4. Strategic behavior: advertising An incumbent (Firm 1) decides how much to invest in advertising in the first stage. The advertising investment becomes publicly known after it has been chosen. In the second stage, a potential entrant (Firm 2) may decide whether to enter the market or not. If it does not, Firm 1 remains the monopoly. If it enters, then it competes with Firm 1 in Bertrand manner, i.e., they set prices simultaneously. Consumers view Firm 1 and 2's goods as imperfect substitutes. If both firms are present, each firm's demand is given by 91 (P1, P2) = 10+ A2P1 P2 92 (P1, P2) = 10-2p2+ P1 where A is the advertisement expenditure Firm 1 invests in the first stage. The cost of A units of advertisement is A/2. The common marginal cost of production for the goods is $1. To enter the market, Firm 2 has to invest in a fixed cost f = 20. In the event that the market has only one firm, then the monopoly demand is 91 (P1, P2) = 14+ A - P. (a) For parts (a) to (e), suppose Firm 2 enters the market. Compute the Bertrand equilibrium in the subgame that follows advertisement level A. Denote the Bertrand equilibrium by (P1 (A), P2 (A)). (b) Does advertisement expenditure make Firm 1 tough or soft? Why? (c) Suppose Firm 1 plans to accommodate Firm 2's entry. What is the optimal level of adver- tisement A*? Check that Firm 2 indeed finds it profitable to enter the market in the second stage following advertising level A*.