Studying the properties of a qua si additive model of preference aggregation

For continuous, double differentiable, devoid of singular points, linear (strictly convex, strictly concave) conditional utility functions with constraints on the magnitude of quasiadditive untility function coefficients $k_1$ and $k_2$ the necessary and sufficient conditions are obtained under which the attitude of the decision maker to risk in terms of each separate factor is extended to the entire set of outcomes $X=X_1\times X_2$.