Scale versus riskiness tradeoff:-
Consider an entrepreneur with a project of variable investment I. The entrepreneur has initial wealth A, is risk neutral, and is protected by limited liability. Investors are risk neutral and demand a rate of return equal to 0. The project comes in two versions: Risky. The project costs I and ends up (potentially) productive only with probability x < 1. The timing goes as follows.
(a) The scale of investment I is selected.
(b) After the investment has been sunk, news accrues as to the profitability of the project. With probability 1 - x, the project stops and yields 0. With probability x, the project continues (without any need for reinvestment).
In the latter case, (c) the entrepreneur chooses an effort; good behavior confers no private benefit on the entrepreneur and yields subsequent probability of success pH; misbehavior confers private benefit BI and yields probability of success pL.
Finally, (d) the outcome accrues: success yields RI and failure 0. Safe. The investment cost, XI with X > 1, is higher for a given size I. But the project is always productive ("x = 1"). The moral hazard and outcome stages are as in the case of a risky choice. We will assume that the contract aims at inducing good behavior. Letting
one will further assume that x > 1/ρ1 and X
(ii) Interpret this condition in terms of a "cost of bringing 1 unit of investment to completion."