多重主理人與多重代理人下代理問題之策略分析

Strategy Analysis for Agent Problems Derived from Multiple Principals and Multiple Agents

本研究有鑑於當代企業所有權與經營權分離的現象盛行，擬在所有人與經營人皆非僅一人的代理問題進行研究，並獲得四項主要結論。第一，當兩位主理人決定共同合作時，主理人給予代理人的邊際獎酬等於主理人的邊際收入，兩位主理人才能達到聯合利潤最大化。第二，在市場需求彈性大時，主理人給予代理人的獎酬與代理人的產量成正相關；而在市場需求彈性小時，則主理人給予代理人的獎酬與代理人的產量成負相關；當市場需求彈性靜、數等於1時，主理人給予代理人獎酬越高，反而會導致主理人的利潤下降。第三，當主理人持有的股份將資金成本加以考慮進去時，當利潤大於資金成本時，假設兩位主理人同時作決策，便會形成兩位主理人各持有一半股份的情況，若假設兩位主理人並非同時做決策，便會形成單一主理人與多位代理人情況；反之，當利潤小於資金成本時，兩位主理人都不會持有股份。最後，如果將利率設定為股份的函數時，若利率函數一階微分等於0，則結果會與當主理人持有股份並將資金成本加以考慮、進去時之經濟意涵相同。 This research is conducted under the premise that it is quite common the ownership of the contemporary enterprise is separated from the right to operate; therefore under the circumstances that the owner and the operator are not the same person status will be researched as result. There are four major conclusions of this research. First, when both principals decide to jointly cooperate with each other, the marginal reward offered to the agent by principal should be equivalent to the marginal income for the principal; then, both principals can reach the goal of maximizing their joint profits. Secondly, when elasticity of demand in the market is big, the agent's reward offered from the principals is positively correlated with agent's output; when elasticity of demand in the market is small, the agent's reward offered from the principals is negatively correlated with agent's output; when elasticity of demand in the market is equal to 1, the higher principals give the agent reward will lead to decrease profits of the principals. Thirdly, as the principals holding shares with the cost of capital to be taken into account, when the profit is greater than the cost of capital, each of the two principals holds half of the shares assuming they make decisions with the same time, or, the principals will form a single case with a number of agents assuming they are not making decisions at the same time. Conversely, when the profit is less than the cost of capital, the two principals will not hold shares. Lastly, if the interest rate is the function of shares and interest rate function first-order differential is equal to 0, the result is the same with the economic content of the cost of capital to be taken into account.