nh and A are concave and homogeneous of degree 1 (hence,

Note that preferences are well defined for all consumption bundles on or above the base indifference surface, but may not be well defined below this surface. This is so because (8) represents consumer preferences only if it is concave in price". But when u < 0, the first term in (8) is convex in prices and for sufficiently small values of u the convexity of this term will dominate the concavity of the second term, violating the fundamental regularity condition for consumer expenditure functions. Of course,

if the base indifference surface does not intersect the positive orthant, preferences are well defined globally.