Problem 3. People in State College love Watcha-call-its!, or WC for short. Their (aggre- gate) demand for WC is Qwo =54 -0.5P. Nevertheless, Incumbent What!? (IW) is the only WC seller in all of State College. One day, IW finds out that another company called Entrant-What! (EW) also wants to start selling WC in State College. If EW enters, then both firms will compete as Cournot duopolists. The marginal cost of producing WC for both firms is MC = 24. Nevertheless, EW (and only EW) must pay a one time set-up (fixed) cost of $300 prior to beginning production. In its panic of EW's impending entrance into the market, IW searches for possible ways to increase its competitiveness. After some effort, IW finds out that, if it invests $500 in 'R&D' before EW enters the market, it can actually reduce its marginal cost of production by half (c.g. MC/w = 12). Importantly, EW observes IW's investment decision before deciding to enter the market. 1. Clearly write down EW's profit maximization problem and best response function for any possible value of IW's investment choice INV = {0, 500}