3. Consider a course allocation problem with strict and non-responsive preferences. Isthere a mechanism that is efficient and strategy-proof? If so, state the mechanismand show that it satisfies efficiency and strategyproofness. {hint serial dictatorship}4. Consider a course allocation problem with responsive preferences and at least 3students. Is there a mechanism that is efficient and strategy-proof that is not theSerial Dictatorship? If so, state the mechanism and show that it satisfies efficiencyand strategyproofness.5. Suggest a mechanism for allocating students to courses in a situation where preferences are non-responsive, and study its properties (efficiency and strategyproofness). Please be creative

2. a) Consider a market where one firm (firm 1) currently produces, but a second firm (firm 2) is intending to enter and sell an identical product. The market has inverse demand given by p = 40 – Q, where Q is the total output sold in the market. Firm 1 has a marginal cost of 16 and firm 2 has a marginal cost of c < 16, with no fixed cost for either firm. Firm 2 has a choice of competing on price or quantity, with firms making their choices simultaneously (i.e. the market will be either a Bertrand or Cournot duopoly). If you were advising firm 2 on entering this market, how would you advise it to compete? To what extent would the size of firm 2’s cost advantage affect your advice?  b) Now assume that firm 2 is aware that other firms are considering entering the market, so the market may over time change from a duopoly to an oligopoly with more than two firms. This would not change the nature of competition (i.e. any additional firms would set price or quantity in line with the first…

1. Consider two firms (i=1,2) interacting in the market. Assume that firms compete in quantities and therefore they choose either to cooperate or not in each round. If a firm deviates it earns monopoly profit for a round and a punishment phase will follow from next round onwards (for ever) where both firms choose the Cournot quantity. Assume a discounting factor & and that firms meet in the market in every period. The demand facing the industry is p = 1 92. Let Q = q1 + 92 denote the aggregate industry output - 91 - level. Assume further that production is costless.