Abstract: Based on the spatial organizational structures of the regions bordering the provinces of China, I build a mathematical model of economic performances for N-dimensional border-regions (i. e.,the regions bordering N provinces)and find that, for a given region with the same conditions of geography and technology, the largest output (F_N^*)of a Ndimensional border-regional system will not exceed that of a N-1-dimensional border-re-gional system, i, e., F₁^*≥F₂^*≥…≥F_N-1^*≥F_N^* Using the model, I present a quantative method to calculate the effect of "administrative borders" on the regional economic development and the application of it in the agricultural system of the region bordering Shanxi, Hebei, Shandong and Henan provinces. The main results show that the potentials for economic development have not been fully utilized and that the annual gross products of the border-region decrease by 10.4% due to the 4-dimensional borders.