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Two firms, Firm A and Firm B produce an identical product.

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1. Two firms, Firm A and Firm B produce an identical product.;The demand function is Q = 50 2p;The cost function for each firm is C(q) = q, the cost per unit is 1.;a. What is the profit function for each firm?;b. What is the reaction function for each firm?;c. What is the NE solution, quantity produced by each firm? What are the profits for each firm?;d. If Firm A and Firm B collude and agree (credibly) on quantities, what quantities would they;produce? Assume they divide the quantity evenly between the two firms. What are the profits to;each firm? How do these quantities and profits differ from the quantities in part (c)?;e. Show that the quantities set in part (d) is not a NE solution for the two separate firms in the;Cournot game.;2. Two firms, Firm A and Firm B own the rights to an oil well with an estimated 120 billion;barrels of oil. The oil can be extracted over two periods.;In the first period the firms choose simultaneously how much oil to extract, and in the second;period they each extract of the remaining oil.;The profit to each firm is A = log(xA) + log[(Y xA - xB)/2] and B = log(xB) + log[(Y xA xB)/2] where xA and xB are the amounts (in billion barrels) extracted by each firm in period 1.;a. Explain why this is a game.;b. What is the profit function for each firm?;c. What is the reaction function for each firm?;d. What is the NE solution, amount of oil extracted by each firm in each period?;e. If Firm A and Firm B agree (credibly) on quantities for the benefit of both firms (common;good) how much would the each extract in the period? How does their profit differ from part;(d)? (Leave your answer in terms of logs.)

 

Paper#31132 | Written in 18-Jul-2015

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