Suppose there are two firms selling a homogenous good, which can be produced with a constant marginal and average cost of 1. The two firms are located at either end of a line of unit length, [0, 1]. Consumers are uniformly distributed over the line with mass 1. Denote x as the position of a consumer from the start of the line at position 0. Each firm can set a price p,- where i E {1,2}. If the consumer purchases from firm 1 then the utility of the consumer is given by: u = r p1 4x If the consumer purchases from firm 2 the utility of the consumer is given by: u = r p2 4 + 4x Each consumer purchases 1 unit so long as their utility is non-negative from whichever firm gives them the highest utility and othenNise does not purchase (for a utility of zero). i) Characterise the prices and profits of the two firms at equilibrium for the case where r = 8. [30 Marks] ii) Describe how your answer would change in the case where r = 6. [20 Marks]