by Milton Harris and Artur Raviv - Faculty

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interactions in a given group are identical in terms of probability of occurrence (later we assume that the benefits of coordinating these interactions are also the same). Formally, assume that the probability of either interaction in P is p, and the probability of either interaction in R is r. We also assume that interactions are independent, and these probabilities are observed by everyone in the firm. 4 We assume p > r, i.e, interactions between A and B and between C and D are the more likely interactions, while interactions between A and C and B and D are less likely. In terms of the above example, the assumption is that interactions within a product line are more likely than those across product lines. If, on the other hand, the economies of scale from combining production activities and those from combining marketing activities are more likely than interactions across functions within product lines, then we would simply relabel the activities so that A is production of Tide, B is production of Cheer, C is marketing of Tide, and D is marketing of Cheer. There are three types of potential managers, project managers (one for each project), middle managers, and a CEO. Project managers are required to generate the projects and participate in managing them but cannot coordinate interactions between projects. They do, however, refer projects to middle management or the CEO for investigation and coordination of possible interactions. If a set of projects does interact, there are benefits to coordinating them. Discovering and reaping these benefits requires investigation and coordination by a middle manager with the correct expertise (or by the CEO). For each interaction ω Ω, a middle manager, denoted m ω, may be hired who can discover and coordinate this interaction and only this interaction. The set of potentially available middle managers is denoted by M = {m ω�ω Ω}. We can think of the middle managers in M as product division managers, managers of functional areas (e.g., marketing manager), country managers, etc., depending on the interpretation of the activities A, B, C, and D. Let M P (M R) denote the set of middle 4 As was pointed out in the Introduction, we abstract from all private information and incentive problems. While these may also be important determinants of organization structure [see Qian (1994), Singh (1985)], we limit the scope of the current paper to a consideration of coordination issues. D:\Userdata\Research\Hierarchies\temp.wpd 11 February 22, 2000 (11:18AM)
managers who can discover and coordinate interactions in P (respectively, R), i.e., M P = {m ω�ω P} and M R = {m ω�ω R}. Incremental benefits from coordinating the pairwise interactions are assumed to be the same for all pairs and are normalized to one. Thus, the probabilities p and r also play the role of expected benefits of the potential interactions. The CEO, denoted m*, is assumed to be able to discover and exploit any interaction, but only the CEO can exploit the company-wide interaction which is assumed to be present if all four pairwise interactions occur. Incremental benefits from coordinating the company-wide interaction are given by s. 5 Incremental benefits produced by the CEO depend on which benefits, if any, middle managers have already exploited. In particular, m* generates benefits of 1 for each interaction present but not exploited by a middle manager plus s if all four pairwise interactions are present. This formalism admits many possible interpretations. For example, A and C can be electrical devices in Chevies and Cadillacs, respectively, and B and D can be chassis of Chevies and Cadillacs, respectively. If project A turns out to be headlight improvement and B crash resistance, then A and B are likely to interact in that both improve the safety of Chevies. If they do interact, exploiting this interaction through a coordinated marketing effort emphasizing safety will produce incremental benefits. If, however, B is roominess, then A and B are unlikely to interact. One can interpret m AB (m CD) as the manager of the Chevy (Cadillac) Division and m AC (m BD) as the head of electronics (chassis). An alternative interpretation is that A and B are innovations in products 1 and 2, respectively, while C and D are new marketing techniques for the two products, respectively. The innovations may have common components calling for coordinated production. The new marketing techniques may call for a common ad campaign for the two products. One can interpret m AB (m CD) as the manager of the 5 One role of the CEO in an organization may be to resolve conflicts in coordinating between two or more interactions involving the same project, e.g., between AB and AC. One can interpret s in our model as the benefit to such conflict resolution. D:\Userdata\Research\Hierarchies\temp.wpd 12 February 22, 2000 (11:18AM)
Page 1 and 2: ORGANIZATION DESIGN by Milton Harri
Page 3 and 4: eports both to the Project A divisi
Page 5 and 6: CEO President, ABC Norway President
Page 7 and 8: paid if the manager is available to
Page 9 and 10: information at the same time. Delay
Page 11: (1971), Khandwalla (1974) and Pugh
Page 15 and 16: order and in which contingencies th
Page 17 and 18: value of the R-hierarchy (net of fi
Page 19 and 20: it is still optimal to use the CEO
Page 21 and 22: hierarchy is that the firm need pay
Page 23 and 24: 5 Comparative Statics For Q Optimal
Page 25 and 26: Figure 5: Optimal Organization Desi
Page 27 and 28: intermediate values of F, the centr
Page 29 and 30: appendix. Proposition 4. Increases
Page 31 and 32: divisional hierarchy. Next we exami
Page 33 and 34: References Baron, David P. and Davi
Page 35 and 36: Recall A(Q) Q(1 p 2 r 2 ) D G Q, B
Page 37 and 38: Similarly, for Q < 2r+r 2 s, K pr(Q
Page 39 and 40: is impossible. Therefore, Q B(p,r)
Page 41 and 42: Case 2: G > Q B(r,p) J and Figure 6
Page 43 and 44: and H(Q) L(Q) A(Q), for Q Q B (r,p)
Page 45 and 46: Case 6: J > Q B(r,p), J > G > Q B(p
Page 47 and 48: L(Q) A(Q), for Q Q B (p,r), C pr (Q
Page 49: for X = M, CP, CR, and CF implies t

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