Equation (8) confirms the importance of these links to calculate the forward effect. Actually, the port production activated by its own demand in an ‘autarchic’ regime is given by (I−APP)−1, which is the driving force in equation (9). But this causes a spill-over effect on the rest of the economy that is greater the larger the matrix ANP is. Such increase in production activates, in turn, the remaining sectors, as expressed by Schur's matrix, S, whose inverse captures the total variation. The final effect is an increase in port service demand, unless the APN matrix is zero. The demand increase, in turn, increases the port output according to its integration measure captured by (I−APP)−1.