Adding up constraints and gross substitution in portfolio models

We consider a static portfolio system that satisfies adding-up constraints and Tobin's gross substitution theorem. We show the relationship of the two conditions to the weak dominant diagonal property of the matrix of interest rate elasticities. This enables us to investigate effects of arbitrary simultaneous changes in interest rates on the asset demands. Finally, we show that all asset demands are invariant under a certain nonnegative, but nonzero, change of the interest rates.