Cоnsider twо grоceries selling honey crispy аpple in а lineаr avenue city. The avenue starts from 0 miles to 10 miles. Two groceries are located in the each of the end from a miles and b miles. Apples in both firm share the identical inherent utility () for consuming one box of the good. Consumer's utility is consisted of paying a price for it (where can be either 1 or 2, depending on which firm they are buying from) and incur in a quadradic adjustment cost (disutility) of when deviating from their favorite type. So, gross consumer surplus is Consumer types are identified with the distance from point 0 as miles. In every point between 0 and 10, only single consumer lives. Suppose firms’ cost functions are as follows: and . a) (5 points) What is the demand function for each firm? Provide a clear expression. b) (5 points) What is the optimal price that each firm will set? c) (5 points) What are the profits for each firm?