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Suppose n identical firms are racing to introduce the same innovation. The per-firm (fixed) cost of R&D is $50. R&D occurs at time t = 0. Assume for simplicity that if the innovation is developed at t = 0, then society benefits in all later periods; but if the innovation is not developed at t = 0, then research does not take place in subsequent periods. If one firm invests in R&D, it will succeed with 25% probability. Assume for simplicity that all successful firms have equal chance of obtaining the patent, and the patent never expires. The discount rate is 10%.

1. What is the expected present value of the patent when five firms invest in R&D? Will five or more firms invest in R&D? Explain.

2. How many firms will invest in R&D? Explain. Note: To support your answer, you can calculate the expected present value of the patent for n = 1, ...6 in Excel.

3. Suppose two firms invest in R&D. What is the expected discounted social value over lifetime? What is the net expected discounted social value over lifetime?