22:37 5A23HAM eoo @ coursehero.com 1. Kyle's model with an imperfectly informed investor. Suppose that in the Kyle (1985) model the informed investor observes a noisy signals = v + 1 about the final valuev ~ N(, 02) of the security, where the noise componentn ~ N (0, 072,) has no correlation either with the security's value v or with the noise traders' order u (Cov(n, v) = Cov(n, u) = 0). (a) Assume that competitive market makers post the following price schedule: p(q) = 1+ Ag, where is the net order flow. Find the optimal value of\\ that they will choose if they conjecture that the informed trader's strategy is the following function of his noisy signal s: X (s) =8 (s u). How does the market depth 1/ chosen by market makers respond to changes in the variance 03, of the informed investor's error? What is the intuitive explanation for this result? If we plot the depth I/A as a function of the aggressiveness3 of informed investors (the former on the vertical axis and the latter on the horizontal axis), how do changes in the varianceaf, affect the position and shape of this curve? (b) In this case, the informed trader too must solve an inference problem in forming his expectation of the security's value. Show that his expectation ofv conditional on the signal s is given by o2 E|s| = p+ v (s p), ls] = n UUQJFU%( 1) and find the value of as a function of market depth 1/A. How does the trading aggressivenessd that informed investors choose respond to changes in the variance 03 of the error term n? What is the intuitive explanation for this result? If we plot [ as informed investors' best response to the depth 1/A chosen by market makers in the same graph described under (a), how do changes in the varianceo; affect the position and shape of this line? (c) Compute the values of A and8 . How do they respond to changes in the variance o3 of the error made by the informed investor? Graphically, does the equilibrium still correspond to the point of minimum depth as in the baseline version of Kyle's model? o (d) Compute the ex-ante expected profit of the informed investor. What is the effect of an increase in o2 on this profit? What is the intuitive explanation for this result