Problem 5 (20 points) Consider the following Cournot dquoly model. Firms 1 and 2 produce the same good. They simultaneously choose their output levels yl, yg, and the resulting price is given by the inverse demand function p = 1 yl '92. If rm 1 produces a (strictly) positive output level, it incurs a a'ed cost is: but no variable cost. Thus. its cost function is , _ [)ify1=[). Cl(91)'{ i,- ify1>[}. Firm 2 faces no cost at all; its cost function is 02 ('92) = l} for all yg .2 U. Show that (i) there is a unique lCournot-Nash equilibrium if the xed cost is is below a lower threshold k? or above an upper threshold [6+ and (ii) there are two Cournot-Nash equilibria when k: E ii; <_- compute the thresholds k2 and equilibrium output levels explicitly>