Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.Which of the following statements are correct? I. If Firm A and Firm B invest, there is a 0.25 probability that Firm A will become a monopolist and make $20 in revenue.II. If Firm A and Firm B invest, there is a 0.25 probability that Firm A will become a duopolist and make $8 in revenue.III. If Firm A invests and Firm B abstains, there is a 0.5 probability that Firm A will become a monopolist and make $20 in revenue.IV. If Firm A invests and Firm B abstains, there is a 0 probability (i.e. it is impossible) that Firm A will become a duopolist and make $8 in revenue. A) I, II, III, and IVB) Only I and IIC) Only III and IVD) Only I, II and IIIE) None of the statements are correct
Firms A and B are contemplating whether or not to invest in R&D. Each has two options: “Invest” and “Abstain.” A firm that invests will invent product X with a probability of 0.5, whereas a firm that abstains is incapable of invention. Investment costs $6. If a firm doesn’t invent X, it makes $0 in revenue. If a firm invests and is the only one to invent X, it becomes a monopolist and generates $20 in revenue. If both firms invent X, each firm becomes a duopolist, and generates $8 in revenue. Revenues are gross figures (i.e. they are not net of investment costs), and there are no costs besides investments costs (i.e. no variable cost of production etc.). The firms are risk-neutral entities, and are uninformed of each other’s investment decisions.
Which of the following statements are correct?
I. If Firm A and Firm B invest, there is a 0.25 probability that Firm A will become a monopolist and make $20 in revenue.
II. If Firm A and Firm B invest, there is a 0.25 probability that Firm A will become a duopolist and make $8 in revenue.
III. If Firm A invests and Firm B abstains, there is a 0.5 probability that Firm A will become a monopolist and make $20 in revenue.
IV. If Firm A invests and Firm B abstains, there is a 0 probability (i.e. it is impossible) that Firm A will become a duopolist and make $8 in revenue.
A) I, II, III, and IV
B) Only I and II
C) Only III and IV
D) Only I, II and III
E) None of the statements are correct
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