1. Suppose the demand for a certain good is given by the following inverse demand cuive: P = 1130 q . There are two firms in the industry, each of which has no fixed costs and a constant marginal cost of $40. a} Suppose the firms act as Cournot competitors. 1iEli-"hat will be the equilibrium price and quantity in the market? 1iEli-"hat will be the profits of each firm? b} Suppose the firms decide to eollude= i.e.._ to act as a single firm= and that they split the quantity and profits evenly between them. 1EEli-"hat will be the equilibrium price and quantity? Tin-"hat will be the profits of each firm? c} Comment on the viability of the outcome in part b}. 2. Suppose a Cournot oligopoly consists of three identical firms. Industry demand is given by P = IOU29. and I'm-TC = AC = if]. a} Derive the symmetric cartel outcome. b) Derive the competitive outcome. o) Derive the Nash equilibrium in terms of price; quantities. and prots. 3. Microscape and Netsoft are the only two firms in the market for personal computers. which is a homogeneous product. The two firms choose their respective quantity. .5... simultaneously. The inverse demand function is equal to P = 3000 Q. where the mdustrv quantity Q = q\" q}... The firms both have constant marginal costs and no fixed costs. However. their marginal costs differ: it is equal to $600 for Microscape and 3900 for Netsoft. In addition= each firm has an absolute capacity constraint at a quantity of 900. i.e.= it is impossible for either of them to produce a quantity above 900. a) Suppose that Microscape and Netsoft maximize their own profits. Derive the Nash equilibrium (there is only one) in terms of the quantity produced by each firm. the market price. and the profits of each firm. b) Graph the reaction functions of the two firms and the Ifash equilibrium. c) Derive the market share of each firm and the I-IerfindahlHirschman index for the market. Also. derive each firm's markup of price over marginal cost as a mction of the elastic-it}? of demand and the firm's market share. d) Suppose instead that the firms are able to collude in a cartel. i.e._. maximize their joint profits. Derive the equilibrium quantity for each firm. the market price. and the profits for each firm. \"returning!!! The firms have different marginal cost, so it will SOT be optimal for the cartel to split the production evenly. e) In what sense is it bad if the cartel agreement works? Are the firms likely to stick to the cartel agreement? Why or whv not? Winch fn'm has a stronger incentive to break the cartel agreement? 4. Consider the Cournot model of oligopol}: it" firms= indexed by 5'. compete in a market for a homogeneous good= where the}! simultaneously choose output quantities= qi. The total market _H.' quantity in the market is denoted by Q = E '53:. The irwerse demand function is given b}? i] PEQ] = a Q. unless a s: Q. in which case P = O. The rms have no xed costs and marginal cost equal to q. The firms= payoffs are their profits. i.e.= firm E's payoff is It". : 13(9):}. Cir}... . . t? . . a) Suppose there are two firms in the market. i_e.. .-"-.-'= 2. and D -:: cl -:: c} -=: ?. Derive the unique Nash equilibrium quantities for the two firms as well as the resulting market price and the profits of the two firms. b} Maintaining the duopoly-assumption from part a): suppose that the cost structure is such that Cl s: c-_ 4:: C: s: a: but 2:} ::- a + c]. Again. derive the unique Nash equilibrium quantities: the market price and the profits ofthe two firms. c) Suppose now that there is an arbitrary number of firms. N, in the market: and that these rms all have the same marginal cost. :7. Dene the symmetric cooperative cartel solution. d} Keeping the symmetric oligopoly setup from pan c]. but assuming that the firms behave non- cooperatively: derive the unique Nash equilibrium quantity of each firm as well as the resulting market price and profits of the firms. Finally: analyze what happens to the Xash equilibrium as _-'.-" } ac and comment. lUOCI Q industry quantity. Both firms have costs given by MC = AC = 2 . If the two rms charge the same price. they split the market demand evenly. Derive the Bertrand equilibrium. What is the output of each firm and of the industry as a whole in equilibrium? where Q is the '3. Two duopolists face the following industry inverse demand curve: P = 6. Consider Untel and Ely-rota;= two firms that supply computer chips for toaster ovens. Market demand is given by P = 12:) ZDQ where Q = qr\". + qt. Neither firm has any fixed costs and both have a constant marginal cost. However= L'ntel can produce chips more cheaply than Cyrox can: marginal cost at Untel is $20. while at Cyrox it is $40. a) The two firms agree to form a cartel and to share all profits equally. What will be the profit- maxirnizing output in total'?' How much will be produced at each firm? What will be the profit ea1ned by each firm? b) Suppose that the cartel agreement breaks dots-n and that Bertrand competition einerges after the breakdown [ts-\"ith the firm splitting demand evenly if they charge the same price). What would be the quantity of output for each firm\"? What would be the market price? What would be the profit of each firm\"? 7". Explain why the outcomes in a the Conrnot and Bertrand duopoly models are so different. Use the concepts of strategic substitutes and complements and a graph of the reaction mctions of each model