1. Consider a monopolist facing the following market demand function:
$$Q = 120 - 2P$$
where  Q denotes quantity demanded and P denotes price. The firm's total cost function is given by: $$TC = 20Q + 100$$
Answer the following questions:
(d) Suppose now that a second firm enters the market and the market structure changes from monopoly to Cournot duopoly. Assume that no tax is imposed in this market.
Firm 1 is the incumbent firm (the former monopolist) with cost function: $$TC_1 = 20q_1 + 100$$ Firm 2 is a new entrant with a different cost structure: $$TC_2 = 30q_2 + 50$$ The market demand remains: $$Q = 120 - 2P, \quad Q = q_1 + q_2$$ where $q_1$ and $q_2$ denote the output of firm 1 and firm 2 respectively. Answer the following questions: