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Unformatted text preview: Solutions to Problem Set 4 1 Cournot Competition with More than 2 Firms (a) The profit of firm i is the difference between its total revenue and total cost, and is therefore a function of the quantities set by all of the firms: i ( q 1 ,...,q n ) = q i P ( Q )- 10 q i = q i (100- Q- 10) = q i (90- q 1-- q n ) (b) Firm i s best response to the other firms quantities is the solution to its profit maximization problem, taking as given the quantities of the other firms. The profit maximization problem is: max q i i ( q 1 ,...,q n ) max q i q i (90- Q ) The first-order condition for the above problem gives us the quantity q i which maximizes i s profit: d i dq i = (90- Q )+ q i - dQ dq i = 90- Q- q i = 0 2 q i = 90- q 1- ...- q i- 1- q i +1- ...- q n q i = 90- q 1- ...- q i- 1- q i +1- ...- q n 2 This is the optimal quantity for firm i given the quantities of the other firms....
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- Spring '08