Amonopolist faces the following inverse demand curve: pp(q) = 400 – 4q and its cost function is given by c(q) = 2q2 + 40. 1. what is the firm's elasticity of demand? 2. recall that a monopolist's supply curve is its marginal cost curve. express the firm's supply curve as a function of q, ps(q). 3. what price and quantity levels maximize total welfare? how is this welfare allocated between consumers and producers? 4. calculate the monopoly price and quantity traded for the firm. calculate the consumer surplus, producer surplus, profit and dead weight loss (dwl) at the monopoly price. 5. compute the lerner's index. suppose the government decides to regulate the industry in which the firm operates with the objective of increasing consumer surplus. it tells the firm that it will be paid $80 dollars for each unit it sells. 6. how much does the firm produce? how much does this subsidy cost the government?