7. (20 points) Consider a monopolist with production costs given by c(y) 50,000+25y and with demand function given by y = D(p) = 5,000 - 20p. (a) (2 points) Obtain the inverse-demand function, p = p(y). = (b) (5 points) Find the output value that maximizes the monopolist's profit, (y) = p(y)y c(y). (Remember to check the SOC.) (c) (1 point) What price will the monopolist set? (d) (2 points) Compute monopolist's profit. (e) (5 points) Recall the concept of price elasticity of demand: the percentage change in quantity in relation to the percentage change in price (ignoring any negative signs). Formally, E -20p 20p = == Ap 5000-20p 5000 -20p = P Compute the price elasticity for this demand at the price set by the monopoly. Is the demand elastic or inelastic at said price? (f) (5 points) In general, would a monopolist ever want to set a price at which their customers' demand is inelastic? Justify your answer.