The effect of immigration on host and origin countries is mediated by the way migrants take their labour supply decisions. We propose a simple way of integrating the traditional random utility maximisation model used to analyse location decisions with a classical labour demand function at destination. Our setup allows us to estimate a general upper bound on the elasticity of the migrant labour supply that we take to the data using the evolution of the numbers and wages of temporary overseas Filipino workers between 1992 and 2009 to different destinations. We find that the migrant labour supply elasticity can be very large. Temporary migrants are very reactive to economic conditions in their potential destinations.