Consider the Hotelling model, in which there's a group of consumers of unit mass uniformly distributed over a city of length "1". Each consumer consumes at most one unit of good produced by firms and values it at "V". In addition, consumers have a total "transportation" cost equal to t * (x - x_i)², where "x" is the position of the consumer and x_i the position of the firm "i". Firms, in turn, produce at a constant marginal (MC) cost equal to "c" and have no fixed costs (FC).

A. If initially there were only one Firm "A" and it had to position itself at the left end of the city, i.e. at "a = 0", what would be the monopoly price it would charge if it were interested in serving all consumers. Determine also profits it would earn.

B. How does your answer A. change if the monopolist could locate the firm anywhere it wanted in the city without incurring any cost for moving the firm. Help: Monopolists would position themselves anywhere in a linear city that maximizes their utility.

C. Suppose now that, Firm "A" is located at a point determined in question B., a second Firm "B" appears, which is located at the far right of the city, i.e., where "b = 0" or equivalently "x = 1". This Firm "B" competes in price with Firm "A". Under these conditions, determine what equilibrium prices and profits of Firms "A" and "B" would be. Note: You must formally arrive at equilibrium prices, i.e., formula from memory doesn't work.

(Course: Microeconomics Level 2 - Imperfect Competition - Hotelling Model)