Two firms, A and B, control the market for a product. Each can charge a high or low price with the following economic profit outcomes: | | B - low price | B - high price | |-------------|---------------|----------------| | A - low price | A's profit = 40, B's profit = 30 | A's profit = 60, B's profit = 50 | | A - high price | A's profit = 80, B's profit = 110 | A's profit = 130, B's profit = 90 | The Nash equilibrium is most likely to occur when: A) Both companies charge a high price. B) A charges a high price and B charges a low price. C) B charges a high price and A charges a low price.
Answer (1)
To determine the Nash equilibrium in this scenario, we need to look at the strategic choices and resulting payoffs for both firms, A and B. A Nash equilibrium occurs when neither firm can increase their profit by unilaterally changing their strategy, given the strategy of the other firm.
We have the following payoff matrix:
If both A and B choose low price :
A's profit = 40
B's profit = 30
If A chooses low price and B chooses high price :
A's profit = 60
B's profit = 50
If A chooses high price and B chooses low price :
A's profit = 80
B's profit = 110
If both A and B choose high price :
A's profit = 130
B's profit = 90
Let's analyze the payoffs to determine the Nash equilibrium:
A charges low price :
If B charges low price, A gets 40, which is lower than the 60 if B charges high price.
Therefore, if A charges low price, it prefers B to charge high price.
A charges high price :
If B charges low price, A gets 80, which is lower than the 130 if B charges high price.
Therefore, if A charges high price, it prefers B to charge high price.
Now, let's look at B's strategies:
B charges low price :
If A charges low price, B gets 30, which is lower than the 110 if A charges high price.
Therefore, if B charges low price, it prefers A to charge high price.
B charges high price :
If A charges low price, B gets 50, which is higher than the 90 if A charges high price.
Therefore, if B charges high price, it prefers A to charge low price.
Given these preferences, the Nash equilibrium is where both companies charge a high price, as neither firm can benefit by changing its own pricing strategy unilaterally in that scenario. So, the most likely Nash equilibrium occurs in option A: Both companies charge a high price.
