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Chapter 4: Coordinating plans and actions

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) .

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Chapter 4: Coordinating plans and actions

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  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. EOM: Chapter 4 (P. Bertoletti)

  2. 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)

  3. 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)

  4. 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)

  5. 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)

  6. Resource allocation problems • Particular attributes of resource allocation problems determine which system of coordination is especially effective. • In problems with design attributes: • A great deal of a priori information about the form of the optimal solution is available; • Failing to achieve the right relationship among the variables is generally more costly than other kind of errors. EOM: Chapter 4 (P. Bertoletti)

  7. 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)

  8. 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)

  9. Assignment problems I • In assignment problemsthere 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)

  10. 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)

  11. 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)

  12. 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)

  13. 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)

  14. 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)

  15. 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)

  16. 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)

  17. Criteria for Comparing Systems • If all the required information were reported honestly and accurately, and processed perfectly and costless, could the system achieve efficiency? • How much information and communication does the system require to achieve its purpose? • 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)

  18. 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: • Either the central coordinator simply specifies the production units’ quantities; • Or the center attempts to guide units’ decisions via price signals. EOM: Chapter 4 (P. Bertoletti)

  19. 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)

  20. Example: Table 4.1, p. 95 Planner’ s Estimates Error Scenario EOM: Chapter 4 (P. Bertoletti)

  21. 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)

  22. 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)

  23. 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)

  24. Example: Table 4.2, p. 96 Planner’ s Estimates Error Scenario EOM: Chapter 4 (P. Bertoletti)

  25. 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)

  26. Example: Table 4.3, p. 97 Planner’ s Estimates Error Scenario EOM: Chapter 4 (P. Bertoletti)

  27. 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)

  28. 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)

  29. 2 Price Control Loss Marginal Benefit Slope = Marginal Cost Slope Quantity Control Loss A Mathematical Formulation II • Suppose, finally, that we do not restrict to integer amounts. • Then: Formula 4.1 EOM: Chapter 4 (P. Bertoletti)

  30. 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)

  31. 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)

  32. tg = MC*’= MC’ = d/(QP - Q), tg  = |MB’ | = D/(QP - Q) MC MB MC* a f P   c  d D b  e  Q Q Q* QP A graphical proof EOM: Chapter 4 (P. Bertoletti)

  33. 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)

  34. 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)

  35. 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)

  36. 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)

  37. 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)

  38. tg = MC’ = D/(QP - Q) , tg  = |MB’ |= |MB*’ | = d/(QP - Q). MC MB* f MB a c D d e b P    Q Q Q* QP Exercise 1, p. 120 EOM: Chapter 4 (P. Bertoletti)

  39. 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)

  40. 2 Quantity Control Loss Price Control Loss Marginal Benefit Slope = Marginal Cost Slope 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! EOM: Chapter 4 (P. Bertoletti)

  41. 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)

  42. 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)

  43. 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)

  44. Example: Table 4.4, p. 99 Planner’ s Estimates Error Scenario EOM: Chapter 4 (P. Bertoletti)

  45. 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)

  46. 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)

  47. 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)

  48. 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)

  49. 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)

  50. 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)

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