x = f(p, q) Demand function for product A y = 8(p, q) Demand function for product B The variables x and y represent the number of units demanded of products A and B, respectively, at a price p for 1 unit of product A and a price q for 1 unit of product B. Normally, if the price of A increases while the price of B is held constant, then the de- mand for A will decrease; that is, fp(p, q) 0. Similarly, if the price of B increases while the price of A is held constant, the demand for B will decrease; that is, gg(p, q) 0. Reasoning simi- larly for complementary products, we arrive at the following test: Test for Competitive and Complementary Products Partial Derivatives Products A and B fa(p. q) > 0 and gp(p, q) > 0 Competitive (substitute) fa(p, q)