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2. (35 points) A risk-neutral firm can perform R&D at constant and exogenously fixed intensity, which incurs a flow cost that is equal to c > 0. The value of successfully completing the research project is I' > 0. At each point in time, the firm must decide whether to continue the research or abandon it. Abandonment is irreversible. Research success is stochastic and described by a Poisson process, which makes the discovery time exponentially distributed: for research over a time period of , the probability of success is given by F() =1-e"", where 1 is the instantaneous probability of success, referred to as the hazard rate. The firm is unsure of how difficult the research is: it can be either easy or difficult. This is captured by the hazard rate being uncertain. With probability p it is equal to 1, (the research is easy) and with probability 1 -p it is equal to , 0. Assumption 2: AV-c 5. a) Interpret the three assumptions economically. b) Show that as time passes without the research being successful, the firm grows more pessimistic about its difficulty, i.e., that A () is a strictly decreasing function of f. b) As long as the R&D has not succeeded yet, the firm must at every point in time decide whether to continue the research or exit. The expected benefit of pursuing the R&D for another instance, di, is equal to 1 () I" , whereas the marginal cost of doing so is equal to c. What is the firm's optimal stopping time, ?", i.e., the time when it chooses to abandon the research? How do we know that this maximizes the firm's expected profit? c) How does the optimal time of abandonment, f, depend on the parameters of the model: V, c, p, 1 , and A, ? Explain the economic intuition