Consider a market in which firms 1,……., N set simultaneously capacities for a homogeneous product and afterwards a third party, which observes market demand and the capacity choice of each firm sets the market clearing price. Suppose that inverse demand is linear and of the form P (q) = a - q, where p is the price, a a positive constant, and q aggregate output, 

q_i is the quantity sold by firm i. Suppose that firm i has constant marginal costs of production c_i (firms have different marginal costs!). Suppose that a > max {c₁,….., c_N}. Suppose furthermore that the parameters of the model are such that each firm produces positive output. Solve for the Nash equilibrium where capacity is the strategic choice of the firms. Determine aggregate output and price level in equilibrium. Determine the output of each firm i.