A theoretical study is presented of multi-component isotope separation cascades. A theory is developed which leads to the multi-component analog of a two component ideal cascade. The multi-component analog is a matched abundance ratio cascade. Multi-component analogs are derived for value functions, separative work, and various relationships of importance in two component isotope separation cascade theory. The theory is applied specifically to the derivation of a multi-component cost formula which could be used to price U containing U/sup 236/. (This cost formula is derived merely as an illustration of the theory and no recognition or commitment on the part of the USAEC is implied.) The multi- component matched abundance ratio cascade does not minimize total cascade flow as does the two component ideal cascade. It is found, however, that for U isotope separation the total flow in the matched U/sup 235//U/sup 238/ abundance ratio cascade exceeds the minimum by an insignificant fraction for a wide range of U/ sup 236/ concentrations. (auth)