Question

Consider the following fixed-investment model. An entrepreneur has cash A and can invest I₁ > A in a project. The project’s payoff is R₁ in the case of sucess and 0 otherwise. The entrepreneur can work, in which case her private benefit is 0 and the probability of success is p_H, or shirk, in which case her private benefit is B₁ and the probability of success p_L. The project has positive net present value (p_HR₁ > I₁), but will not be financed if the contract induces the entrepreneur to shirk. The (expected) rate of return demanded by investors is 0. What is the threshold value of A such that the project is financed?

Answer 1

	Project Success	Project Failure
Work (pH : Success prob)	0,R1	0,0
Shirk(pL : Success prob)	B1,R1	B1,0

If she works, payoff for her is 0, while payoff for project is pHR1 > I1 > A

If she shirk, payoff for her is B1, while payoff for project is pLR1

Total payoff if she works = pHR1 > I1 > A

Total payoff is she shirks = B1 + pLR1

Ttotal payoff when she works > Total payoff when she shirks

pHR1 > B1 + pLR1

Thus threshold value for A should be equal to B1 + pLR1