1. Show that the ordering of market structures, established by Arrow with respect to their incentives for innovation, holds for drastic innovations as well as small ones.

2. From the text, the private values of an innovation under competition and monopoly are given by Vc and Vm , respectively. The change in total welfare, however, includes the gain in consumer surplus from the innovation. Let Sc and Sm be the gain in consumer surplus from innovation under competition and a monopoly.

For a linear market demand, p = a -bq, and an innovation that lowers the (constant) marginal cost of production from ch to cl shows that Sc ≥ 0 and Sm > 0. Consider both nondrastic and drastic innovations. (The marginal revenue to a monopolist is a - 2bq.)

Let the total welfare gain from the innovation be given by W = V + S. Compute expressions for W for both competition and monopoly.