Economies of scale in innovations with block-busters

D. Sornette

Quantitative Finance, 2002, vol. 2, issue 3, 224-227

Abstract: Are large-scale research programmes that include many projects more productive than smaller ones with fewer projects? This problem of economies of scale is relevant for understanding recent mergers, in particular in the pharmaceutical industry. We present a quantitative theory based on the characterization of distributions of discounted sales S resulting from new innovations. Assuming that these complementary cumulative distributions have fat tails with approximate power law structure S-α, we demonstrate that economies of scales are realized if and only if α<1. 'Economies of scale' is here understood according to the criterion that the probability to earn more than any fixed factor proportional to its size N is larger for the merged company C=A+B of size NA+NB than for any of the two component companies A and B with size NA and NB. In essence, the mechanism underlying the 'economies of scale' is that a very large payoff from a successful project can pay for all of the losing projects. Some empirical evidence suggests that α≅2/3 for the pharmaceutical industry. This could provide a simple rationalization for recent mergers or alternatively for portfolio diversification since the same effect could also be achieved in part if each firm held shares in all of its competitors.

Date: 2002
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DOI: 10.1088/1469-7688/2/3/305

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