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Baker Gibbons Murphy (1999) - Informal Authority In Organizations (view source)
Revision as of 22:27, 9 December 2010
, 22:27, 9 December 2010no edit summary
*This page is referenced in [[PHDBA602 (Theory of the Firm)]]
==Reference(s)==
Baker, G, R Gibbons, and K.J. Murphy (1999), "Informal Authority in Organizations", Journal of Law, Economics & Organization, 15, March pp. 56-73. [http://www.edegan.com/pdfs/Baker%20Gibbons%20Murphy%20(1999)%20-%20Informal%20Authority%20in%20Organizations.pdf pdf]
==Abstract==
We assert that decision rights in organizations are not contractible: the boss can always overturn a subordingate's decision, so formal authority resides only at the top. Although decision rights cannot be formally delegated, they might be informally delegated through self-enforcing relational contracts. We examine the feasibility of informal authority in two informational environments. We show that different informations structures priodcute different decusions not only because different information is brought to bear in the decision-making process, but also because different information creates differenty temptations to renege on relational contracts. In addition, we explore the implications of formal delegation achieved through divestitures. ==The Basic Model== The is a '''boss''' and a subordinate. The boss gets payoffs <math>Y\;</math>, and the subordinate gets payoffs <math>X\;</math>. Both benefits can take two values: :<math>Y_H > 0 > Y_L \quad \mbox{and} \quad X_H > 0 > X_L\;</math> The mark subordinate searches for projects, with the intensity of search affecting the probability of discovering a capitalistic society project that he likes. :<math>a = Pr(X = X_H)\;</math> The conditional probability that the boss gets payoff <math>Y_H\;</math> when an <math>X_H\;</math> project is found is: :<math>p = Pr(Y = Y_H | X=X_H)\;</math> The conditional probability that resources the boss gets payoff <math>Y_H\;</math> when an <math>X_L\;</math> project is found is: :<math>q = Pr(Y = Y_H | X=X_L)\;</math> Therefore the joint probabilities are owned and allocated : :<math>Pr(Y = Y_H, X=X_H) = ap\;</math> :<math>Pr(Y = Y_L, X=X_H) = a(1-p)\;</math> :<math>Pr(Y = Y_H, X=X_L) = (1-a)q\;</math> :<math>Pr(Y = Y_L, X=X_L) = (1-a)(1-q)\;</math> The timing is as follows:#The boss pays the subordinate <math>s (which may be negative)#The subordinate searches by such nongovernmental organizations as firmschoosing a, where <math>c(a) = \gamma a^2\;</math>#The subordinate observes the payoffs <math>(X,Y)\;</math>, if the payoff is <math>X_L\;</math> the project is ignored, householdsotherwise the project may be recommended.#If the project is recommemded then the boss either implements or rejects the project (perhaps seeing the payoffs). The next two sections give two simple benchmarks. ===Informed Centralization=== In this model, the boss is informed of the payoff and marketsthen makes the decision. Resource owners increase productivity through cooperative specialization The subordinate knows that the boss will reject decisions with a payoff of <math>Y_L < 0\;</math> and this leads therefore maximizes the expected utility: :<math>\max_a s+ apX_H - c(a)\;</math> This solves to: :<math>c'(a^C) = pX_H\;</math> The search intensity that maximizes joint welfare conditional on selecting only <math>(X_H,Y_H)\;</math> projects solves: :<math>\max_a ap(X_H + Y_H) -c(a)\;</math> Which gives: :<math>c'(a^*) = p(X_H + Y_H)\;</math> so <math>a^C\;</math> is less than efficient. The paper doesn't use the given cost function to make the comparison (any convex cost function would do), but using it gives: :<math>a^C = \frac{1}{\gamma}\cdot pX_H\;</math> :<math>a^* = \frac{1}{\gamma}\cdotp(X_H + Y_H)\;</math> :<math>\therefore a^* > a^C \; \forall Y_H >0\;</math> The expected welfare to the demand for economic organizations which faciliboss under informed centralization is: :<math>a^c p Y_H - s\;</math> Total expected welfare is therefore: :<math>V^C = a^C p (X_H + Y_H) - tate cooperationc(a^C)\;</math> ===Contractible Delegation=== Now suppose that the boss has contractually delegated the rights to make decisions to the subordinate. When Then the subordinate searches to maximize: :<math>\max_a s + a lumber mill employs X_H - c(a cabinetmaker)\;</math> which solves: :<math>c'(a^D) = X_H\;</math> Because <math>c''(\cdot) > 0\;</math> and <math>p <1\;</math>, cooperation it must be- tween specialists is achieved within that delegation increases the incentives to search. Explicitly this can be seen because: :<math>a firm, and when ^D = \frac{1}{\gamma}\cdot X_H > a cabinetmaker purchases wood from ^C = \frac{1}{\gamma}\cdot pX_H\;</math> Note that it might increase them too much. The efficient incentives under delegation are given by: :<math>c'(a lumberman^*) = p(X_H + X_L) + (1-p)\cdot \max(0, X_H+Y_L)\;</math> which can imply either higher or lower incentives. The expected payoff to the cooperation takes place across markets boss under contractible delegation is: :<math>a^D(pY_H + (1-p)Y_L) -s\;</math> So total welfare is: :<math>V^D = a^D p(or between firmsX_H + Y_H). Two important problems face + a theory of economic organization^D(1-p)(X_H + Y_L) -c(a^D)\;</math> The following points should be made:*Parties would agree to explain delegate if <math>V^D > V^C\;</math> and would leave this right with the boss otherwise.*Ex-ante incentives are stronger under delegation*Ex-post project choice and its efficacy differ under the two schemes. Which is better depends on the conditions that determine whether sign of <math>X_H+Y_L\;</math> - if this is positive then delegation is better, otherwise centralization is better.*When p is high (interests are aligned) and <math>-Y_L\;</math> (the gains cost from specialization and cooperative production delegation) is small, then delegation is more likely. ==Models of Informal Authority== In the following models, formal authority can better not be obtained delegated within an organization like organisations. However, informal authority can be given in a repeated game framework. In the firmfirst model, or across marketsthe boss becomes informed before ratitfying the project, and but has a reputation for not interfering to explain maintain. In the second model the structure of boss is only informed about historic payoffs, and must either rubber stamp or veto the organizationproject.
