Delaying income recognition:-

Consider the timing in figure. Assume the following.

• The discount factor is δ = 1. There is no moral hazard. A manager's probability of success depends only on the manager's current ability. Managers do not respond to monetary incentives and get a constant wage normalized at 0. They just get private benefit B per period of tenure. All incomes (y₁, y₂, y₃) go to investors.

A manager with high current ability succeeds with probability α , while one with low current ability succeeds with probability

• The entrepreneur's date-1 ability is high with probability α and low with probability 1 - α (no one knows this ability). The correlation of ability between dates 1 and 2 is equal toThat is, the entrepreneur's ability remains the same at date 2 with probability ρ. To simplify computations, assume that the manager's ability does not change between dates 2 and 3 (this assumption is not restrictive; we could simply require that the date-3 ability be positively correlated with the date-2 ability).
• At date 1, the entrepreneur privately observes the date-1 profit. If the entrepreneur has been successful (y₁= R₁), she can defer income recognition. The reported profit is then yˆ1 = 0. These savings increase the probability that y₂= R₂by a uniform amountindependent of type), presumably at a cost in terms of NPV (R₁> τR₂).105
• Investors at the end of date 2 have the opportunity to replace the entrepreneur with an alternative manager who has probability αˆ of being a high-ability manager. (There is no commitment with regards to this replacement decision.) This decision is preceded by a careful audit that prevents the entrepreneur from manipulating earnings (yˆ2 = y2). One can have in mind a yearly report or a careful audit preceding an opportunity to replace management by a new managerial team.

Find conditions under which a "pooling equilibrium," in which the entrepreneur keeps a low profile (yˆ1 = 0) when successful (y₁ = R₁), prevails.