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Ec101F10MT2_101130V1

# Ec101F10MT2_101130V1 - c Copi Ec101 Fall 2010 Midterm 2...

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ˇ Copiˇ c, Ec101, Fall 2010, Midterm 2, 11/30/2010. Version 1. There are 14 questions and 1 extra-credit question. You have 60min to answer these ques- tions. The questions have appropriate indications as to whether they are easy, medium, or hard. Each question has one correct answer. Important! READ the questions and answers carefully so that you do not make unnecessary mistakes, and so you can do your best! It is a bad idea to cheat - you cheat yourself and others, and if the world is just, you get in trouble. Text A. Suppose there is a market with a linear demand, Q = K - P . There are three kinds of firms producing the product, all with a constant marginal cost. Some have a high cost, c h , some have a medium cost c m , and some have a low cost, c l , 0 < c l < c m < c h < K . Firms compete by choosing quantities to produce. Text B. Consider the two games in figures 1 and 2, and refer to them. There are two players, who play these games in a number of consecutive periods. The discounting between two periods is given by δ = 1 1+ r . In exercises referring to this text, SPNE refers to subgame- perfect Nash equilibrium. Text C. On an island, Eden, there live 2 kinds of inhabitants, Adams and Eves. There are very many of each, and for each Adam, there is precisely one Eve. On the island there is arugula and there are coconuts. There are no other goods on the island. An endowment of an inhabitant is given by e = ( e 1 , e 2 ), where e 1 is the number of pounds of arugula, and e 2 is the number of pounds of coconut. All Adams have the same endowment, e A = ( e A, 1 , e A, 2 ), and all Eves have the same endowment, e E ( e E, 1 , e E, 2 ). Denote by x = ( x 1 , x 2 ) the consumption vector of an individual, where x 1 again denotes the amount of arugula the individual consumes, and x 2 denotes the individual’s consumption of coconuts. All Adams have the same utility over their consumption, u A ( x 1 , x 2 ) = x 0 . 5 1 x 2 , and all Eves have the same utility over their consumption, u E ( x 1 , x 2 ) = x 1 x 0 . 5 2 . In what follows, denote by p 1 the price of arugula, and by p 2 the price of coconuts, and denote by p = ( p 1 , p 2 ) the price vector. 1

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Problem 1. (easy) There are two firms in a market with a linear demand curve Q = K - P . Which of the following is true? a. A monopolist produces a quantity q M = K . b. In a duopoly situation, when costs are equal to zero, the total quantity produced under price competition is K . c. In a duopoly situation, when costs are equal to zero, the total quantity produced under quantity competition is K . d. In a duopoly situation, when costs of the two firms are positive, then under quantity competition, the total quantity produced is K .
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