Productivity dispersion and output fluctuations: an evolutionary model

Abstract

We develop a model of technology choice with search costs. Innovators develop technology of varying quality or productivity. Firms acquire technology after paying a search cost to find high productivity technology. The resulting model has mixed equilibria with productivity dispersion. However, such mixed equilibria are unstable under the logit dynamic from evolutionary game theory. Instead, the economy converges to limit cycles, whose existence we verify numerically. We conclude, therefore, that mixed equilibria is not a robust explanation of productivity dispersion in our model. Instead, such productivity dispersion is a cyclical phenomenon. An additional implication is that cyclical productivity dispersion contributes to endogenous fluctuations in aggregate output.