3. Two firms produce a homogeneous good whose inverse market demand is given by p = 10 - Q where Q is the total output produced by the firms. The common and constant marginal cost of production is 2 per unit. The two firms act as Bertrand competitors, simultaneously announcing prices. The firm that announces the lower price then captures the entire market demand at the announced price. If both firms announce the same price, then they share the market demand equally. Suppose the two firms interact infinitely often. Firms discount future profits at rate 6. Derive the lower bound & such that for all o 2 8, the announcement of (pm, pm), (where pm is the price level that would be announced by a monopolist) can be sustained as a subgame perfect equilibrium of the infinitely repeated game. (10 marks)