# Ownership structure, value of the firm, and the bargaining power of the manager.

I. Introduction

In their seminal article, Michael Jensen and William Meckling developed a theory of the corporate ownership structure that took into account "the trade-offs available to the entrepreneur-manager between inside and outside equity and debt" |5, 312~. Jensen and Meckling concentrated on the principal-agent problem and the agency costs that arise from the introduction of outside equity into the firm. This was done without any consideration of what effects such an action might have had on the bargaining power of the owner-manager in negotiating wages with the current employees of the firm.

Several years later Masahiko Aoki |1; 2, 61-91~ introduced a model of the firm that emphasized "its aspect as a quasi-permanent organization of stockholders and employees" |1, 600~. He asserted that as a result of their association with the firm, the employees acquire skills and knowledge that, when combined with the physical assets supplied by the stockholders, can produce some economic gains--the so-called organizational rent. Such rents would not be possible through the employment of external factors of production (such as workers that have no knowledge of the workings of the firm). The organizational rent can be produced only through the cooperation of the stockholders (supplying the physical assets) and the existing employees. As such, the situation is tantamount to a two-person cooperative game, and the question becomes, how then is the organizational rent to be distributed between stockholders and employees. Aoki proposed that the solution to this particular distribution problem could be accomplished by use of a bargaining process attributed to Frederik Zeuthen and John Harsanyi that leads to the Nash bargaining solution.

Implicit in Aoki's analysis was that all equity was outside equity. Therefore, no attention was given to how alternative ownership structures of the firm affect (1) the bargaining power of the manager and (2) the distribution of the organizational rent. One could start out with an owner-managed firm and examine the distribution of the organizational rent under such an ownership structure. It would then be important to understand how the introduction of outside equity into the firm a la Jensen and Meckling, would affect, if at all, the distribution of the organizational rent.

This paper demonstrates that the introduction of outside equity into a heretofore owner-managed firm increases the bargaining power of a risk averse owner-manager. As a result, the employees' share in the organizational rent will decrease, which will in turn lead to an increase in the value of the firm.

Section II of this paper introduces a simple model of the firm that makes possible the explicit derivation of the organizational rent from the existing market conditions. In addition, section II sets the stage for the bargaining process that determines the distribution of the organizational rent between stockholders and skilled workers. This process takes the form of negotiations for the determination of a wage rate for skilled workers (and, therefore, the capitalized value of the firm).

A solution to the bargaining problem is derived in section III. Thereafter in section IV, we conclude with an examination of the introduction of outside equity, its effects on the manager's bargaining power and, through that, its effects on the equilibrium of the bargaining process and the value of the firm.

An appendix, available directly from the authors, contains an explicit derivation of the bargaining power of management and skilled workers and the more technical derivations and mathematical proofs.

II. The Model

We consider a firm that at period t faces a set of outstanding orders for its product, quantity |q.sub.t~. The orders that are filled must be filled at the unit price |p.sub.t~, announced at the end of last period. The manager must decide on what quantity q to produce (q |is less than or equal to~ |q.sub.t~) at the given price. For purposes of simplicity, we assume away the possibility of negative inventories (i.e., backlogging) or positive inventories, so that unfilled orders represent lost sales.(1)

To introduce the concept of what Aoki |1~ refers to as organizational rent, we make three assumptions.

ASSUMPTION 1. Workers, through their association with the firm for at least one period, acquire skills and knowledge that are firm-specific. These workers are referred to as skilled workers.

ASSUMPTION 2. At period t the firm can retain either all or none of the |N.sub.t-l~ skilled workers.

ASSUMPTION 3. Given |p.sub.t~ and |q.sub.t~, if skilled workers are paid the same wage rate as unskilled workers, |w.sub.0~, the firm's choice to retain all of its |N.sub.t-1~ skilled workers is both (a) feasible (i.e., with the possible addition of unskilled workers will enable the firm to fill its outstanding orders) and (b) uniquely optimal.

With the above assumptions we can now describe how the organizational rent arises. First, assume that the firm chooses to retain all of its skilled workers and those workers accept the same wage as unskilled workers, |w.sub.0~. The profits under this optimal policy (Assumption 3) are:

|Mathematical Expression Omitted~

where |C.sup.*~(|q.sub.t~;|w.sub.0~) denotes the cost function under this assumption. If the firm chooses the alternative and employs only unskilled workers, its profits will be maximized at some output |q.sub.t~(|q.sub.t~ |is less than or equal to~ |q.sub.t~) and they will be equal to

|Mathematical Expression Omitted~

where |C.sup.0~(|q.sub.t~;|w.sub.0~) denotes the cost function when only unskilled workers are employed. Then,

|Mathematical Expression Omitted~

represents the organizational rent that would result from the cooperation of the skilled workers with the firm in period t. By Assumption 3, ||pi~.sub.t~ |is greater than~ 0.

Clearly, the potential for organizational rent offers benefits to both, the owners of the firm (higher profits and consequently an increase in the firm's capitalized value) and to skilled workers (higher wage income). But this rent is only earned if management and skilled workers cooperate by agreeing on how it will be distributed. It is on this distribution problem that we turn our attention now.

Given a discount rate r, let |V.sup.0~ denote the capitalized value of the firm if only unskilled workers are used and hence no organizational rent is earned. By Assumption 1, in the absence of cooperation, skilled workers cannot use their skills outside the firm so they can earn only |w.sub.0~. Next, let us assume that in the event of cooperation, the skilled workers' share of the organizational rent will be reflected in the wage rate |w.sub.t~ that these workers agree to in return for their cooperation. That is, let |w.sub.t~ = |w.sub.0~ + |u.sub.t~, where |u.sub.t~ represents the portion of the wage rate received by skilled workers that emanates from the organizational rent.

Since there are |N.sub.t-1~ skilled workers, the total amount of the organizational rent that goes to skilled workers is |u.sub.t~|N.sub.t-1~ = (|w.sub.t~ - |w.sub.0~)|N.sub.t-1~, while the remaining amount ||pi~.sub.t~ - (|w.sub.t~ - |w.sub.0~)|N.sub.t-1~ goes to the firm. However, the capitalized value of the firm cannot fall below |V.sup.0~. Therefore, given |w.sub.0~, and a discount rate r, we can write the capitalized value of the firm V as a function of the wage rate |w.sub.t~, for |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), that is

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

Hence, the capitalized value of the firm is a linear, decreasing function of the wage rate that attains its maximum value at |w.sub.t~ = |w.sub.0~ (all rent goes to the firm) and its minimum value at |w.sub.t~ = |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~) (all rent goes to labor). Therefore the capitalized value of the firm vs. the wage rate can be represented as in Figure 1. The curve V(|w.sub.t~) in this figure can be interpreted as the bargaining possibilities frontier where skilled workers prefer points close to the |w.sub.t~-axis while stockholders prefer points close to the V-axis. Viewed from this perspective, bargaining over the distribution of the organizational rent is equivalent to bargaining over the level of the wage rate |w.sub.t~ which is tantamount to bargaining over a point on the V(|w.sub.t~) curve.

III. A Solution to the Bargaining Problem

Bargaining for the determination of a wage rate (and, therefore, the value of the firm) takes place between the manager of the firm and a "representative" skilled employee |1, 604~.

We assume that the "typical" skilled worker is guided in this process by a von Neumann-Morgenstern utility indicator |U.sub.L~ with wage rate |w.sub.t~ as its sole argument. In addition, we assume that |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~.

Likewise, the manager of the firm is guided in this process by a von Neumann-Morgenstern utility indicator |U.sub.M~ with wealth W as its sole argument, i.e., |U.sub.M~ = |U.sub.M~(W). In particular, we assume that the manager has a direct personal interest at stake from the outcome of this process because, in addition to his other financial assets, |W.sub.F~, |W.sub.F~ |is greater than or equal to~ 0, he owns a fraction |alpha~, 0 |is less than~ |alpha~ |is less than or equal to~ 1, of the firm. Given the amount of the manager's other financial wealth |W.sub.F~, the manager's total wealth W, can be written as a function of the wage rate |w.sub.t~, that is, |Mathematical Expression Omitted~. Therefore,

|U.sub.M~ = |U.sub.M~(W) = |U.sub.M~(|W.sub.F~ + |alpha~V(|w.sub.t~)). (5)

We assume that |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~.

At this juncture, there are several avenues that one can follow for solving the bargaining problem set forth. One approach would be to follow that which has been suggested by Aoki |1; 2~ who used a process suggested by Zeuthen |8~ to derive directly the bargaining power of management and labor, respectively, as functions of the wage rate |w.sub.t~. A unique solution to the bargaining problem can then be obtained by finding the wage rate ||w.sup.*~.sub.t~ that equates the bargaining power of the two parties. However, Harsanyi |4~ has shown that Zeuthen's process leads precisely to Nash's |6; 7~ bargaining solution. Therefore, from a static point of view, an alternative, but equivalent, approach would be to use Nash's method to obtain a solution to the bargaining problem. Since the latter approach is intuitively easier to follow, we use it here. The explicit derivation of the bargaining power of the two parties is provided in the Appendix.

The dependency of both the manager's and the typical skilled worker's utility functions on the variable over which bargaining takes place (i.e., the wage rate |w.sub.t~) makes our model a fixed threat bargaining model |3~, with the point (|w.sub.0~, |V.sup.0~) representing the fixed threat of the two parties. Therefore, Nash's bargaining solution to this problem can be obtained by finding the wage rate ||w.sup.*~.sub.t~ that maximizes the product of the utility gains of the two parties:

|Mathematical Expression Omitted~

Differentiating equation (6) with respect to |w.sub.t~ and setting the result equal to zero we obtain that:

|Mathematical Expression Omitted~

which is equivalent to:

|Mathematical Expression Omitted~

By assuming an interior solution over the range |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), the wage rate ||w.sup.*~.sub.t~ that solves equation (7) is the unique solution to the bargaining problem between skilled workers and management. This wage rate determines a unique point on the bargaining frontier of Figure 1 and consequently the value of the firm V||w.sup.*~.sub.t~.

It is at this point that the explicit derivation of the bargaining power of the two parties has its advantages. For example, in a particular sense, the left hand side of equation (7), as a function of |w.sub.t~, can be designated as the bargaining power of skilled workers at time t, that is, L|B.sub.t~ (|w.sub.t~). Hence:

|Mathematical Expression Omitted~

while the right hand side of equation (7), also as a function of |w.sub.t~, can be designated as the bargaining power of management at time t, that is, M|B.sub.t~(|w.sub.t~). Hence:

|Mathematical Expression Omitted~

Under our assumptions regarding strictly concave utility functions, it is clear that L|B.sub.t~ is a decreasing function of |w.sub.t~ while M|B.sub.t~ is an increasing function of |w.sub.t~. Therefore, using (8) and (9) the bargaining situation can be depicted as in the following diagram.

At wage rates smaller than ||w.sup.*~.sub.t~, such as |Mathematical Expression Omitted~ in the above diagram, the skilled workers' bargaining power exceeds that of management so skilled workers can bargain and receive higher wages. Conversely, at wage rates higher than ||w.sup.*~.sub.t~, such as |Mathematical Expression Omitted~, management's bargaining power exceeds that of skilled workers so management can ask and receive wage concessions from the skilled workers. Only at the wage rate ||w.sup.*~.sub.t~ is the bargaining power of the two parties equalized so that neither party can ask and receive wage concessions from the other. (Equivalently, as developed in the Appendix, the resolve of each party to bear the risk of conflict is equalized only at ||w.sup.*~.sub.t~)

IV. Introducing Outside Equity and the Manager's Bargaining Power

We are now in a position to describe how a sell off of a portion of the firm will affect the equilibrium position on the bargaining possibility frontier. Specifically, we will investigate how V(||w.sup.*~.sub.t~) and ||w.sup.*~.sub.t~ systematically change from a situation where the manager is 100 percent owner to a situation where the manager sells off a portion of the firm to outsiders.(2)

Without loss of generality we can assume that at the beginning of period t the owner-manager has no financial wealth, only firm-specific wealth, and further he owns 100 percent of the firm, i.e., |alpha~ = 1. Therefore, any financial wealth that enters his utility function must come from a sale of a portion |epsilon~, 0 |is less than~ |epsilon~ |is less than or equal to~ 1, of the firm. With |alpha~ representing the portion of the firm retained by the manager, |alpha~ + |epsilon~ = 1.

Now, suppose that, faced with a demand by labor for an increase of the wage rate equal to h, the owner-manager considers selling a portion |epsilon~ of his interest in the firm to outsiders, thus, converting interest in the firm to financial assets. This conversion of interest in the firm to financial assets will involve some wealth costs to the owner-manager that we assume to be a function of |epsilon~ and denote by c(|epsilon~). We further assume that c(|epsilon~) is continuous and twice differentiable for all |epsilon~ |is greater than~ 0.

It is intended that the function c(|epsilon~) captures all wealth costs that result from the transactions involved in converting interest in the firm to financial assets. In particular, we assume that (a) the owner-manager will be retained in his role as a manager under the new ownership structure of the firm at least for the current period, and (b) acting in his own best interests, his managerial tasks will include negotiating a wage rate with the skilled workers. Therefore, in addition to any other costs, such as commissions paid to third parties and income taxes on capital gains, it is intended that the cost function c(|epsilon~) captures the agency costs considered by Jensen and Meckling |5~. It will be reasonable, then, to assume that

|Mathematical Expression Omitted~

Let V represent the market value of the firm at the beginning of period t, both (a) before a wage rate for the skilled workers has been determined, and (b) exclusive of any wealth costs that are captured by the cost function |Mathematical Expression Omitted~. Then, the net receipts from the sale of a portion |epsilon~ of the firm and, therefore, the manager's financial wealth at period t will be

|W.sub.F~(|epsilon~) = |epsilon~V - c(|epsilon~). (11)

An implication of equation (11) is that for 0 |is less than~ |epsilon~ |is less than or equal to~ 1, the manager's wealth can be represented as

|Mathematical Expression Omitted~

for any wage rate |w.sub.t~, |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), that skilled workers and management can agree upon. If negotiations break down, the value of the firm will be |V.sup.0~, and the manager's wealth in this case will be:

|Mathematical Expression Omitted~

Using equations (12) and (13), we can rewrite the manager's bargaining power in (9) as a function of |epsilon~, for any |w.sub.t~, that is,

|Mathematical Expression Omitted~

Case i--Zero Selloff Costs

As a preliminary to the general case, and in order to get an intuitive understanding of the process, let us suppose for a moment that there are no costs involved in selling a portion of the firm by the manager. In particular, let us suppose that V = V(|w.sub.t~). Then, from equation (12), W = V(|w.sub.t~), for any |epsilon~, and from equation (13), |w.sub.0~ = |alpha~|V.sup.0~ + |epsilon~V(|w.sub.t~). Substituting into (14) we obtain

|Mathematical Expression Omitted~

On the other hand, for |alpha~ = 1, i.e., for |epsilon~ = 0,

|Mathematical Expression Omitted~

In comparing the two, the case where |alpha~ |is less than~ 1, with the case where |alpha~ = 1, it is easily seen (and demonstrated in the Appendix) that concavity of the utility function implies that

|Mathematical Expression Omitted~

which means that the manager's bargaining power always increases as he substitutes ownership interest in the firm with financial wealth.

With V = V(|w.sub.t~), and c(|epsilon~) = 0, for all |epsilon~, the manager would have nothing to lose by selling a portion of the firm. In fact, he could always guarantee himself a wealth level equal to V with certainty if he were to sell the entire firm. Therefore, with free "insurance" in the event that negotiations break down, together with the assumption that he is retained to negotiate the wage rate in his own best interest, the manager would have nothing to lose by rejecting any demand for an increase in the wage rate. In particular, under the current assumptions of this preliminary case, the manager could impose any wage rate, however low, as long as it exceeds the market wage rate |w.sub.0~, so that skilled workers would prefer employment with the firm.

Case ii--Positive Selloff Costs

Let us proceed now to examine the more realistic case where there are costs involved in selling off a portion of the firm as we have assumed in equation (10), c(|epsilon~) |is greater than~ 0.

Note that, W(|w.sub.t~;|epsilon~) - |W.sup.0~(|epsilon~) = |alpha~(V(|w.sub.t~) - |V.sup.0~). Therefore, multiplying both the numerator and the denominator of the right hand side of (14) by (V(|w.sub.t~) - |V.sup.0~), setting |Mathematical Expression Omitted~, |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~, we can rewrite equation (14) as

M|B.sub.t~(|epsilon~) = Ab(|epsilon~)/B(|epsilon~) (15)

for any given wage rate |w.sub.t~ in the relevant range, which we can take to be some wage rate |w.sub.t~ that serves as the basis for negotiations between management and skilled workers.

In equation (15), the value of A is determined by the given wage rate |w.sub.t~, as above, so it is independent of |epsilon~. On the other hand, in Figure 3, a graph of the manager's utility function, b(|epsilon~) represents the slope of |U.sub.M~ at the wealth level W(|w.sub.t~;|epsilon~), and B(|epsilon~) represents the slope of the straight line joining the two points on the graph corresponding to |U.sub.M~(|W.sup.0~(|epsilon~)) and |U.sub.M~(W(|w.sub.t~;|epsilon~)), respectively. The slopes b and B represent the manager's feelings concerning changes in wealth.

Specifically, b measures the manager's evaluation of small changes in wealth at W(|w.sub.t~;|epsilon~), such as changing |w.sub.t~ by some small amount h, while B measures the manager's evaluation of large changes in wealth over the range W to |W.sup.0~ (i.e., what may happen if negotiations break down). Therefore, given any wage rate |w.sub.t~, as demonstrated above, the manager's bargaining power is proportional |by a factor |Mathematical Expression Omitted~~ to the ratio of the slopes, b(|epsilon~)/B(|epsilon~).

For a strictly concave utility function, b(|epsilon~) |is less than~ B(|epsilon~), for any |epsilon~ such that W(|w.sub.t~;|epsilon~) |is greater than~ |W.sup.0~(|epsilon~). In particular, if for |epsilon~ = 0, we write V(|w.sub.t~) = W(|w.sub.t~; 0), and |V.sup.0~ = |W.sup.0~(0), then W(|w.sub.t~; 0) |is greater than~ |W.sup.0~(0), so, if the manager does not sell any portion of the firm, his bargaining power is A(b(O)/B(0)) |is less than~ A. On the other hand, as |epsilon~ tends to 1, both W(|w.sub.t~;|epsilon~) and |W.sup.0~(|epsilon~) tend to the same certain wealth of (V - c(1)), which implies that b(|epsilon~) tends to |Mathematical Expression Omitted~, and B(|epsilon~) tends to |Mathematical Expression Omitted~ (derived in the Appendix). Therefore, as the manager comes closer and closer to selling the entire firm, i.e., as |epsilon~ tends to 1, b(|epsilon~)/B(|epsilon~) tends to 1, and M|B.sub.t~(|epsilon~) tends to A.

Intuitively, this is of course what we would expect. As the owner-manager tends to be a pure manager, his bargaining power will be greater than in the case where he retains ownership of the entire firm. The question is whether we can obtain a similar result for intermediate cases when the owner retains interest in the firm.

Observe that, for |epsilon~ |is greater than~ 0, the wealth functions in (12) and (13) are differentiable. Therefore, for |epsilon~ |is greater than~ 0 we can define the functions |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ as follows:

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

PROPOSITION 1. Assume that either |Mathematical Expression Omitted~, or |Mathematical Expression Omitted~, for all |epsilon~ |is greater than~ 0. Then, M|B.sub.t~(|epsilon~) is an increasing function of |epsilon~, |epsilon~ |is greater than~ 0.

The results of Proposition 1 (proof provided in Appendix) in conjunction with the previous results that M|B.sub.t~(0) |is less than~ A and M|B.sub.t~(|epsilon~) tends to A as |epsilon~ tends to 1, are sufficient to establish Proposition 2.

PROPOSITION 2. Assume that either |Mathematical Expression Omitted~, or |Mathematical Expression Omitted~, for all |epsilon~ |is greater than~ 0. Then, there exists an |epsilon~, 0 |is less than or equal to~ |epsilon~ |is less than~ 1, such that M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0), for all |epsilon~ |is greater than~ |epsilon~.

This establishes that a sufficiently large sell-off by the manager will increase his bargaining power. Sufficient conditions for this result are that: (a) the sell-off increases wealth in the event of a breakdown in negotiations and reduces or leaves wealth unchanged when negotiations are successful; and (b) the gain in wealth under a breakdown in negotiations exceeds the loss in wealth when negotiations are successful.

This condition may be interpreted (as in the preliminary case where costs were assumed to be zero) as a form of insurance in the event that negotiations break down. The "cost of insurance" in the present case would be |Mathematical Expression Omitted~, the reduction in wealth of the manager under the "best-case" outcome when labor concedes. The protection he receives, in the event that negotiations break down is |Mathematical Expression Omitted~. Hence, our results here are similar to those when we assumed no costs. The bargaining power of the manager increases as long as the protection he receives in the event of a strike exceeds the cost of his "insurance."

Unless |epsilon~ = 0 in Proposition 2, a sell-off of a small portion of the firm, |epsilon~ |is less than~ |epsilon~ may lower the manager's bargaining power. The reason is the presence of lump-sum costs. Suppose for a moment that lump-sum costs of c are incurred when the manager sells part of his equity. Then from (11), as |epsilon~ approaches 0, the proceeds from the sale approach 0 while costs approach c. Hence, regardless of the outcome of negotiations, the manager's wealth is less than it would have been under no sale of equity. As a consequence, even though by Proposition 1, the manager's bargaining power is an increasing function of |epsilon~, for |epsilon~ |is greater than~ 0, there may be a range of |epsilon~ such that M|B.sub.t~(|epsilon~) stays below M|B.sub.t~(0). This occurs because the manager's wealth is now lower due to the lump-sum cost c.(5) Clearly since lump sum costs lower the manager's bargaining power only when a sell-off makes the manager unambiguously worst off, it is safe to assume that such an outcome would be unlikely.

In the absence of lump-sum costs M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0). More formally the following proposition is valid.

PROPOSITION 3. Assume that (a) there are no lump-sum costs and (b) either |Mathematical Expression Omitted~ or |Mathematical Expression Omitted~. Then M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0), for all |epsilon~ |is greater than~ 0.

In conjunction with Proposition 1, Proposition 3 implies that the manager's bargaining power increases as he sells a larger share of the firm and is always larger than when he retains full ownership.

We now turn our attention to the effects of a sell-off on the value of the firm. The propositions above establish that under general conditions a sell-off of the firm will, for any given wage rate, increase the manager's bargaining power. This means that a sell-off will shift the M|B.sub.t~ curve (initially presented in Figure 2) towards the northwest as depicted in Figure 4.

Recall from section III, that the equilibrium wage is established at the wage which equalizes the manager's and labor's bargaining power. Hence the sell-off which shifts the M|B.sub.t~ curve northwest to |Mathematical Expression Omitted~, results in a lowered equilibrium wage of |Mathematical Expression Omitted~. Stockholders now capture a larger portion of the organizational rent, and as a result the value of the firm increases.

V. Conclusions

In this paper we demonstrated that the introduction of outside equity in an owner-managed firm can increase its value. Outside equity provides the owner insurance that lessens the financial impact of a breakdown in labor negotiations on his wealth. With this insurance, the owner can tolerate a higher risk of a strike and therefore pushes labor for a more favorable wage settlement. As a result, the firm garners a larger share of the organization rent, and increases in value. We have shown that the conditions under which the owner will introduce outside equity are similar to the conditions under which a firm would purchase insurance. The firm must be risk adverse, the sell-off increases wealth in the event of the "worst case" outcome, a strike, but reduces wealth in the "best case" outcome, labor accepts management's wage offer. Lump sum costs and increasing marginal transaction costs make it more likely that the owner will sell a substantial part but not his whole interest in the firm.

Our assumptions preclude the possibility that the new stockholders are the current employees of the firm. An interesting extension would be to examine how the results reported here are altered if labor purchases a portion of the firm.

1. In a bargaining model the possibility of positive or negative inventories may alter the bargaining power of management and labor. This possibility is not considered here.

2. The conclusions of this section will not be altered if the manager initially owned less than 100 percent of the firm.

5. Mathematically the function M|B.sub.t~(|epsilon~) is not differentiable at |epsilon~ = 0 if c |is greater than~ 0.

References

1. Aoki, Masahiko, "A Model of the Firm as a Stockholder-Employee Cooperative Game." American Economic Review, September 1980, 600-610.

2. -----. The Co-Operative Game Theory of the Firm. New York: Oxford University Press, 1984, pp. 61-91.

3. Friedman, James W. Game Theory with Applications to Economics. New York: Oxford University Press, 1986, pp. 152-159.

4. Harsanyi, John C., "Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hicks', and Nash's Theories." Econometrica, April 1956, 144-57.

5. Jensen, Michael C. and William H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure." Journal of Financial Economics, October 1976, 305-60.

6. Nash, John F., "The Bargaining Problem." Econometrica, April 1950, 155-62.

7. -----, "Two-Person Cooperative Games." Econometrica, January 1953. 128-40.

8. Zeuthen, Frederik. Problems of Monopoly and Economic Warfare. London: Routledge & Kegan Paul, 1930.

In their seminal article, Michael Jensen and William Meckling developed a theory of the corporate ownership structure that took into account "the trade-offs available to the entrepreneur-manager between inside and outside equity and debt" |5, 312~. Jensen and Meckling concentrated on the principal-agent problem and the agency costs that arise from the introduction of outside equity into the firm. This was done without any consideration of what effects such an action might have had on the bargaining power of the owner-manager in negotiating wages with the current employees of the firm.

Several years later Masahiko Aoki |1; 2, 61-91~ introduced a model of the firm that emphasized "its aspect as a quasi-permanent organization of stockholders and employees" |1, 600~. He asserted that as a result of their association with the firm, the employees acquire skills and knowledge that, when combined with the physical assets supplied by the stockholders, can produce some economic gains--the so-called organizational rent. Such rents would not be possible through the employment of external factors of production (such as workers that have no knowledge of the workings of the firm). The organizational rent can be produced only through the cooperation of the stockholders (supplying the physical assets) and the existing employees. As such, the situation is tantamount to a two-person cooperative game, and the question becomes, how then is the organizational rent to be distributed between stockholders and employees. Aoki proposed that the solution to this particular distribution problem could be accomplished by use of a bargaining process attributed to Frederik Zeuthen and John Harsanyi that leads to the Nash bargaining solution.

Implicit in Aoki's analysis was that all equity was outside equity. Therefore, no attention was given to how alternative ownership structures of the firm affect (1) the bargaining power of the manager and (2) the distribution of the organizational rent. One could start out with an owner-managed firm and examine the distribution of the organizational rent under such an ownership structure. It would then be important to understand how the introduction of outside equity into the firm a la Jensen and Meckling, would affect, if at all, the distribution of the organizational rent.

This paper demonstrates that the introduction of outside equity into a heretofore owner-managed firm increases the bargaining power of a risk averse owner-manager. As a result, the employees' share in the organizational rent will decrease, which will in turn lead to an increase in the value of the firm.

Section II of this paper introduces a simple model of the firm that makes possible the explicit derivation of the organizational rent from the existing market conditions. In addition, section II sets the stage for the bargaining process that determines the distribution of the organizational rent between stockholders and skilled workers. This process takes the form of negotiations for the determination of a wage rate for skilled workers (and, therefore, the capitalized value of the firm).

A solution to the bargaining problem is derived in section III. Thereafter in section IV, we conclude with an examination of the introduction of outside equity, its effects on the manager's bargaining power and, through that, its effects on the equilibrium of the bargaining process and the value of the firm.

An appendix, available directly from the authors, contains an explicit derivation of the bargaining power of management and skilled workers and the more technical derivations and mathematical proofs.

II. The Model

We consider a firm that at period t faces a set of outstanding orders for its product, quantity |q.sub.t~. The orders that are filled must be filled at the unit price |p.sub.t~, announced at the end of last period. The manager must decide on what quantity q to produce (q |is less than or equal to~ |q.sub.t~) at the given price. For purposes of simplicity, we assume away the possibility of negative inventories (i.e., backlogging) or positive inventories, so that unfilled orders represent lost sales.(1)

To introduce the concept of what Aoki |1~ refers to as organizational rent, we make three assumptions.

ASSUMPTION 1. Workers, through their association with the firm for at least one period, acquire skills and knowledge that are firm-specific. These workers are referred to as skilled workers.

ASSUMPTION 2. At period t the firm can retain either all or none of the |N.sub.t-l~ skilled workers.

ASSUMPTION 3. Given |p.sub.t~ and |q.sub.t~, if skilled workers are paid the same wage rate as unskilled workers, |w.sub.0~, the firm's choice to retain all of its |N.sub.t-1~ skilled workers is both (a) feasible (i.e., with the possible addition of unskilled workers will enable the firm to fill its outstanding orders) and (b) uniquely optimal.

With the above assumptions we can now describe how the organizational rent arises. First, assume that the firm chooses to retain all of its skilled workers and those workers accept the same wage as unskilled workers, |w.sub.0~. The profits under this optimal policy (Assumption 3) are:

|Mathematical Expression Omitted~

where |C.sup.*~(|q.sub.t~;|w.sub.0~) denotes the cost function under this assumption. If the firm chooses the alternative and employs only unskilled workers, its profits will be maximized at some output |q.sub.t~(|q.sub.t~ |is less than or equal to~ |q.sub.t~) and they will be equal to

|Mathematical Expression Omitted~

where |C.sup.0~(|q.sub.t~;|w.sub.0~) denotes the cost function when only unskilled workers are employed. Then,

|Mathematical Expression Omitted~

represents the organizational rent that would result from the cooperation of the skilled workers with the firm in period t. By Assumption 3, ||pi~.sub.t~ |is greater than~ 0.

Clearly, the potential for organizational rent offers benefits to both, the owners of the firm (higher profits and consequently an increase in the firm's capitalized value) and to skilled workers (higher wage income). But this rent is only earned if management and skilled workers cooperate by agreeing on how it will be distributed. It is on this distribution problem that we turn our attention now.

Given a discount rate r, let |V.sup.0~ denote the capitalized value of the firm if only unskilled workers are used and hence no organizational rent is earned. By Assumption 1, in the absence of cooperation, skilled workers cannot use their skills outside the firm so they can earn only |w.sub.0~. Next, let us assume that in the event of cooperation, the skilled workers' share of the organizational rent will be reflected in the wage rate |w.sub.t~ that these workers agree to in return for their cooperation. That is, let |w.sub.t~ = |w.sub.0~ + |u.sub.t~, where |u.sub.t~ represents the portion of the wage rate received by skilled workers that emanates from the organizational rent.

Since there are |N.sub.t-1~ skilled workers, the total amount of the organizational rent that goes to skilled workers is |u.sub.t~|N.sub.t-1~ = (|w.sub.t~ - |w.sub.0~)|N.sub.t-1~, while the remaining amount ||pi~.sub.t~ - (|w.sub.t~ - |w.sub.0~)|N.sub.t-1~ goes to the firm. However, the capitalized value of the firm cannot fall below |V.sup.0~. Therefore, given |w.sub.0~, and a discount rate r, we can write the capitalized value of the firm V as a function of the wage rate |w.sub.t~, for |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), that is

|Mathematical Expression Omitted~

|Mathematical Expression Omitted~

Hence, the capitalized value of the firm is a linear, decreasing function of the wage rate that attains its maximum value at |w.sub.t~ = |w.sub.0~ (all rent goes to the firm) and its minimum value at |w.sub.t~ = |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~) (all rent goes to labor). Therefore the capitalized value of the firm vs. the wage rate can be represented as in Figure 1. The curve V(|w.sub.t~) in this figure can be interpreted as the bargaining possibilities frontier where skilled workers prefer points close to the |w.sub.t~-axis while stockholders prefer points close to the V-axis. Viewed from this perspective, bargaining over the distribution of the organizational rent is equivalent to bargaining over the level of the wage rate |w.sub.t~ which is tantamount to bargaining over a point on the V(|w.sub.t~) curve.

III. A Solution to the Bargaining Problem

Bargaining for the determination of a wage rate (and, therefore, the value of the firm) takes place between the manager of the firm and a "representative" skilled employee |1, 604~.

We assume that the "typical" skilled worker is guided in this process by a von Neumann-Morgenstern utility indicator |U.sub.L~ with wage rate |w.sub.t~ as its sole argument. In addition, we assume that |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~.

Likewise, the manager of the firm is guided in this process by a von Neumann-Morgenstern utility indicator |U.sub.M~ with wealth W as its sole argument, i.e., |U.sub.M~ = |U.sub.M~(W). In particular, we assume that the manager has a direct personal interest at stake from the outcome of this process because, in addition to his other financial assets, |W.sub.F~, |W.sub.F~ |is greater than or equal to~ 0, he owns a fraction |alpha~, 0 |is less than~ |alpha~ |is less than or equal to~ 1, of the firm. Given the amount of the manager's other financial wealth |W.sub.F~, the manager's total wealth W, can be written as a function of the wage rate |w.sub.t~, that is, |Mathematical Expression Omitted~. Therefore,

|U.sub.M~ = |U.sub.M~(W) = |U.sub.M~(|W.sub.F~ + |alpha~V(|w.sub.t~)). (5)

We assume that |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~.

At this juncture, there are several avenues that one can follow for solving the bargaining problem set forth. One approach would be to follow that which has been suggested by Aoki |1; 2~ who used a process suggested by Zeuthen |8~ to derive directly the bargaining power of management and labor, respectively, as functions of the wage rate |w.sub.t~. A unique solution to the bargaining problem can then be obtained by finding the wage rate ||w.sup.*~.sub.t~ that equates the bargaining power of the two parties. However, Harsanyi |4~ has shown that Zeuthen's process leads precisely to Nash's |6; 7~ bargaining solution. Therefore, from a static point of view, an alternative, but equivalent, approach would be to use Nash's method to obtain a solution to the bargaining problem. Since the latter approach is intuitively easier to follow, we use it here. The explicit derivation of the bargaining power of the two parties is provided in the Appendix.

The dependency of both the manager's and the typical skilled worker's utility functions on the variable over which bargaining takes place (i.e., the wage rate |w.sub.t~) makes our model a fixed threat bargaining model |3~, with the point (|w.sub.0~, |V.sup.0~) representing the fixed threat of the two parties. Therefore, Nash's bargaining solution to this problem can be obtained by finding the wage rate ||w.sup.*~.sub.t~ that maximizes the product of the utility gains of the two parties:

|Mathematical Expression Omitted~

Differentiating equation (6) with respect to |w.sub.t~ and setting the result equal to zero we obtain that:

|Mathematical Expression Omitted~

which is equivalent to:

|Mathematical Expression Omitted~

By assuming an interior solution over the range |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), the wage rate ||w.sup.*~.sub.t~ that solves equation (7) is the unique solution to the bargaining problem between skilled workers and management. This wage rate determines a unique point on the bargaining frontier of Figure 1 and consequently the value of the firm V||w.sup.*~.sub.t~.

It is at this point that the explicit derivation of the bargaining power of the two parties has its advantages. For example, in a particular sense, the left hand side of equation (7), as a function of |w.sub.t~, can be designated as the bargaining power of skilled workers at time t, that is, L|B.sub.t~ (|w.sub.t~). Hence:

|Mathematical Expression Omitted~

while the right hand side of equation (7), also as a function of |w.sub.t~, can be designated as the bargaining power of management at time t, that is, M|B.sub.t~(|w.sub.t~). Hence:

|Mathematical Expression Omitted~

Under our assumptions regarding strictly concave utility functions, it is clear that L|B.sub.t~ is a decreasing function of |w.sub.t~ while M|B.sub.t~ is an increasing function of |w.sub.t~. Therefore, using (8) and (9) the bargaining situation can be depicted as in the following diagram.

At wage rates smaller than ||w.sup.*~.sub.t~, such as |Mathematical Expression Omitted~ in the above diagram, the skilled workers' bargaining power exceeds that of management so skilled workers can bargain and receive higher wages. Conversely, at wage rates higher than ||w.sup.*~.sub.t~, such as |Mathematical Expression Omitted~, management's bargaining power exceeds that of skilled workers so management can ask and receive wage concessions from the skilled workers. Only at the wage rate ||w.sup.*~.sub.t~ is the bargaining power of the two parties equalized so that neither party can ask and receive wage concessions from the other. (Equivalently, as developed in the Appendix, the resolve of each party to bear the risk of conflict is equalized only at ||w.sup.*~.sub.t~)

IV. Introducing Outside Equity and the Manager's Bargaining Power

We are now in a position to describe how a sell off of a portion of the firm will affect the equilibrium position on the bargaining possibility frontier. Specifically, we will investigate how V(||w.sup.*~.sub.t~) and ||w.sup.*~.sub.t~ systematically change from a situation where the manager is 100 percent owner to a situation where the manager sells off a portion of the firm to outsiders.(2)

Without loss of generality we can assume that at the beginning of period t the owner-manager has no financial wealth, only firm-specific wealth, and further he owns 100 percent of the firm, i.e., |alpha~ = 1. Therefore, any financial wealth that enters his utility function must come from a sale of a portion |epsilon~, 0 |is less than~ |epsilon~ |is less than or equal to~ 1, of the firm. With |alpha~ representing the portion of the firm retained by the manager, |alpha~ + |epsilon~ = 1.

Now, suppose that, faced with a demand by labor for an increase of the wage rate equal to h, the owner-manager considers selling a portion |epsilon~ of his interest in the firm to outsiders, thus, converting interest in the firm to financial assets. This conversion of interest in the firm to financial assets will involve some wealth costs to the owner-manager that we assume to be a function of |epsilon~ and denote by c(|epsilon~). We further assume that c(|epsilon~) is continuous and twice differentiable for all |epsilon~ |is greater than~ 0.

It is intended that the function c(|epsilon~) captures all wealth costs that result from the transactions involved in converting interest in the firm to financial assets. In particular, we assume that (a) the owner-manager will be retained in his role as a manager under the new ownership structure of the firm at least for the current period, and (b) acting in his own best interests, his managerial tasks will include negotiating a wage rate with the skilled workers. Therefore, in addition to any other costs, such as commissions paid to third parties and income taxes on capital gains, it is intended that the cost function c(|epsilon~) captures the agency costs considered by Jensen and Meckling |5~. It will be reasonable, then, to assume that

|Mathematical Expression Omitted~

Let V represent the market value of the firm at the beginning of period t, both (a) before a wage rate for the skilled workers has been determined, and (b) exclusive of any wealth costs that are captured by the cost function |Mathematical Expression Omitted~. Then, the net receipts from the sale of a portion |epsilon~ of the firm and, therefore, the manager's financial wealth at period t will be

|W.sub.F~(|epsilon~) = |epsilon~V - c(|epsilon~). (11)

An implication of equation (11) is that for 0 |is less than~ |epsilon~ |is less than or equal to~ 1, the manager's wealth can be represented as

|Mathematical Expression Omitted~

for any wage rate |w.sub.t~, |w.sub.0~ |is less than or equal to~ |w.sub.t~ |is less than or equal to~ |w.sub.0~ + (||pi~.sub.t~/|N.sub.t-1~), that skilled workers and management can agree upon. If negotiations break down, the value of the firm will be |V.sup.0~, and the manager's wealth in this case will be:

|Mathematical Expression Omitted~

Using equations (12) and (13), we can rewrite the manager's bargaining power in (9) as a function of |epsilon~, for any |w.sub.t~, that is,

|Mathematical Expression Omitted~

Case i--Zero Selloff Costs

As a preliminary to the general case, and in order to get an intuitive understanding of the process, let us suppose for a moment that there are no costs involved in selling a portion of the firm by the manager. In particular, let us suppose that V = V(|w.sub.t~). Then, from equation (12), W = V(|w.sub.t~), for any |epsilon~, and from equation (13), |w.sub.0~ = |alpha~|V.sup.0~ + |epsilon~V(|w.sub.t~). Substituting into (14) we obtain

|Mathematical Expression Omitted~

On the other hand, for |alpha~ = 1, i.e., for |epsilon~ = 0,

|Mathematical Expression Omitted~

In comparing the two, the case where |alpha~ |is less than~ 1, with the case where |alpha~ = 1, it is easily seen (and demonstrated in the Appendix) that concavity of the utility function implies that

|Mathematical Expression Omitted~

which means that the manager's bargaining power always increases as he substitutes ownership interest in the firm with financial wealth.

With V = V(|w.sub.t~), and c(|epsilon~) = 0, for all |epsilon~, the manager would have nothing to lose by selling a portion of the firm. In fact, he could always guarantee himself a wealth level equal to V with certainty if he were to sell the entire firm. Therefore, with free "insurance" in the event that negotiations break down, together with the assumption that he is retained to negotiate the wage rate in his own best interest, the manager would have nothing to lose by rejecting any demand for an increase in the wage rate. In particular, under the current assumptions of this preliminary case, the manager could impose any wage rate, however low, as long as it exceeds the market wage rate |w.sub.0~, so that skilled workers would prefer employment with the firm.

Case ii--Positive Selloff Costs

Let us proceed now to examine the more realistic case where there are costs involved in selling off a portion of the firm as we have assumed in equation (10), c(|epsilon~) |is greater than~ 0.

Note that, W(|w.sub.t~;|epsilon~) - |W.sup.0~(|epsilon~) = |alpha~(V(|w.sub.t~) - |V.sup.0~). Therefore, multiplying both the numerator and the denominator of the right hand side of (14) by (V(|w.sub.t~) - |V.sup.0~), setting |Mathematical Expression Omitted~, |Mathematical Expression Omitted~, and |Mathematical Expression Omitted~, we can rewrite equation (14) as

M|B.sub.t~(|epsilon~) = Ab(|epsilon~)/B(|epsilon~) (15)

for any given wage rate |w.sub.t~ in the relevant range, which we can take to be some wage rate |w.sub.t~ that serves as the basis for negotiations between management and skilled workers.

In equation (15), the value of A is determined by the given wage rate |w.sub.t~, as above, so it is independent of |epsilon~. On the other hand, in Figure 3, a graph of the manager's utility function, b(|epsilon~) represents the slope of |U.sub.M~ at the wealth level W(|w.sub.t~;|epsilon~), and B(|epsilon~) represents the slope of the straight line joining the two points on the graph corresponding to |U.sub.M~(|W.sup.0~(|epsilon~)) and |U.sub.M~(W(|w.sub.t~;|epsilon~)), respectively. The slopes b and B represent the manager's feelings concerning changes in wealth.

Specifically, b measures the manager's evaluation of small changes in wealth at W(|w.sub.t~;|epsilon~), such as changing |w.sub.t~ by some small amount h, while B measures the manager's evaluation of large changes in wealth over the range W to |W.sup.0~ (i.e., what may happen if negotiations break down). Therefore, given any wage rate |w.sub.t~, as demonstrated above, the manager's bargaining power is proportional |by a factor |Mathematical Expression Omitted~~ to the ratio of the slopes, b(|epsilon~)/B(|epsilon~).

For a strictly concave utility function, b(|epsilon~) |is less than~ B(|epsilon~), for any |epsilon~ such that W(|w.sub.t~;|epsilon~) |is greater than~ |W.sup.0~(|epsilon~). In particular, if for |epsilon~ = 0, we write V(|w.sub.t~) = W(|w.sub.t~; 0), and |V.sup.0~ = |W.sup.0~(0), then W(|w.sub.t~; 0) |is greater than~ |W.sup.0~(0), so, if the manager does not sell any portion of the firm, his bargaining power is A(b(O)/B(0)) |is less than~ A. On the other hand, as |epsilon~ tends to 1, both W(|w.sub.t~;|epsilon~) and |W.sup.0~(|epsilon~) tend to the same certain wealth of (V - c(1)), which implies that b(|epsilon~) tends to |Mathematical Expression Omitted~, and B(|epsilon~) tends to |Mathematical Expression Omitted~ (derived in the Appendix). Therefore, as the manager comes closer and closer to selling the entire firm, i.e., as |epsilon~ tends to 1, b(|epsilon~)/B(|epsilon~) tends to 1, and M|B.sub.t~(|epsilon~) tends to A.

Intuitively, this is of course what we would expect. As the owner-manager tends to be a pure manager, his bargaining power will be greater than in the case where he retains ownership of the entire firm. The question is whether we can obtain a similar result for intermediate cases when the owner retains interest in the firm.

Observe that, for |epsilon~ |is greater than~ 0, the wealth functions in (12) and (13) are differentiable. Therefore, for |epsilon~ |is greater than~ 0 we can define the functions |Mathematical Expression Omitted~ and |Mathematical Expression Omitted~ as follows:

|Mathematical Expression Omitted~

and

|Mathematical Expression Omitted~

PROPOSITION 1. Assume that either |Mathematical Expression Omitted~, or |Mathematical Expression Omitted~, for all |epsilon~ |is greater than~ 0. Then, M|B.sub.t~(|epsilon~) is an increasing function of |epsilon~, |epsilon~ |is greater than~ 0.

The results of Proposition 1 (proof provided in Appendix) in conjunction with the previous results that M|B.sub.t~(0) |is less than~ A and M|B.sub.t~(|epsilon~) tends to A as |epsilon~ tends to 1, are sufficient to establish Proposition 2.

PROPOSITION 2. Assume that either |Mathematical Expression Omitted~, or |Mathematical Expression Omitted~, for all |epsilon~ |is greater than~ 0. Then, there exists an |epsilon~, 0 |is less than or equal to~ |epsilon~ |is less than~ 1, such that M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0), for all |epsilon~ |is greater than~ |epsilon~.

This establishes that a sufficiently large sell-off by the manager will increase his bargaining power. Sufficient conditions for this result are that: (a) the sell-off increases wealth in the event of a breakdown in negotiations and reduces or leaves wealth unchanged when negotiations are successful; and (b) the gain in wealth under a breakdown in negotiations exceeds the loss in wealth when negotiations are successful.

This condition may be interpreted (as in the preliminary case where costs were assumed to be zero) as a form of insurance in the event that negotiations break down. The "cost of insurance" in the present case would be |Mathematical Expression Omitted~, the reduction in wealth of the manager under the "best-case" outcome when labor concedes. The protection he receives, in the event that negotiations break down is |Mathematical Expression Omitted~. Hence, our results here are similar to those when we assumed no costs. The bargaining power of the manager increases as long as the protection he receives in the event of a strike exceeds the cost of his "insurance."

Unless |epsilon~ = 0 in Proposition 2, a sell-off of a small portion of the firm, |epsilon~ |is less than~ |epsilon~ may lower the manager's bargaining power. The reason is the presence of lump-sum costs. Suppose for a moment that lump-sum costs of c are incurred when the manager sells part of his equity. Then from (11), as |epsilon~ approaches 0, the proceeds from the sale approach 0 while costs approach c. Hence, regardless of the outcome of negotiations, the manager's wealth is less than it would have been under no sale of equity. As a consequence, even though by Proposition 1, the manager's bargaining power is an increasing function of |epsilon~, for |epsilon~ |is greater than~ 0, there may be a range of |epsilon~ such that M|B.sub.t~(|epsilon~) stays below M|B.sub.t~(0). This occurs because the manager's wealth is now lower due to the lump-sum cost c.(5) Clearly since lump sum costs lower the manager's bargaining power only when a sell-off makes the manager unambiguously worst off, it is safe to assume that such an outcome would be unlikely.

In the absence of lump-sum costs M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0). More formally the following proposition is valid.

PROPOSITION 3. Assume that (a) there are no lump-sum costs and (b) either |Mathematical Expression Omitted~ or |Mathematical Expression Omitted~. Then M|B.sub.t~(|epsilon~) |is greater than~ M|B.sub.t~(0), for all |epsilon~ |is greater than~ 0.

In conjunction with Proposition 1, Proposition 3 implies that the manager's bargaining power increases as he sells a larger share of the firm and is always larger than when he retains full ownership.

We now turn our attention to the effects of a sell-off on the value of the firm. The propositions above establish that under general conditions a sell-off of the firm will, for any given wage rate, increase the manager's bargaining power. This means that a sell-off will shift the M|B.sub.t~ curve (initially presented in Figure 2) towards the northwest as depicted in Figure 4.

Recall from section III, that the equilibrium wage is established at the wage which equalizes the manager's and labor's bargaining power. Hence the sell-off which shifts the M|B.sub.t~ curve northwest to |Mathematical Expression Omitted~, results in a lowered equilibrium wage of |Mathematical Expression Omitted~. Stockholders now capture a larger portion of the organizational rent, and as a result the value of the firm increases.

V. Conclusions

In this paper we demonstrated that the introduction of outside equity in an owner-managed firm can increase its value. Outside equity provides the owner insurance that lessens the financial impact of a breakdown in labor negotiations on his wealth. With this insurance, the owner can tolerate a higher risk of a strike and therefore pushes labor for a more favorable wage settlement. As a result, the firm garners a larger share of the organization rent, and increases in value. We have shown that the conditions under which the owner will introduce outside equity are similar to the conditions under which a firm would purchase insurance. The firm must be risk adverse, the sell-off increases wealth in the event of the "worst case" outcome, a strike, but reduces wealth in the "best case" outcome, labor accepts management's wage offer. Lump sum costs and increasing marginal transaction costs make it more likely that the owner will sell a substantial part but not his whole interest in the firm.

Our assumptions preclude the possibility that the new stockholders are the current employees of the firm. An interesting extension would be to examine how the results reported here are altered if labor purchases a portion of the firm.

1. In a bargaining model the possibility of positive or negative inventories may alter the bargaining power of management and labor. This possibility is not considered here.

2. The conclusions of this section will not be altered if the manager initially owned less than 100 percent of the firm.

5. Mathematically the function M|B.sub.t~(|epsilon~) is not differentiable at |epsilon~ = 0 if c |is greater than~ 0.

References

1. Aoki, Masahiko, "A Model of the Firm as a Stockholder-Employee Cooperative Game." American Economic Review, September 1980, 600-610.

2. -----. The Co-Operative Game Theory of the Firm. New York: Oxford University Press, 1984, pp. 61-91.

3. Friedman, James W. Game Theory with Applications to Economics. New York: Oxford University Press, 1986, pp. 152-159.

4. Harsanyi, John C., "Approaches to the Bargaining Problem Before and After the Theory of Games: A Critical Discussion of Zeuthen's, Hicks', and Nash's Theories." Econometrica, April 1956, 144-57.

5. Jensen, Michael C. and William H. Meckling, "Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure." Journal of Financial Economics, October 1976, 305-60.

6. Nash, John F., "The Bargaining Problem." Econometrica, April 1950, 155-62.

7. -----, "Two-Person Cooperative Games." Econometrica, January 1953. 128-40.

8. Zeuthen, Frederik. Problems of Monopoly and Economic Warfare. London: Routledge & Kegan Paul, 1930.

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Author: | Whitney, Gerald |
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Publication: | Southern Economic Journal |

Date: | Oct 1, 1992 |

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