3 2 stores, Techlegend and Cross Link, are selling homogeneous laptops and compete in price. Techlegend is the entrant, while Cross Link is the incumbent. There are 2 types of consumers, loyal consumers and disloyal consumers. Cross Link has several loyal consumers who are willing to purchase the laptop from Cross Link regardless of the price charged. The mass of loyal customers is denoted as n. The disloyal customers can search the price of Techlegend and Cross Link and buy the lowest one. If they do not search, the disloyal customers will buy one from Cross Link with a probability of or buy one from Techlegend with probability of. The mass of disloyal customers is 1. Let Pr denote price charged by Techlegend and Pc denote the price charged by Cross Link where PT S Pc as Cross Link has lower incentive to attract disloyal consumers. Cross Link cannot discriminate between loyal and disloyal consumers. The disloyal customers have search cost at, where t is the amount of time devoted to search activities and a is the opportunity cost of search. a is uniformly distributed over the interval [0,1]. Assume customers value the laptop at k. Write Down the expected utility of disloyal customer who search and the expected utility of disloyal customer who did not search. b. Find a of the indifferent consumer. Assume 0 cost of production for both Stores. Write down the profit functions of Techlegend and Cross Link. d. Solve for the equilibrium price maximizing Pand Pc a. c. 3 2 stores, Techlegend and Cross Link, are selling homogeneous laptops and compete in price. Techlegend is the entrant, while Cross Link is the incumbent. There are 2 types of consumers, loyal consumers and disloyal consumers. Cross Link has several loyal consumers who are willing to purchase the laptop from Cross Link regardless of the price charged. The mass of loyal customers is denoted as n. The disloyal customers can search the price of Techlegend and Cross Link and buy the lowest one. If they do not search, the disloyal customers will buy one from Cross Link with a probability of or buy one from Techlegend with probability of. The mass of disloyal customers is 1. Let Pr denote price charged by Techlegend and Pc denote the price charged by Cross Link where PT S Pc as Cross Link has lower incentive to attract disloyal consumers. Cross Link cannot discriminate between loyal and disloyal consumers. The disloyal customers have search cost at, where t is the amount of time devoted to search activities and a is the opportunity cost of search. a is uniformly distributed over the interval [0,1]. Assume customers value the laptop at k. Write Down the expected utility of disloyal customer who search and the expected utility of disloyal customer who did not search. b. Find a of the indifferent consumer. Assume 0 cost of production for both Stores. Write down the profit functions of Techlegend and Cross Link. d. Solve for the equilibrium price maximizing Pand Pc a. c