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Unformatted text preview: ˇ Copiˇ c, Ec101, Fall 2010, Relevant questions from Fall 2009 midterm 2 and the final. Each question has only one correct answer. Problem. Which of the following is true in a Cournot model of competition between two firms where the firms set quantities (there is a linear demand given by q = K p . a. The two firms undercut each other quantities until both of them produce nothing at all. b. The result is no different than if the two firms competed by setting prices. c. The profit of each firm is strictly larger than the profit if each firm were a monopolist. d. Each firm can decide how much it will produce regardless of the production of the other firm. e. If the firms don’t collude, the total amount of production will be greater than if there were a single monopolist firm. Problem. Suppose there is a linear inversedemand function given by p ( q ) = K q , where K=60. There are two firms and their production costs are given by c 1 = 10 and c 2 = 20 per unit, so that it costs firm i c i q i to produce a quantity q i . Recall that if the two firms produce quantities q 1 ,q 2 the profit to firm 1 is given by Π( q 1 ,q 2 ) = p ( q ) q i c i q i , where q is the total output q 1 + q 2 . If the firms compete by setting quantities (Cournot competition) then they will produce a. q 1 = 100 ,q 2 = 100 b. q 1 = 20 ,q 2 = 10 c. q 1 = 10 ,q 2 = 5 d. q 1 = 30 ,q 2 = 15 Problem. Suppose there is a linear inversedemand function given by p ( q ) = K q , where K = 43 . 5 . There are two firms and their production costs are given by c 1 = 10 and c 2 = 5 per unit, so that it costs firm i c i q i to produce a quantity q i . Recall that if the two firms produce quantities q 1 ,q 2 the profit to firm 1 is given by Π( q 1 ,q 2 ) = p ( q ) q i c i q i , where q is the total output q 1 + q 2 . If the firms compete by setting quantities (Cournot competition) then they will produce 1 a. q 1 = 8 ,q 2 = 16 b. q 1 = 5 ,q 2 = 10 c. q 1 = 9 . 5 ,q 2 = 14 . 5 d. q 1 = 10 ,q 2 = 20 Problem. Suppose there is a linear inversedemand function given by p ( q ) = K q , where. There are two firms with cost functions given by c i q i for each firm i . Which of the following is true. a. If c 1 = c 2 they compete by setting prices (Bertrand) then they obtain as much profit as if they competed by setting quantities. b. If firm 1 is a monopolist (there is no firm 2), it obtains a higher profit if it can choose one price at which to sell the quantity demanded at that price than if it chose a quantity and sold it at the best price it could get for that quantity. c. If the two firms compete by setting quantities then the price in the market would equal their costs. d. If the two firms compete by setting quantities then the sum of their profits is less than if the firm with the lower production cost were a monopolist....
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 Fall '08
 Buddin
 Game Theory, Barack

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