Preferences and normal goods: An easy-to-check necessary and sufficient condition

We provide a necessary and sufficient condition for goods to be normal when utility functions are differentiable and strongly quasi-concave. Our condition is equivalent to the condition proposed by Alarie et al. (1990), but it is easier to check: it only requires to compute the minors associated with the border column (or row) of the bordered Hessian matrix of the utility function.