In the classical solution for an isotropic elastic wedge subjected to uniform tractions on the sides of the wedge, the stresses become infinite when the wedge angle equals to one of the critical angles. The paradoxon was resolved by \textit{J. P. Dempsey} [J. Elasticity 11, 1-10 (1981; Zbl 0492.73003)] and \textit{T. C. T. Ting} [Q. J. Mech. Appl. Math. 38, 245-255 (1985; Zbl 0559.73017)]. This paper considers a more general case in which the tractions are proportional to \(r^ n\), \(n\geq 0\). The uniform tractions considered by Dempsey and Ting correspond to \(n=0\). The paradoxon for \(n>0\) is resolved by employing the approach used by Ting in which a homogeneous solution is superimposed on a particular solution. The coefficient of the homogeneous solution is chosen in such a way that, at the critical wedge angle, the homogeneous solution tends to infinite just like the particular solution but with an opposite sign. The limit of the solution as the wedge angle approaches a critical angle exists. The solution, without taking the limit, is valid for the wedge angle close to a critical angle.