In all your answers, you need to show your work. We are going to recycle some of the data from Assignment '7. Thus: 1.' There are three consumers in the market for widgets. Their inverse demand function, given the prices of the rest of goods and the consumers' incomes, are P1(q) = 10 _ q, P3(1) = 10 - 2'1, Where q represents number of widgets. Widgets are produced by one (monopolistic, of course) rm with cost function C (q) = iqz. a) You have obtained the market demand for this market before. You can use your computations or compute it again. Now, compute the optimal output and price for the monopolist serving this market. Also, compute the deadweight loss associated to the monopolist's market power. b) Compute the market power of this monopolist, as measured by its Lerner index. Then, using the relationship between this index and the elasticity of demand (that follows from the rst order condition of the monopolist's prot maximization), what is the elasticity of demand at the monopolist's output