This paper investigates the incentive for developing adaptation technology in a world with changing climate within the directed technical change framework. Consistent with the market size effect, we show that technological change will tend to be biased in favour of the sector that employs the greater share of the work force over time, when the inputs are sufficiently substitutable. An economy with dominant climate sensitive sector can maintain sustained economic growth if it is capable of undertaking frontier innovations in the form of adaptation technology that increases the productivity of the inputs employed in the climate sensitive sector.