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 a success (H) or failure (L). Suppose that if success happens with a probability of π ∈ (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 − π. 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 assumes 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 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. Suppose that V = 2000, H = 2000, C = 900, and π = 12 Please show that the risk-neutral wishes to initiate the project while the risk-averse partner uses his veto power to block that.

b. 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?

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aIn this case the riskneutral partner wish to initiate the project because th... View the full answer