Gross substitutes

The term gross substitutes is used in two slightly different meanings:
 * 1) In microeconomics, two commodities $$X$$ and $$Y$$ are called gross substitutes, if $$\frac{\Delta \text{demand}(X)}{\Delta \text{price}(Y)} >  0$$. I.e., an increase in the price of one commodity causes people to want strictly more of the other commodity, since the commodities can substitute each other (bus and taxi are a common example).
 * 2) In auction theory and competitive equilibrium theory, a valuation function is said to have the gross substitutes (GS) property if for all pairs of commodities: $$\frac{\Delta \text{demand}(X)}{\Delta \text{price}(Y)}\geq 0$$. I.e., the definition includes both substitute goods and independent goods, and only rules out complementary goods. See Gross substitutes (indivisible items).