Consider the model proposed by Kyle [1148] and described in Sect. 10.1. By making use of the multivariate normality assumption on the random variables \(\left(\tilde{d}, \tilde{y}_{1}, \ldots, \tilde{y}_{N}, \tilde{z}\right.\) ), prove Proposition 10.1 (compare also with Kyle [1148, Appendix A]).

Data From Proposition 10.1

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Proposition 10.1 In the context of the above model (see Kyle [1148]), it holds that Tinf = td + t + Cinf (N-1)t and Tun = td + Qun NTE, (10.6) where Qinf and Qun are two constants belonging to the interval [0, 1]. Moreover, in correspondence of a symmetric linear equilibrium (X, Y) of the form (10.4), it holds that Pinf= (N-1) (N-1) +TE N and un = (10.7) N +01