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3. (4 points) Consider an industry with N rms producing a homogeneous good. The inverse demand function is D (Q) = 100 C2"3 (3) where Q = 23:195. Moreover, for j = 1, ...,N, the total cost function of rm j is given by TCKQE) = { 0' qi = 0 (4) where K > 0. (a) Suppose that N is exogenous (i.e., xed). i. Set up rm is maximization problem. (0.5 points) ii. Find rm is bestresponse as a function of Q_1-. (1 point) iii. Plot rm i's bestresponse as a function of Q4. (1 point) iv. Find the Cournot equilibrium, quantities and price. (1 point) (b) Suppose that N is endogenous. Find the number of rms (denoted as N *) such that the prot of each rm is positive (i.e., no incentive to exit and no incentive to enter). (0.5 points)