The Balassa-Samuelson effect ("BS effect") has attracted attention as a theory to explain the stagnation of the Japanese economy over the past 30 years. In particular, it has been used to explain the long-term depreciation of the real effective exchange rate since 1995. Furthermore, macroeconomic data show that the BS effect explains well Japan's long-term economic stagnation. However, the BS effect was originally derived theoretically for small open economies, not for large economies like Japan. In other words, the BS effect cannot be theoretically applied to large economies. This is a serious problem in applying the BS effect empirically. In this paper, we embed Balassa-Samuelson's original argument into the optimal growth theory framework. That is, we set up an optimal growth problem for large countries. It is then shown that there exists a stable optimal steady state and that the BS effect is more directly valid in that optimal steady state. In other words, as a long-run property, the BS effect is applicable to large as well as small countries, although, contrary to the small open economy case, it does not depend on the capital shares of the two sectors.