3. (4 points) Consider an industry with N firms producing a homogeneous good. The inverse demand function is D(Q) 100 Qd where Q = 1;. Moreover, for j = - (3) 1,, N, the total cost function of firm j is given by where K > 0. = TCi(qi) SK K+q, qi>0 = 0, qi 0 (4) (a) Suppose that N is exogenous (i.e., fixed). i. Set up firm i's maximization problem. (0.5 points) ii. Find firm i's best-response as a function of Qi. (1 point) iii. Plot firm i's best-response as a function of Qi. (1 point) iv. Find the Cournot equilibrium, quantities and price. (1 point) (b) Suppose that N is endogenous. Find the number of firms (denoted as NC) such that the profit of each firm is positive (i.e., no incentive to exit and no incentive to enter). (0.5 points)