Two manufacturers, denoted I and 2, are competing for 100 identical cus. tomers. Each manufacturer chooses both the price and quality of its prod. uct, where each variable can take any nonnegative real number. Let p, and x, denote, respectively, the price and quality of manufacturer i's product. The cost to manufacturer i of producing for one customer is 10 + 5r. Note In this expression that the cost is higher when the quality is higher. If manufacturer / sells to g, customers, then its total cost is g, (10 + 5p). Each customer buys from the manufacturer who offers the greatest value, where the value of buying from manufacturer / is 1,000 + x - p; higher quality and lower price mean more value. A manufacturer's payoff is its profit, which equals g(py - 10 - 5x). If one manufacturer offers higher value, then all 100 customers buy from it. If both manufacturers offer the same value, then 50 customers buy from manufacturer 1 and the other 50 from manufacturer 2. Find all symmetric Nash equilibria