This article studies the impact of a minimum wage on growth and on employment for an innovator country. It uses a standard endogenous growth model in open economy with a non traded services sector. Primarily, the key results indicate that a minimum wage speeds up growth proportionally to trade opening. A short econometric study on 12 OECD states for 1975-90 period confirms this conclusion. Secondly, in open economy, a minimum wage doesn't necessarily induce a strong unemployment increase because services may create jobs.