Consider two partners who jointly own a firm and need to decide whether

or not to go ahead with a project. The project provides monetary returns based on whether or

not the outcome is success (H) or failure (L). Suppose that if successful which happens with a

probability of (0, 1), the project delivers an additional monetary return of H. Meanwhile, the

project will deliver no additional returns if is not successful with a probability of 1 . On the

other hand, the monetary cost of the project to the firm is C. The current monetary value of the

firm is given by V and assume that the two decision makers are equal partners; thus, they share

the value as well as the returns and costs equally. The decision protocol requires their unanimous

agreement to undertake the project (in other words, each partner has a veto power).

Assume that the first partner is risk neutral and has a money utility function u1(x) = x for every

monetary amount x 0. Meanwhile, the second is risk averse and has a money utility function

u2(x) =

x for every monetary amount x 0.

a. (15 pts.) Suppose that V = 2000, H = 2000, C = 900, and =

1

2

. Please show that the

risk neutral wishes to initiate the project while the risk averse partner uses his veto power to

block that.

b. (15 pts.) Consider the following proposal of an outside consultant: The first partner is to

compensate the second with an amount of 50 in case of failure. Would the firm (each of the

partners) accept this proposal and initiate the project?