Consider two firms selling a differentiated product, with demand functions qi = 12pi +pj for all firm i = 1,2 and j does not equal i. Firm 2's (the entrants) marginal cost is 0. Firm 1's (incumbents) marginal cost is initially 1=2, but if the incumbent invests a fixed amount I = 0:205, it acquires a new technology that reduces its marginal cost to 0.
(a) Consider the timing: The incumbent chooses whether to invest; then the entrant observes the incumbents investment decision; then the firms compete in prices. Show that in subgame perfect equilibrium (SPNE) the incumbent does not invest.
(b) Show that if the investment decision is not observed by the entrant, the incumbents investing is part of the equilibrium. Comment.
(c) describe why the conclusion in problem (a) may be affected if the entrant faces a fixed entry cost, F.
Does it matter whether the potential entrant makes its entry decision before or after the incumbents investment decision? (Just give the argument; you do not need to compute anything.)