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The least productive agents in an economy can be vital in generating growth by spurring technology diffusion. We develop an analytically tractable model in which growth is created as a positive externality from risk taking by firms at the bottom of the productivity distribution imitating more productive firms. Heterogeneous firms choose to produce or pay a cost and search within the economy to upgrade their technology. Sustained growth comes from the feedback between the endogenously determined distribution of productivity, as evolved from past search decisions, and an optimal, forward-looking search policy. The growth rate depends on characteristics of the productivity distribution, with a thicker-tailed distribution leading to more growth.
Perla et al. (2014) studied this question.