Problem 1. Consider a Salop model with a unit mass of consumers uniformly distribu uted over a circle of circumference 1 km. Each consumer wants to buy one unit of a homogeneous good, which they value at R. Four firms sell this homogeneous good at locations that correspond to 12 o'clock, 3 o'clock, 6 o'clock and 9 o'clock. These loca- tions are fixed and cannot be changed. The production costs are zero. Consumers face quadratic transportation costs: they incur d' for every d units travelled. Assume R is large enough in all configurations to ensure that the market is fully covered. a. Calculate the optimal prices and the resulting profits in a symmetric equilibrium when all four firms are active. Carefully explain your derivation and provide economic reasoning where necessary. [8 marks] b. Suppose now that each firm faces a fixed operating cost of F > 0. For which values of F all four firms are able to earn enough profits to cover their operating costs? For which values of F only three of the firms are able to earn enough profits to cover their operating costs? For which values of F only two of the firms are able to earn enough profits to cover their operating costs? Carefully explain your derivation and provide economic reasoning where necessary. [20 marks]