There is a remarkable expansion of the lithium-ion battery business in recent years. The major manufacturers, including Panasonic, LG Chem, Samsung SDI and CATL, are ramping up capital expenditure. They are adding capital to drive down unit costs, but it also results in significant overcapacity. Manufacturers are either losing money or making very thin profits, but they all have plans to expand. Consider the decision of investing in excess capacity. Suppose there is an incumbent monopoly in the lithium-ion battery market. A potential entrant is considering entering the market. The market demand is p = 110 -Q, where Q = qi + q, with q; to be incumbent's output and q to be entrant's output. Both firms have a fixed cost of $2000. The entrant's marginal cost is $50. The incumbent's marginal cost is $50 if it does not invest in additional capital; its marginal cost is $5 if it invests in additional capital that increases its fixed cost by $4200. a. Suppose the potential entrant does not enter the market, find the monopoly's output, market price and profits if it doesn't invest in additional capital. (4%) b. Suppose the potential entrant decides to enter the market. The market becomes a Cournot duopoly market. Find the outputs of each firm, market output, market price and profits of each producer in the Cournot equilibrium, if the monopoly doesn't invest in additional capital. (6%)