We present a model for determining analytically the critical threshold for investment in carbon capture and storage technology in a region where carbon costs are volatile and assuming the cost of investment decreases. We first study a deterministic model with quite general dependence on carbon price and then analyse the effect of carbon price volatility on the optimal investment decision by solving a Bellman equation with an infinite planning horizon. We find that increasing the expected carbon price volatility increases the critical investment threshold and that adoption of this technology is not optimal at current prices, in agreement with other works. However, reducing carbon price volatility by switching from carbon permits to taxes or by introducing a carbon floor as in Great Britain would accelerate the optimal adoption of this technology. Our deterministic model provides a good description of this decision problem.