A Grossman-Helpman-Romer-type (Grossman and Helpman in Innovation and growth in the world economy, 1991; Romer in J Polit Econ 98:71-102, 1990) endogenous-growth model is developed in this study. This model has two countries in which there are knowledge spillovers that are partially local. Owing to these spillovers, the innovation costs in a particular country decrease as the number of firms locating in both that country and the other country increases. If international knowledge spillovers are symmetric, the innovation sector is in the country with the larger market. However, if international knowledge spillovers are asymmetric, the innovation costs may be in the small-market country. When innovation costs are lower in the country with a large market, the growth rate increases with a reduction of transportation costs. However, when innovation costs are lower in the country with the smaller market, the growth rate decreases with a reduction in transportation costs.