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the following information relates to questions 8 and 9. Assume
that there exists an unlimited number of different approaches to
developing a new drug, each costing $1. The probability that the
drug will be discovered by at least one of the approaches is
increasing in the number of approaches undertaken. In particular
the probability is given by:

P = 1 – e-0.5085*n

where n is the number of approaches undertaken.

If the drug is developed, it will generate total surplus if

From a social welfare perspective, how many research approaches
should be undertaken? Hint: define the expected social gain as the
probability (P) multiplied by $25 and the cost as being the number
of approaches (n) multiplied by $1. Use calculus to find the
optimal value of n, i.e. maximize the function expected gain minus


Now assume that each research approach represents a separate
firm that might join the “race” to develop the drug. If firms make
their entry decisions individually, how many firms will enter the
race to develop the drug? Assume firms will only join the race if
the expected payoff exceeds the cost of entering, which is still $1
per firm. Assume that the winning firm obtains the entire $25
benefit. Hint: the solution to the equation in which expected
social gain divided by n equals 1 is n=25.