an idea can be represented by a triple (v, c, p), where v is the consumer surplus when the technology is competitively supplied, c is the cost of developing the idea into a technology, and p is the probability the firm fails to develop the idea into a technology. Suppose there are n firms joining a patent race, each with the same idea (10, 16, 0.45). The discounted time T=20 and pi =0.,25. Standard patent race assumptions apply.

a suppose n=5 calculate each firm's expected profit

b calculate the number of firms in the race at equilibrium