eom: chapter 4 (p. bertoletti)1 chapter 4: coordinating plans and actions in many sectors of the...

EOM: Chapter 4 (P. Bertoletti) 1

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.


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.


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.


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.


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)


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


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.


Criteria for Comparing Systems1. 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?)


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.


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.


Units Total Benefit

Marginal Benefits

Total Costs

Marginal Costs

Net Benefit

Total Costs

Marginal Costs

Net Benefit

4 40 5 35 17 23

5 50 10 12 7 38 20 3 30

6 58 8 20 8 38 24 4 34

7 64 6 29 9 35 29 5 35

8 68 4 39 10 29 35 6 33

9 70 2 50 11 20 42 7 28

10 70 0 62 12 8 50 8 20

Planner’ s Estimates Error Scenario

Example: Table 4.1, p. 95


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).


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).


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.


Units Total Benefit

Marginal Benefits

Total Costs

Marginal Costs

Net Benefit

Total Costs

Marginal Costs

Net Benefit

4 42 5 37 17 25

5 50 8 12 7 38 20 3 30

6 58 8 20 8 38 24 4 34

7 66 8 29 9 37 29 5 37

8 74 8 39 10 35 35 6 39

9 82 8 50 11 32 42 7 40

10 90 8 62 12 28 50 8 40




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.


Units Total Benefit

Marginal Benefits

Total Costs

Marginal Costs

Net Benefit

Total Costs

Marginal Costs

Net Benefit

4 40 5 35 17 23

5 50 10 12 7 38 20 3 30

6 60 10 20 8 40 24 4 36

7 60 0 29 9 31 29 5 31

8 60 0 39 10 21 35 6 25

9 60 0 50 11 10 42 7 18

10 60 0 62 12 -2 50 8 10




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.


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.


A Mathematical Formulation II

• Suppose, finally, that we do not restrict to integer amounts.

• Then:

=Price Control Loss

Quantity Control Loss

Marginal Benefit Slope

Marginal Cost Slope

2

Formula 4.1


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.


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.


A graphical proof

Q

MB

b

Q*

P

e

MC*

QPQ

MC

a

c

f

Dd

tg = MC*’= MC’ = d/(QP - Q), tg = |MB’ | = D/(QP - Q)


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.


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).


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.


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.


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*.


Exercise 1, p. 120

Q

MB

b

Q*

Pe

MC

QPQ

ac

f

Dd

MB*

tg = MC’ = D/(QP - Q) , tg = |MB’ |= |MB*’ | = d/(QP - Q).


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.


Exercise 1: conclusion

• It follows that:

• [(Q* - Q)d]/[(QP - Q*)D] = (d/D)2

• i.e.,

• just the opposite than in Formula 4.1!

=Quantity Control Loss

Price Control Loss Marginal Cost Slope

Marginal Benefit Slope2



• 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.


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.


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.


Units Total Benefit

Marginal Benefits

Total Costs

Marginal Costs

Net Benefit

Total Costs

Marginal Costs

Net Benefit

4 40 32 8 28 12

5 50 10 40 8 10 35 7 15

6 58 8 48 8 10 42 7 16

7 64 6 56 8 8 49 7 15

8 68 4 64 8 4 56 7 12

9 70 2 72 8 -2 63 7 7

10 70 0 80 8 -10 70 7 0




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.


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).


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.


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).


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.


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.


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)).


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.


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.


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.


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.


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).


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.


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.



• 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.


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.


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).


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.


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.


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”.


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.


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.


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.


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.


The optimal date of product introduction

date of introduction

€

T* T

TMCMB

MC1

MC2


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.


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.


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.


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).



• 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..


Exercise 2 (1), p. 120.

t* = 6 t

TMC

MB

MC1

MC2

12

345

12

MC3

tg = 2



• 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.


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).


A Formal Model of Design Decision II

• The resources allocated to facility n = 1, …, N are indicated by xn = (x1

n, x2n, …, xK

n). Of course, nxk

n 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.


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.


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, nCn/yn = R/y, nCn/tn = R/t.


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.


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).


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.


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.


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 first-order effects on profit!


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 ) = inCi/yi > 0.


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.


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.


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).


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, …


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).


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.


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/xixj 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.


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.


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.


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).


Figure 4.3, p. 111

Batch size

Var

iety

Coherent combinations

Optimal Variety

Optimal Batch size

M

T


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).


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.


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.


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.


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.


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.


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.


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.


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)1 chapter 4: coordinating plans and actions in many sectors of the...

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