This paper extends the expanding-varieties growth model in a two-countries-two-goods setup, and describes the dynamics of growth rates and terms of trade when the industry-based economy is the innovation leader, while the tourism-based economy is the follower (i.e. increases the number of intermediate inputs by readapting innovations developed abroad). Two types of transitional dynamics may exist: technological catching-up and technological falling-behind. Contrary to the standard result, technological catching-up by the follower is associated with lower growth rates with respect to the leader, whereas terms-of-trade effects guarantee positive growth differentials for the tourism-based economy when the technological gap with the leader increases over time. The underlying principle of increased relative demand might explain the good economic performance observed in tourism-dependent economies.