A monopolist faces two types of buyers. There are n buyers of each type. Each buyer buys one unit of the good. Buyer willingness to pay for a good of quality s is for low demand and for high demand where > . A monopolist can either produce a single version of quality s to q buyers at a cost of = 1 2 2 or they can produce both a low quality (sL) version to qL buyers and a high quality version (sH) to qH buyers at a cost of = 1 2 ( ) 2 + 1 2 () 2 a) (10 marks) One version. Find the profit maximizing price, quality and output if the monopolist sells only one version and (i) serves high demand only (ii) serves both types. (iii) Derive the condition for which the monopolist will serve high demand only. b) (10 marks) Two versions. (i) Find the profit maximizing prices, qualities and output if the monopolist sells both low and high quality versions. (ii) Use your solutions to determine whether the monopolist is practicing price discrimination. (iii) Derive the condition for which the monopolist offers 2 versions instead of serving high demand only. (iv) Derive the welfare function for the two version case and determine the welfare maximizing levels of quality. Does the monopolist over or under provide quality when they provide two product quality versions?