Bargaining, Profit-Sharing and Irreversible Investment Decisions In An Oligopoly Jyh-bang Jou National Taiwan University Tan Lee Yuan Ze University

2 Abstract This article considers a firm in an oligopoly as a quasi-permanent organization of shareholders and employees. The firm undertakes incremental investment and the investment expenditures are fully sunk. The firm’s employees receive a fixed wage rate as well as share a portion of the firm’s profits. The profit-sharing rate is determined by the firm’s manager, who finds a cooperative game solution through mediating between the shareholders and employees. The firm’s manager will grant a lower profit-sharing rate to the employees and will install a smaller capacity when facing more competitors. However, the choice of capacity for the industry as a whole will increase as competition becomes more intense.

3 I. Literature Review Weitzman (1983,1985): Argue that profit- sharing schemes might affect labor productivity, the unemployment rate, and wage rate. Aoki (1980): The relative bargaining power between shareholders and employees affects the distribution of profits between them. Moretto and Rossini (1995): The shut-down option as well as the relative bargaining power between shareholders and employees affect distribution of the firm’s profits.

4 II. The purpose of This Article a. How does competitive pressure affect investment incentives? Answer: Given a firm’s profit-sharing rate, increasing competition induces a firm to invest later. This is just opposite to Grenadier’s finding (2002).

5 Why does this divergence arise? Answer: This article allows capital and labor to be substitutable each other, while Grenadier assumes that capital, the only input, produces output corresponding to a one-to-one relationship.

6 b. How does competitive pressure affect the profit-sharing rate? Answer: A firm facing more competitors will grant a lower share of profits to its employees.

7 Why does this happen? Answer: Employees not only receive a fixed wage rate that is determined by the external labor market, but also receive a bonus out of the firm’s profits. However, a firm’s profits will be lower as more firms exist in the industry. Increasing competition thus exerts more harm on shareholders than on employees because the pie that shareholders can share shrinks. Consequently, as a mediator, the firm’s manager must grant a larger share to its shareholders, or equivalently, a lower share to its employees when facing more competitors.

8 III. Basic Assumptions a. An industry that is composed of N identical firms. b. Each firm employs Cobb-Douglas technology with labor and capital as its inputs. c. Constant-elastic demand function whose multiplicative demand-shift factor following geometric Brownian motion. d. Shareholders and Employees share the firm’s profits.

9 IV. Solution Procedures and The Main Findings (i) Solving the short-run output decision made by the firm’s manager who acts on behalf of shareholders. The portion of the firm’s profits to its shareholders and total compensation for the firm’s employees are then derived.

10 (ii) Solving the long-run investment decision made by a firm’s manager. The firm’s net value to its shareholders and the firm’s net value to its employees are then derived.

11 Proposition 1: (a) Given the capital stock for the industry as a whole, a firm will invest later when facing more competitors. (b) Given an individual firm’s stock of capital, the firm will invest later when facing more competitors.

12 Proposition 2: A firm’s desired capital stock will be lower if (a) the profit-sharing rate attributed to employees is higher, (b) competition becomes more intense, and (c) demand uncertainty is more significant.

13 Corollary 1: As compared to a firm that does not employ any profit- sharing plans, a firm that optimally chooses its profit-sharing schemes will install a smaller capacity.

14 (iii) A representative employee will bargain for the profit-sharing rate with the manager immediately before the manager makes investment decisions.

15 Proposition 3: A firm’s manager will grant a lower profit-sharing rate to employees as (a) the firm faces more competitors, (b) the firm’s employees have a relatively lower bargaining power, (c) the price elasticity of demand is larger, and (d) the output elasticity of labor is higher.

16 Proposition 4: The profit-sharing premium, i.e., profit-sharing bonuses over total wage payment, is lower as competition becomes more intense.

17 Proposition 5: (a) As the bargaining power of employees is decreasing relative to that of shareholders, a firm’s optimal capacity will increase. (b) As competitive pressure increases, a firm’s choice of capital stock will decrease, yet the desired capital stock for the industry as a whole will decrease.

18 V. Conclusion a. The main results shown by Propositions 1-5 can be empirically tested for future study. b. It is possible to construct a model that allows a firm to resell its installed capital stock. c. It is possible to allow other parameters to vary over time. d. It is possible to consider two types of employees, senior and junior ones as indicated by Aoki (1982).