Answer:
Nash equilibrium will occur at the following conditions P1 = P2 = 10 and x1 = x2 = 0.
Explanation:
The term or concept known as the Nash equilibria is very important and it is often used in the determination of the kind of price strategies companies that are competing against one another will use in order to acquire more customers than the others.
So, in this question/problem we are given that there are two manufacturer that is manufacturer 1 and manufacturer 2. Also, the total number of customers both manufacturers are competing for is equal to 100.
Kindly note that we are given from the question that ''Each manufacturer chooses both the price and quality of its product, where each variable can take any non-negative real number''
If each of the manufacturer has 50 customers each that is symmetric condition.
Assuming we have a condition or situation where p1 is less than p2 for manufacturer 1, it means that manufacture 1 lessens its price, therefore manufacturer 1 will have all all the profit = 100(p1 - 10 - 5x1).
Assuming manufacturer 1 reduces both the quality and the price this time around to the point that it is justifiable to lower the price because of the quality , it means that we will have 1000 + (x1 = 0) + (p1 - compensation m).
For any of the manufacturer, If m> x' and we have that x1 = x'>0[ which is for the quality], then, the profit will be 100(10 + 5x'- m -10).
Also, For any of the manufacturer, if we have x'<m<5x' and x1 for the representation of quality, then, Customers will buy from both manufacturer making m<5x'.
Therefore, Nash equilibrium will occur at the following conditions: P1 = P2 = 10 and x1 = x2 = 0.
