Adoption Costs, Age of Capital and Technological Substitution

In this paper we introduce adoption costs in a vintage capital model. We assume that the incorporation of technological innovations into the production sector requires an extra labor cost during a fixed period. First, we show how adoption crucially matters in the shape of short run and asymptotic dynamics. Then, we analyze the consequences of adoption costs in technological substitution extending the model in two ways: we let adoption costs depend on the technical growth rate, and we endogenize them, depending on the technological gap. When adoption costs depend on the technical growth rate, the effect of growth on optimal lifetime of machines is indeterminate; the creative destruction effect can be compensated by the adoption effect, and faster growth rates delay the technological substitution. Finally, when adoption costs are endogenous, we recover the typical obsolescence effect in vintage capital models and show that technological progress has a negative effect on the technological gap.