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Practice+Final+1_Solution

# Practice+Final+1_Solution - FirmsandMarkets Spring2010...

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2 Firms and Markets Spring 2010 Final Exam QUESTION 1. Cournot Competition [35 points] Nickel is a commodity whose market is dominated by two players Quarter Inc. and Dime Inc. The two companies must decide simultaneously (without knowledge of each other’s decision) how much nickel to produce and supply to the market. Once both firms select their output quantity, the market price adjusts to clear the market. So, each firm really acts as a “quantity taker, price maker”: it chooses its quantity based on a conjecture about the quantity it expects its competitor to choose, taking into account how its own quantity decision affects the market price. The market price for nickel is determined as follows: if the total quantity (in tons) extracted by the firms is Q , then the market price per ton is given by the relationship: . For instance, if Quarter Inc. decides to extract 20 tons and Dime Inc. decides to extract 30 tons, the market price would be \$65 per ton ( = 90 – ½(20+30) ). Quarter Inc. and Dime Inc. must each individually and simultaneously decide between supplying only three quantities: 50 tons, 60 tons or 80 tons. The marginal cost of extracting and supplying nickel is zero for both firms. You should assume as usual that Quarter Inc. and Dime Inc. are both rational firms seeking to maximize their own profits. Below is a chart of the market prices and profits for different choices that Quarter and Dime can make; some of the cells have been filled in. Q QUARTER Q DIME Market Price PROFITS QUARTER PROFITS DIME 50 50 40 2000 2000 50 60 50 80 60 50 60 60 30 1800 1800 60 80 80 50 80 60 20 1600 1200 80 80
3 Firms and Markets Spring 2010 Final Exam a) [8 points] Represent the competition between Quarter Inc. and Dime Inc. as a normal‐form game, and draw and fill out the payoff matrix.

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