Firm 1 is the incumbent in a market lasting two periods with inverse demand curve p=74 -9Q. Its first-period costs are C(q) =15 +20q and it faces entry in the second period by Firm 2, which has identical costs. There is an asymmetry between the firms, however, in that only Firm 1 has the option of investing $63.5 in R&D in the first period in order to reduce its second-period marginal costs to $2 per unit. Show that it would not be optimal for Firm 1 to make the investment if there were no threat of entry. Also show that it is optimal for Firm 1 to make this investment even though Firm 2 enters regardless.