Suppose that equity depends on two sort of activities, one being the usual productive effort(m)and the other a socially harmful behavior, e.g. violation of some environmental regulations(n). The expected value of management's equity is given by aG(m, n), where a is the fraction of outstanding equities securities that management owns and G() is the expected value of firm equity Equity is determined the following way: it is one with probability m +n and zero with probability 1-m-n. Thus, the expected value of equity G(m,n)=m+n The expected private value of management's socially harmful behavior is E(n), where En >0 and Enn <0. Management's effort cost is C(n, m) here Cn>0, Cm>0, Cnn >0, 0, and Cmn >0 While n denotes the management's influence over the probability that corporate crime will occur, let u be an independent random influence variable with distribution function F(. Assuming n and u have additive effects social damage occurs if and only if n +u>0. Thus, the probability of social damage being observed is Pr(n+u>0=1-F(n)= P(n), the probability of crime being continuously increasing in n, Pn>0 and Pn >0 It is assumed that the government cannot actually observe n. However if the social bad occurs, the government can, with probability o, detect the agent's harmful activity and punish accordingly. Management bears, in that event,a penalty sa while the employer bears a penalty sp The fixed component of the salary of the management is w. The expected profits of the(risk neutral)management are U=w+a(m+n)+E(n)-C(n, m)-P(n)osa (1) e expected profits of the owners of the firm are (1-a)(m+n)-w-P(n)as The optimal contract when the employer can observe m and n is described by maximizing the expected profits of the owners of the firm subject to the participation constraint,U> k, where k is the agent's reservation utility. Rearranging expected profits, we can write V=m+n+E(n)-C(n, m)-P(n)o(sa+sp)-k
Suppose that equity depends on two sort of activities, one being the usual productive effort (m) and the other a socially harmful behavior, e.g. violation of some environmental regulations (n). The expected value of management’s equity is given by αG(m, n), where α is the fraction of outstanding equities securities that management owns and G(.) is the expected value of firm equity. Equity is determined the following way: it is one with probability m + n and zero with probability 1 − m − n. Thus, the expected value of equity is G(m, n) = m + n. The expected private value of management’s socially harmful behavior is E(n), where En > 0 and Enn < 0. Management’s effort cost is C(n, m), where Cn > 0, Cm > 0, Cnn > 0, Cmm > 0, and Cmn > 0. While n denotes the management’s influence over the probability that corporate crime will occur, let u be an independent random influence variable with distribution function F(.). Assuming n and u have additive effects, social damage occurs if and only if n + u > 0. Thus, the probability of social damage being observed is P r(n + u > 0) = 1 − F(−n) = P(n), the probability of crime being continuously increasing in n, Pn > 0 and Pnn ≥ 0. It is assumed that the government cannot actually observe n. However, if the social bad occurs, the government can, with probability σ, detect the agent’s harmful activity and punish accordingly. Management bears, in that event, a penalty sa while the employer bears a penalty sp. The fixed component of the salary of the management is ω. The expected profits of the (risk neutral) management are: U = ω + α(m + n) + E(n) − C(n, m) − P(n)σsa (1) The expected profits of the owners of the firm are: V = (1 − α)(m + n) − ω − P(n)σsp (2) The optimal contract when the employer can observe m and n is described by maximizing the expected profits of the owners of the firm subject to the participation constraint, U ≥ k, where k is the agent’s reservation utility. Rearranging expected profits, we can write: V = m + n + E(n) − C(n, m) − P(n)σ(sa + sp) − k (3) 6
The first-order conditions of the problem are Cn=0 Vn=1+ En -Cn-Pna(sa+sp)=0 Since second-order conditions are satisfied, we derive the optimal contract (m*, n*). The socially harmful activity is decreasing in the policy parameters (o, Sa, sp), whereas the productive effort is increasing in those same parame- ters(because Cmn>0) As in the usual framework(Polinsky and Shavell, 2000), we consider social welfare to be the sum of the payoffs of the employer and of the management minus the social damage caused by the socially harmful activity. Social welfare is given by W=m+n+e(n)-C(m, n)-P(m)H-h where H is social harm. Notice that the difference between the government's objective and the employer's is the social damage. By setting Sa +s H/o, the government can make the employer's objective identical to its own Nevertheless this is not a first best outcome because enforcement is costly Becker, 1968) It is not very relevant who is actually punished since management and ployer can bargain er ante and reallocate sanctions. It is equally effective to set sa=H/o and sp=0 or sp=H/o and sa=0. Furthermore, individual liability of management alone induces efficient behavior Corporate liability is not needed or necessary unless there wealth onstraint that limits sa. Suppose there is a binding liquidity constraint so that sa=o<H/o. Then, we should have sp=H/o-o to fully internalize social damage Corporate liability is justified on the grounds that managers do not have enough wealth to pay for social damage(Polinsky and Shavell 1993; Shavell,1997). n our model, the principal is the government, not the corporation. The corporation and its management team are the agents. There is virtually no distinction between corporation and management because their interests can be aligned at no cost. Once the alignment of interests is costly, the manager is the agent, but the corporation becomes a supervisor or a quasi-enforcer
The first-order conditions of the problem are: Vm = 1 − Cm = 0 (4) Vn = 1 + En − Cn − Pnσ(sa + sp) = 0 (5) Since second-order conditions are satisfied, we derive the optimal contract hm∗ , n∗ i. The socially harmful activity is decreasing in the policy parameters hσ, sa, spi, whereas the productive effort is increasing in those same parameters (because Cmn > 0). As in the usual framework (Polinsky and Shavell, 2000), we consider social welfare to be the sum of the payoffs of the employer and of the management minus the social damage caused by the socially harmful activity. Social welfare is given by: W = m + n + E(n) − C(m, n) − P(n)H − k (6) where H is social harm. Notice that the difference between the government’s objective and the employer’s is the social damage. By setting sa + sp = H/σ, the government can make the employer’s objective identical to its own. Nevertheless this is not a first best outcome because enforcement is costly (Becker, 1968). It is not very relevant who is actually punished since management and employer can bargain ex ante and reallocate sanctions. It is equally effective to set sa = H/σ and sp = 0 or sp = H/σ and sa = 0. Furthermore, individual liability of management alone induces efficient behavior. Corporate liability is not needed or necessary unless there is a wealth constraint that limits sa. Suppose there is a binding liquidity constraint so that sa = ¯ω < H/σ. Then, we should have sp = H/σ − ω¯ to fully internalize social damage. Corporate liability is justified on the grounds that managers do not have enough wealth to pay for social damage (Polinsky and Shavell, 1993; Shavell, 1997). In our model, the principal is the government, not the corporation. The corporation and its management team are the agents. There is virtually no distinction between corporation and management because their interests can be aligned at no cost. Once the alignment of interests is costly, the manager is the agent, but the corporation becomes a supervisor or a quasi-enforcer. 7