III. A monopoly firm, Firm C, has a constant marginal cost $2. A potential entrant, Firm D, is considering whether to enter into the market. Entry requires a fixed cost $f, with 0 < f < 1/2. By paying f, Firm D can enter into the market and offer the same product as Firm C at a lower (constant) marginal cost $1/2. (Firms have no other cost.)

There is only one consumer in the market, who purchases at most one unit of the product. The consumption value of the product is $4.

Consider the following game: Firm D first decides whether to spend f to enter into the market. If Firm D does not enter, then Firm C maintains its monopoly and charges the monopoly price; but if Firm D enters, the two firms engage in Bertrand competition and simultaneously offer a price to the consumer, who then makes the purchasing decision.

In this part of questions, note that: (i) A consumer does not face any budget constraint. He makes the purchasing decision to maximize consumer surplus; and if he doesn't buy, consumer surplus is zero. (ii) Upon indifference between the offer of the two firms, a consumer will buy from Firm D. (iii) Firm D will enter and make a sale as long as its profit is not strictly negative.