Suppose you are a firm in a duopoly and have to decide whether to produce a high
ID: 1217917 • Letter: S
Question
Suppose you are a firm in a duopoly and have to decide whether to produce a high quantity or a low quantity. Your profit depends not only on what you choose, but also on what your competitor chooses. Your profits are outlined in the table below, with your profit listed first, your competitor's profit listed second. Describe how your choice interacts with your competitor's choice, and why the profits are as outlined the payoff matrix. What is the Nash Equilibrium (or Equilibrium) in this case? Explain how you solved for it.Explanation / Answer
a. In a duopoly, there is mutual interdependence of firms on each other. The profits of firm 1 depends on the move it takes and what strategy the firm 2 adopts. Profits are not fixed and that is why the profits are outlined in a pay-off matrix.
Say, when You choose to produce low quality output, and your opponent producues high quality product, the profit earned by you is $1, whereas your competitior would earn $45 or your profits increase to $20 if your opponent deicdes to produce low quality products. Now that you have another option and earning a profit of $1 would tend you to try other strategy, You would now have an option to produce high quality product, earning a profit of $5 if the competitor also produces high quality product or earn a profit of $45 if the competitor produces low quality.
b. The nash equilibrium would at (high quality, high quality). Both the firms would produce high quality products. This is because, producing making profits by products low quality products, is uncertain for either of the firms as the profits entirely depend on the move of the other, and each firm would either earn $1 or $20. So any of the two firm would rather choose to produce high quality product so bythat making a profit of either $5 or $45.
Thus the nash equilibrium would be at ($5, $5) of both the firms and having no tendency to deviate.