I'd like to ask you question (h)

((1) Write A2 and A3 as scalars times A . Guess a general formula for A\" for all n 2 1 and (f) Compute the revenue Raw\" that the corporation can get (over the same period) by the (g) How can the corporation outperform the equilibrium approach over the same period? (11) Design a strategy that would bring more than 6Roqui] over the rst ten years. 3. Greedy monopolist The market for a certain product is governed by the equation dn+l = dn + \"(dn _ Sn) + 6(3n _ sn+llu where d" and SR represent the market demand and supply levels at year it E N. respectively. The parameter (1 corresponds to the rate of change of the demand with respect to the excess demand for the previous year and the parameter 6 measures the market reaction to the supply uctuations. A corporation took over control of all supply resources and decided to implement a greedy approach: to set the level of supply every year such that the revenue is maximised. Assume that the price is proportional to the demand and the production costs remain unchanged so the revenue at year 11 is given by the equation 1}. : anhyd,1 6). In this question you nd out whether the greedy approach performs well in a long term for this model. In the following set so = do = 10. o = i, ,5 = %, 7 = 2. 6 =1. (a) Given xed d," 3,. show that f(:r) = :1: (7(dn + (1(dn s") + (303,, 3)) 6) has unique global maximum. This point is the level of supply Sn.\" at year 11 + 1. (b) Find a matrix A and a vector b such that (:n+1) = A (3") + b. n+1 n (c) Find a vector u. that u. = An + b. Show that (3\"!) u = A\"+1 ((30) u) . dn+1 prove that your formula is correct. Find expressions for 3,, and (in. (e) Using the formula 2:0 A' = 1-1:: I write an exact explicit expression for the total [3] revenue of the corporation over the rst ten years REM = :11 snhdn 6). equilibrium approach: setting 3n = so for all n = 1, . . . .10. Approximate RWd/Reqml to two decimal places. [3] [2] [ll [2] [1]