When can it be not optimal to adopt a new technology? A viability theory solution to a two-stage optimal control problem of new technology adoption

SUMMARY

Politicians often deplore economic agents’ behaviour when they do not accept new technologies. For a new technology to be adopted, the new technology value function needs to dominate the old technology value function. If this is the case, a technology switch will occur. We characterise the value functions, without computing them, using the fact that their hypographs are viability kernels of some auxiliary control problems and study whether the graphs intersect. If they do not, the corresponding value functions do not dominate each other, and the switch cannot occur at a positive time. Using this characterisation, we analyse a technology adoption problem and show how to recognise the models, for which the switch will occur at time zero or never, without solving an optimal control problem. We conclude that the current control regime may not change if the economic agents’ preferences are modelled as an integral of discounted differences between a reward from the flow variable (control) and a penalty from the stock variable (state).Copyright © 2011 John Wiley & Sons, Ltd.