<p>The little monopolist in the city.</p><p>In the Circular City, which is located on a circular road around The Lake, there are N identical firms, located equidistantly along the road. The dwellers of the city have unit demands and they are uniformly located along the city. The typical Circularian has unit demand: he buys one unit from a firm only if the utility he derives from this purchase (U=1-p-0.5d, where p is the price and d is the distance between the consumer and firm) is greater than zero; otherwise he does not buy anything. Of course, if he can get positive utility by buying from more than 1 firm, he will buy from the firm that gives him the highest utility.<br/>The goods produced by the N firms are identical, The Circular Road has a length of 12 kilometers, the number of Circularians is normalized to 12, and firms have zero production costs.<br/>Assume that in equilibrium each firm behaves as a monopolist (there are so few firms that they do not actually compete with other — the monopolistic region of Salop’s model).<br/><strong>a.</strong> If a firm charges a price P, how much it will sell?<br/><strong>b.</strong> What is the optimal price a firm should charge?<br/><strong>c.</strong> How much profit would a firm obtain?<br/><strong>d.</strong> What is the maximum number of firms consistent with the monopoly assumption?<br/><strong>e.</strong>
                <em>In the long run, when there is free entry and exit, it is not possible that these firms operate as monopolists, indifferent of the size of the fized costs. </em>Can you provide an argument for this assertion? </p>