
Planning with Design Attributes II
•
•
•
Problems of synchronization arise frequently in
business.
For example, when introducing a new car, an
automobile company must synchronize
production facilities on a product introduction
date. This requires that the product team
communicate the target date, rather than marginal
values for early completion.
And all new parts must fit together, with
coordination needs that do not speak “the
language of prices”.
EOM: Chapter 4 (P. Bertoletti)
64
Planning with Design Attributes III
•
•
•
In design attribute problems, the unfitness of
prices is not due to any theoretical impossibility.
Rather, it arises out of unreasonable informational
requirements, and of the brittleness of the system.
To illustrate, suppose that there are 10 suppliers
that have to coordinate on 5 completion dates.
Defining “contingent commodities” by their time
of delivery, we are dealing with 50 inputs in all,
which would require 50 separate prices.
EOM: Chapter 4 (P. Bertoletti)
65
Planning with Design Attributes IV
•
•
If the number of supplier, delivery dates and
component design is large, the number of prices
will need to be correspondingly large.
But the FTWE applies, and if all prices are set so
that the coordinator would want to buy one unit of
one design of each input at some particular date T,
and if each supplier finds it most profitable to
deliver one unit of the corresponding design at T,
so that market clears, then the list of dates at which
supplies of each type of component become
available is guaranteed to be efficient.
EOM: Chapter 4 (P. Bertoletti)
66
Planning with Design Attributes V
•
•
•
But determining 50 prices to solve the previous
synchronization problem is unnecessary,
wasteful and foolish.
All the coordinator needs to know to check
whether a a proposed introduction date is
optimal is whether the total marginal cost of
introducing the product a bit earlier - taking
into account the extra costs incurred by the
suppliers – is equal to the marginal benefit of
doing so.
Which is just the 10 numbers representing the
marginal costs of a speed-up for each supplier.
EOM: Chapter 4 (P. Bertoletti)
67
Planning with Design Attributes V
•
•
•
•
Consider an extreme case, depicted in the
following Figure (Fig. 4.2, p. 105).
There are just 2 supplier, but a continuum of
possible dates.
The decreasing marginal cost curves show the cost
to each component supplier of speeding up the
introduction by a small amount, given any
particular target date. They imply that the cost
grows increasingly as the planned date is moved up
(i.e., earlier).
The increasing marginal benefit curve implies that
also the cost of delays grows increasingly.
EOM: Chapter 4 (P. Bertoletti)
68
The optimal date of product introduction
MB
TMC
€
MC2
MC1
T*
T
date of introduction
EOM: Chapter 4 (P. Bertoletti)
69
Planning with Design Attributes V
•
•
In the previous example, to verify whether any
particular list of prices leads to optimal choices
the planner would need to know what costs
each supplier would incur for each possible
delivery date (an infinite list of information).
To verify the actual date, however, taking
advantage of special knowledge about the
problem, three numbers (the marginal benefit of
a speed up and the 2 suppliers’ marginal cost)
are enough.
EOM: Chapter 4 (P. Bertoletti)
70
Planning with Design Attributes VI
•
•
•
The cost of mistakes. In problems with design
attributes, the most costly sorts of errors are
failure of synchronization or fit.
And are these 2 characteristics (predictable
elements of fit and high cost of small errors of
fit) which explain why the price system
performs poorly on both the communication
and the brittleness criteria.
Coordination is achieved in these kind of
problem by communication of the design
variable themselves.
EOM: Chapter 4 (P. Bertoletti)
71
Planning with Design Attributes VII
•
•
Ex: each rower must know the intended stroke
rate and the timing; the target introduction date
must be communicated to all members of the
production innovation team; and the
ambulance driver must be told which crisis to
attend, where and when.
It can be proved that this minimizes
communication by the HC, and reduces the
cost of error associated with more indirect
methods.
EOM: Chapter 4 (P. Bertoletti)
72
Exercise 2, p. 120.
•
•
The introduction of a new product in t months
will generate a revenue/profit of:
• R = 144 – t2 if t  12,
and 0 otherwise.
3 departments need all to be ready before
production begins, and their costs are given by:
• C1 = 3(12 - t),
• C2 = 4(12 - t),
• C3 = 5(12 - t).
EOM: Chapter 4 (P. Bertoletti)
73
Exercise 2: continuation
•
•
•
•
What is the optimal date t* of introduction?
Overall net profit is given by:
• (t) = R(t) – (C1(t) + C2(t) + C3(t)),
and the FOC requires:
• ’(t) = - 2t + (3 + 4 + 5) = 12 – 2t = 0,
which implies t* = 6, * = (6) = 36.
The situation is illustrated in next Figure, in
which MR = - R’(t), MCi’ = - Ci’(t), i = 1, 2,
3, TMC = MC1 + MC2 + MC3..
EOM: Chapter 4 (P. Bertoletti)
74
Exercise 2 (1), p. 120.
MB
tg  = 2
TMC
12
5
4
3
MC3
MC2
MC1

t* = 6
12
EOM: Chapter 4 (P. Bertoletti)
t
75
Exercise 2: conclusion
•
What will be net profit if all departments are
mistakenly hurried to deliver after 5 or 7 months?
• (5) = 119 – (21 + 28 + 35) = 35,
• (7) = 95 – (15 + 20 + 25) = 35.
What will be net profit if just department 2 is
mistakenly hurried to deliver after 5 or 7 months?
•  = 108 – (18 + 28 + 30) = 32,
•  = 95 – (18 + 20 + 30) = 27.
EOM: Chapter 4 (P. Bertoletti)
76
A Formal Model of Design Decision I
•
•
•
In the Appendix of Chapter 4 the introduction
of a new product is studied formally, showing
that the informationally efficient way to handle
such a problem is to announce the design
attributes.
Suppose that N system components are
necessary to the making of the product, each
developed by a separate facility.
Available resources are of K different types,
and are indicated by the list x = (x1, x2, …, xK).
EOM: Chapter 4 (P. Bertoletti)
77
A Formal Model of Design Decision II
•
•
•
The resources allocated to facility n = 1, …,
N are indicated by xn = (x1n, x2n, …, xKn). Of
course, nxkn  xk, k = 1, …, K.
The total cost of facility n to be ready a tn with
capacity yn is Cn(yn, tn; xn, zn), where the
parameter zn is known only to the local
manager.
It is assumed that Cn is increasing in yn and
decreasing in tn.
EOM: Chapter 4 (P. Bertoletti)
78
A Formal Model of Design Decision III
•
•
Since each unit of the new product requires a
unit of each component, we can write the
revenue function as:
• R[Min{y1, …, yN}, Max{t1, …, tN}],
where R(y, t) increases wrt its first argument
and decreases wrt its second argument.
Accordingly, the firm maximizes:
•  = R[Min{y1,.., yN}, Max{t1,.., tN}]
- nCn (yn, tn; xn, zn),
subject to nxn  x.
EOM: Chapter 4 (P. Bertoletti)
79
A Formal Model of Design Decision IV
Under the assumption that each facility
uses each resource (and that the FOCs
characterize the optimal solution) it can
be shown that the following conditions
must hold (n = 1, …, N):
1. yn = y*, tn = t*, Cn/xkn = pk, k = 1,…,
K;
2. nxn = x, nCn/yn = R/y, nCn/tn
= R/t.
EOM: Chapter 4 (P. Bertoletti)
80
A Formal Model of Design Decision V
•
Conditions (1) say that facilities’ capacity
and readiness date are the same, and that the
impact of the allocation of each resourse k
on any facility n is the same (the “price” pk).
•
Conditions (2) say that resources are fully
utilized, and that the marginal costs and
benefits of either adding capacity or being
ready sooner just balance.
EOM: Chapter 4 (P. Bertoletti)
81
A Formal Model of Design Decision VI
•
•
•
The solution certifies that we are dealing with a
“design decision”: even without knowing Cn and R,
we can state that the capacities and date will have to
be the same.
Exactly for this reason, the Hurwicz theorem does
not apply and the use of a price system does not
need to be informationally efficient.
Moreover, by using Hurwicz’s framework, F. Sato
(1981) proved that, in addition to communicate the
NK + 2 pieces of information which do constitute
the plan itself (x, y, t), K + 2N numbers must be
“broadcasted”, for a total of NK + 2 + K + 2N = (N
+ 1)(K + 2).
EOM: Chapter 4 (P. Bertoletti)
82
A Formal Model of Design Decision VII
•
•
For example, the central coordinator
announces prices, date and capacity, i.e.,
K + 2 numbers. Each manager replies
with the amount of resources he wants,
and with marginal costs for capacity and
time: these are again K + 2 data which
allow to check the efficiency conditions.
Overall this amounts to K + 2 + N(K + 2)
= (N + 1)(K + 2) pieces of information,
which establishes informational efficiency.
EOM: Chapter 4 (P. Bertoletti)
83
A Formal Model of Design Decision VIII
•
•
Consider the alternative use of a price system,
assuming that there were T alternatives date: a
plan would involve the allocation of NK
resources plus the description of capacity of
any possible date, which means additional NT
data.
Then a price for each resource and a price for
the capacity of each facility at any date would
require additional K + NT, reaching an amount
of overall pieces of information given by NK +
NT + K + NT = (N + 1)K + 2NT, which exceeds
of 2[N(T – 1) - 1] the efficient minimun.
EOM: Chapter 4 (P. Bertoletti)
84
A Formal Model of Design Decision IX
•
•
•
The other hallmark of a problem with design
attributes is the high relative cost of failure of fit.
Suppose that a small error of designing either y or
t occurs: i.e., either yn = y* +  or tn = t* +  (n =
1, …, N).
The way to evaluate these errors is to substitute
their values in the profit expression, to take
derivatives with respect to  and to evaluate them
at  = 0 (the first-order loss would be
proportional to ). But then the previous FOCs
(2) show that these errors would have zero firstorder effects on profit!
EOM: Chapter 4 (P. Bertoletti)
85
A Formal Model of Design Decision X
•
•
•
On the contrary, suppose that a single
facility n is getting its capacity wrong.
If yn - y* =  > 0, then the first-order
approximation to the profit loss is given by:
• Cn/yn > 0
while if y* - yn =  > 0, then the first-order
approximation to the profit loss is given by:
• (R/y - Cn/yn ) =  inCi/yi > 0.
EOM: Chapter 4 (P. Bertoletti)
86
A Formal Model of Design Decision XI
•
The previous expressions (which come from
using respectively the right and left derivative
of the profit function wrt ) have intuitive
economic interpretations, but the important
message is that decisions concerning timing and
scale do have design attributes.
•
Explicit coordination of these decisions by a
manager or a central coordinator, rather than
decentralized decisions guided by prices, is
predictably the norm for decisions of these
kinds.
EOM: Chapter 4 (P. Bertoletti)
87
Coordination and Business Strategy
•
•
Strategic business decisions often present
design (and in particular innovation)
attributes. In addition, in many sectors
there are important economies of scale.
Both these aspects work against the use of
decentralised means of coordination, and
in particular the use of prices, and favor
direct communication and systematic,
centralized control systems.
EOM: Chapter 4 (P. Bertoletti)
88
Scale, Scope and Core Competencies
•
•
•
Notice that the Operational Scale is itself a
design variable.
In other words, depending on the volume of
sales that a firm anticipates, a set of
coherent actions must be taken by a number
of people who need a shared vision.
Also notice that the anticipated scale of a
firm’s operations affects its degree of
specialization and its vertical integration (GM
vs Toyota).
EOM: Chapter 4 (P. Bertoletti)
89
Scale and Scope
•
•
In fact, firms that are large enough to assign
different management functions to different
decision makers invest a lot to forecast
market conditions in order to plan and
coordinate their activities.
A similar point applies also to economies of
scope, which might arise in the production of
(components that are used in each of) several
products. Ex: Casio liquid crystal displays,
used to realize calculators, watches,
electronic books, …
EOM: Chapter 4 (P. Bertoletti)
90
Core Competencies
•
•
•
There are scale economies which arise at the
level of product development, when a firm
introduces new products (in a set of related
markets) frequently.
These are sometimes called core competencies
of the firm, and are just another kind of shared
component, with the special feature that many
sharing products do not yet exist.
In this case long-term investment strategies are
needed, which take into account demands of
generations of products not yet even imagined
(next best thing).
EOM: Chapter 4 (P. Bertoletti)
91
National Industrial Planning
•
•
A controversial application of the same idea
is to national industrial planning (Japan,
Corea?), by which groups of industries to
promote are identified by their fitting
together with each other and with the
country’s competencies and advantages.
A related idea is complementarity.
Complementarities among a set of activities
are an important source of design attributes.
EOM: Chapter 4 (P. Bertoletti)
92
Complementarities I
•
•
•
Several activities are said to be mutually
complementary if doing more of any one increases
the marginal profitability of each other in the
group.
Formally, if the smooth profit function (x)
depends on the list x = (x1, …, xn), we say that two
activities xi and xj are mutual complements if
2/xixj  0.
For example, if there are economies of scale in
producing a component, then the productions of
two products which use that component become
complements.
EOM: Chapter 4 (P. Bertoletti)
93
Complementarities II
•
•
•
Clearly, complementarities lead to predictable
relationships among activities (the levels of activities
of two complements should move together).
In the case of strong complements, design attributes
are always present, and the coherence of the different
parts of the business strategy becomes crucial.
Ex (“Modern Manufacturing”): producing a wide
range of related products with specialized needs
involves a high level of flexibility (frequent product
redesign), avoiding inventories (just in time), strong
communications, with deep and self-reinforcing
implications for the compensation policies, supplier
relations and the accounting system.
EOM: Chapter 4 (P. Bertoletti)
94
Complementarities III
•
•
•
With complementarities, alignment alone is
generally not enough: the various managers must
adapt their choices to each other’s.
Think of the manufacturing and the marketing
managers having to choose respectively the batch
size (how much to produce in the product line
before switching to next product) and the product
variety.
In general, the larger the batch size (which raises
the level of inventories), the smaller is the optimal
number of product (given total production). And
viceversa.
EOM: Chapter 4 (P. Bertoletti)
95
Complementarities IV
•
•
The previous situation is likely to
produce a coordination failure, if
managers are suppose to take decision
independently.
Drawing the individually optimal (“best
replies”) curves, as in Fig. 4.3, p. 111,
illustrates the fact that there might be
several coherent combinations (but
perhaps a single overall optimal choice).
EOM: Chapter 4 (P. Bertoletti)
96
Figure 4.3, p. 111
Optimal Variety
Coherent combinations
Variety
M
Optimal Batch size
T
Batch size
EOM: Chapter 4 (P. Bertoletti)
97
Complementarities V
•
•
•
Combination T can be linked to the “Model
T” Ford strategy, while combination M
somehow corresponds to the “Modern
Manufacturing” approach.
It might be the case that managers are able to
self coordinate on some coherent choice
(“Nash equilibria”), but explicit coordination
(managerial meetings and information
sharing) should work faster and better.
However, nothing guarantees that a coherent
solution is the best one (the dimension of
overall profit is missing in the picture).
EOM: Chapter 4 (P. Bertoletti)
98
Strategic Coordination
•
•
•
A key problem is that the environment
changes, and even if the curves (and the
coherent combinations) might be little
affected, the underlying relative profitability
may change a lot.
Suppose that conditions suggest a switch from
T to M (or viceversa): local managers might be
able to practice local small adaptations, but a
radical switch has the nature of a design
decision with innovation attributes.
Understanding the complementarities in the
system is likely to require a central
coordination by top management.
EOM: Chapter 4 (P. Bertoletti)
99
Management, and the Means of Coordination
•
•
•
When the price system fails because of its
brittleness or because it requires too much
communication, a demand for
management usually arises.
Formally, consider a set of (groups of)
individuals who have various decisions to
make and actions to perform.
A particular decision is decentralised if it
is left to individuals alone.
EOM: Chapter 4 (P. Bertoletti)
100
Centralization vs Decentralization I
•
•
•
In contrast, a centralized decision is made at
higher level and communicated to or
imposed on the individuals.
The higher level can be thought of as an
individual who have the power to make the
decision, as in a managerial hierarchy or
under state planning, or as a sort of a
collective body.
From this perspective, the price system and
the assembly line represent the two polar
cases.
EOM: Chapter 4 (P. Bertoletti)
101
Centralization vs Decentralization II
•
•
•
In complex organizational decisions, neither
decentralization nor complete centralization is
likely to be optimal.
Crucial information always resides with
individual, and to transmit it or ignore it
according to the centralized solution are costly
alternatives, as it is to run the risk of a
coordination failure if the decentralized
approach is chosen.
Notice that centralized decisions serve to
define the parameters of the decentralized
ones, and to constrain local decision makers.
EOM: Chapter 4 (P. Bertoletti)
102
The coordinating role of management I
•
•
The key role of management in
organizations is to ensure coordination,
within a feasible plan of action that
should promote the organization’s goals,
and adjust as circumstances change.
Ensuring motivation of the participants is
very important as well, but incentives
become an issue only once a plan is
being carried out.
EOM: Chapter 4 (P. Bertoletti)
103
The coordinating role of management II
•
•
•
The first step is organizational design,
determining which decisions are to be
centralized and who should make them, and
what information will be transmitted upwards
to support centralized decision making, and
back down to guide who will implement the
plan.
Then design variables need to be determined in
a centralized fashion. Examples are timing and
scale.
But considerable autonomy should also be left
to local managers who exploit their knowledge.
EOM: Chapter 4 (P. Bertoletti)
104
The coordinating role of management III
•
•
•
In deciding what and how to communicate , the
cost of information transfer and the brittleness
of the planning system become important.
Finally, when complementarities lead to
multiple possible coherent patterns of
behaviour, a centralized decision is called for,
whose need becomes more acute when the
choice involves innovation attribute.
In the last case a special assignment problem
arises in which a new strategic design must be
determined and communicated.
EOM: Chapter 4 (P. Bertoletti)
105
Senior Management’s Role
•
•
The last task is typically performed by senior
management and its staff.
Early in the history of the company, while
thinking about how a company like this should
be managed, I kept getting back to one
concept: If we could simply get everybody to
agree on what our objectives were and to
understand what we were trying to do, then we
could turn everybody loose and they would
move along in a common direction.
David Packard, Hewlett-Packard co-founder
EOM: Chapter 4 (P. Bertoletti)
106