Homework 6 Solution

# Homework 6 Solution - Spring 2008 UGBA 143 Homework 6...

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Spring 2008, UGBA 143 Homework 6 Solution Problem 1 (Price Competition) A B ) Profit = Revenue - Cost Define as profit for firm A, as profit for firm B Total profit of A is: Profit/Unit * Total Quantity = ( -2)* 1 Where 10- 2 1 a) Therefore, ( -2)*(10- 2 Sim A A A A B A A A B p Q Q p p p p p Π Π = + Π = + ) ) A 2 2 1 iliary ( -2)*(10- 2 1 b) ( -2)*(10- 2 1 10 - -20 2 - 2 1 - 12 -20- 2 To find the best response, we need to maximize (by taking deriva B B B A A A A B A A A B A B A A A B B p p p p p p p p p p p p p p p p p Π = + Π = + = + + = + + Π tive and setting it to 0) 1 2 12 0 2 1 6 <--- Firm A's best response to firm the price set by firm B 4 A A B A A B p p p p p B Π = - + + = = +

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A B A B c) Notice the symmetry in the profit function as shown in part a), the best response function 1 of firm B is therefore: 6 4 We know, p = p , so substituting p for p into the best resp B A p p = + ) ) onse function for A, we get 1 6 4 8 8 Therefore: 1 ( - 2)*(10- (8- 2)*(10-8 4) 36 2 1 ( - 2)*(10- 36 2 In equilibrium, both firm w A A A B A A A B B B B A p p p p p p p p p p = + = = Π = + = + = Π = + = ill charge \$8 per unit and their expected profit is \$36.
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• Spring '08
• XuanmingSu
• English-language films, Harshad number, small firm, Big Firm, profit function

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