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 ${\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}>0}$. 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: ${\displaystyle {\frac {\Delta {\text{demand}}(X)}{\Delta {\text{price}}(Y)}}\geq 0}$. I.e., the definition includes both substitute goods and independent goods, and only rules out complementary goods. See Gross substitutes (indivisible items).

References

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1. Polterovich, V.M.; Spivak, V.A. (1983). "Gross substitutability of point-to-set correspondences". Journal of Mathematical Economics. 11 (2): 117. doi:10.1016/0304-4068(83)90032-0.