N evenly-spaced firms with MC = c competes in prices on a circular city. Each consumer has unit demand, and receives utility of v - p - tz2 if she buys from a firm located a distance of z away at price p.

a. Assume v is sufficiently high that all consumers are served in equilibrium. Find the equilibrium price and profits for each firm.

b. Assume v is sufficiently low that not all consumers are served in equilibrium. Find the equilibrium price and profits of each firm.

c. What condition that relates v, t, and c must hold in order for all consumers to be served in equilibrium.