1.Intellectual Property (23 points)

Suppose n identical firms are racing to introduce the same innovation. The per-firm (fixed) cost of R&D is $100. 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 40% probability. All successful firms have equal chance of obtaining the patent. Assume for simplicity that the patent never expires. The discount rate is 10%.

(a)(7 points) What is the socially optimal number of firms investing in R&D? How many firms will invest in R&D? Please explain. To support your answers, complete the table below. That is for each n from 1 to 11, find the values of

Probability that at least one firm will succeed, ?(n)

Social value (expected discounted), S

Social cost

Net social value

Marginal value

Marginal cost

Patent value (the expected present value of the patent), ?

# of Prob. Social Social Net social Marg. Marg. Patent firms value cost value value cost value 1=50 0 0 UAWNE 12