Analyzing the case where private benefits are not comonotonic with total revenues in Section 5.1.2, attention is restricted to compensating schemes such that \(t_{s}^{\prime}=0\) and \(t_{s} \leq 1\).

(a) Show why \(t_{s}\) will not be greater than 1 .

(b) Show that \(t_{s}^{\prime}=0\) is optimal compared to other situations with \(t_{s}^{\prime}>0\).

Data From Section 5.1.2:-

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In this section, the case where the entrepreneur has full control is studied. This means that the entrepreneur chooses the action a. The action will therefore be chosen so as to maximize the entrepreneur's reward and will be given by a(0,, s) = arg max{t,y +1, +1}, for i=g, b and j = g, b. In order to describe the nature of the different contracts that may arise in this context, we say that a contract is efficient if the action chosen is the optimal action for the realized state of nature. Also, we say that a contract is feasible if the investor expects to obtain at least as much as the amount invested, K. First, consider the case where the private benefits (1) satisfy the inequalities and >. In that case, it is said that the private benefits (1) are comonotonic' with the total revenues (y + 1). It is fairly simple to show that, in this situation, a contract with a schedule t(s, r) given by a constant t, independent of the signal perceived and of the return obtained, is efficient. Under the assumption of comonotonic pri- vate benefits, 1+1 > 1+18 t+1 > 1+1, thus ensuring that the revelation of a good state (i = g) implies a = ag and the revelation of a bad state (i = b) implies a = a,. In other words,