Question

Consider the following fixed-investment model. An entrepreneur has cash A and can invest I1 > A...

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 pH, or shirk, in which case her private benefit is B1 and the probability of success pL. The project has positive net present value (pHR1 > 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?

Homework Answers

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

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