An analytic expression for the escape yield of a radical pair (RP) in a micelle under high magnetic fields is derived by the supercage model. This model is a two time scale model which divides the time evolution into two consecutive stages. The short time stage describes the initial separation of the partners of the RP, and the magnetic field dependence of the recombination yield can be described by the usual radical pair theory of freely diffusing radicals. The decay of a quasi-equilibrium during the second stage is described by rate equations for the spin density matrix, which for well-defined conditions can be reduced to a set of equations for the diagonal elements of the density matrix in the basis of true eigenstates of the Hamiltonian of the free radicals. In the present work we examine the applicability of the high-field limit of this approximation, which is closely related to the kinetic approach of H. Hayashi and S. Nagakura (Bull. Chem. Soc. Jpn. 1984, 57, 322). General analytic expressions for the magnetic field and relaxation dependence of the recombination yield during the second stage and for the decay constants are derived. The decay constants derived by H. Hayashi and S. Nagakura agree with our results. We show that the contribution from the first stage is significant and how it can be included.