Gross substitution and complementarity are not symmetric relations

Abstract

I construct an example of well-behaved (convex, continuous, monotone) preferences over two goods, x and y, such that x is a gross substitute for y but y is a gross complement for x. A sufficient (but not necessary) condition for preventing this "pathology" is that the demand for either good be a strictly increasing function of income.Substitution; complementarity; consumer theory;