Consider a simple one-period model where a creditor provides $I$ as investment to a firm and firm produces $\pi_G$ or $\pi_B$ depending on its performance. Let $R_i$ the portion of the profit that the firm transfers to investor, where $i=\{G,B\}$.
My Questions
(1) If we enforce limited liability structure in an agency problem, why is it that:
$$\pi_i\geq R_i.$$
(2) In an agency problem, is it reasonable to have this assumption? Why have limited liability as constraint at all?
(1) The limited liability constraint ensures that the agent does not pay out of her own pocket the investors dividends. The investor can only take as much as the company made, and cannot charge the agent money she did not produce.
(2) It is reasonable in a sense. In the real world, we believe investors cannot force a manager to pay for bad performance from her own bank account (at least I believe it).
Relatedly, on a technical note, limited liability is necessary to make problems "interesting" in Principal-Agent models. It is well known that is both agent and principal are risk-neutral, the principal "sells the firm" to the agent, and the agent does the optimal thing, and we actually do not have a moral hazard problem, in the sense that we can achieve first best.
To make the problem interesting, we usually assume either:
(i) the agent is risk averse or
(ii) we have limited liability.
