Nimbus, Inc., and Cleansweep, Inc., are the only producers of flying brooms. Each firm has two strategies: Spend 30,000 galleons a year on research and development (R&D) or spend nothing on R&D. If neither firm spends on R&D, Nimbus' economic profit is 80, 000 galleons and Cleansweep's economic profit is 40,000 galleons. If each firm conducts R&D, market shares are maintained, but each firm's profit is lower by the amount spent on R&D. If Nimbus conducts R&D and Cleansweep does not, Nimbus makes an economic profit of 120,000 galleons, while Cleansweep incurs an economic loss of 20,000 galleons. If Cleansweep conducts R&D and Nimbus does not, Cleansweep makes a profit of 60,000 galleons while Nimbus loses 10,000 galleons.
a) Construct a payoff matrix for the game that Nimbus and Cleansweep must play.
b) Find the Nash equilibrium. In the Nash equilibrium, what is each firm's equilibrium profit?
c) What is the cooperative outcome? Would the firms make more economic profit if they collude to achieve the cooperative outcome?

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The Answer of Nimbus, Inc., and Cleansweep, Inc., are the only producers of flying brooms. Each firm has two strategies: Spend 30,000 galleons a year on research and development (R&D) or spend nothing on R&D. If neither firm spends on R&D, Nimbus' economic profit is 80, 000 galleons and Cleansweep's economic profit is 40,000 galleons. If each firm conducts R&D, market shares are maintained, but each firm's profit is lower by the amount spent on R&D. If Nimbus conducts R&D and Cleansweep does not, Nimbus makes an economic profit of 120,000 galleons, while Cleansweep incurs an economic loss of 20,000 galleons. If Cleansweep conducts R&D and Nimbus does not, Cleansweep makes a profit of 60,000 galleons while Nimbus loses 10,000 galleons.
a) Construct a payoff matrix for the game that Nimbus and Cleansweep must play.
b) Find the Nash equilibrium. In the Nash equilibrium, what is each firm's equilibrium profit?
c) What is the cooperative outcome? Would the firms make more economic profit if they collude to achieve the cooperative outcome?