Question 1 (12 marks) A. producer is facing the market demand flmction Q\" = 1, 20!] [1 f 21p for Type A consumers and Qt. = 900 [1 f 2}}: for Type B conslmicrs1 where Q\" and 1%,. is total quantity demanded from Type A and Type E consumers respectively1 when the seller charges a constant price of p dollars fer every unit of output sold. Marginal costs of production are zero. a] Suppose the seller is a competitive rm. Find the competitive price1 the total quantity consumed by Type A consumers1 and the total quantity consumed by Type B censumrs's. {1 mark] Find consumers' surplus for both types of consrnucrs1 and producer's surplus-31 and illustrate with a graph. {1.5 mark} h] Suppose the seller is a monopolist practicing rst-degree price discrimination. Find the monopolisth prots for each type of consumer and calculate produoer's surplus [1 mark}. Ilhlstrate your answer with a graph. [0.5 mark}. Find the total quantity consumed by Type A consmnera and the total quantity consumed by Type B consumers [0.5 mark}. Find surplus Jfor both types of consmners {0.5 mark}. c] Compare total surplus {i.e Consumers'+Producer's surplus] in part a, to total surplus in part b. Basal on this observation. explain whether you agree or disagree with the following statement, and why: \"The concept of Pareto cicicucy has nothing to do with a) f} the concept offaimess\". {1.5 marl-r} Let QED?\" denote the quantity bought by Type A consumers in part b1 and mgoso the producer's surplus from Type A consumers in part b. Dene similarly Q39\" and mgp for Type B consumers. Suppose the seller carmot observe the type of each consumer. The seller makes the following annoimcement to the consumers: \"First, you tell me your type. If it is Type A, I will give you QED?\" for a total of min?\" dollars. If it is Eyre B, I will give you QED?\" for a total of \"sign?\" dollars\". Find the surplus that Type A consimiers receive if they truthfully report their type, and their surplus if they misreport their type as Type B to the seller. [1 mark] Illustrate your answer with a graph [ELE nlark}. Use your answers in part d to explain why the monopolist's announoement in part d is not inoentive compatible. (ELE- rnark} l:Ionsirler the following alternative anuolmcement: \"Fiaat, you tell me your type. If it is Type A, I will give you QED?\" for a total of a: dollops. If it is Eyre B, I will gins you QED?\" for a total ofy dollars\" Find values for a: and y that maximize the monopolist's prots without violating inoentive oompatibility. {1.5 mark}. Find surplus for both types of consumers and oompare it to their surplus in part b. [0.5 mark}. Find the monopoly prots, and compare to prots in part b. {0.5 mark} Maintain the assumption that the monopolist cannot observe the type of each mnsumer. Use a graph to show that the monopolist can increase their prots relatively to part e with an incentive compatible pricing mechanism different to the one you found in part e. {1 mark]