Tony has two uses for milk: to complement regular coffee and to complement espresso. When he drinks coffee, he uses just a splash of milk. When he makes espresso, he steams nearly a cup of milk to go with the drink. Because he uses so much more milk with his espresso, a price increase in milk causes Tony to consume more coffee and less espresso. Are coffee and milk complements or substitutes?The answer is substitutes. If this surprises you, you're probably not alone. This is a tricky question that exposes the way that economists define complements and substitutes.
Although we loosely describe complements as goods that are "consumed together," that's not the definition of complements that you'll see in a microeconomics text. Two goods are complements when an increase in the price of one leads to a decrease in demand for the other. This definition is roundabout, but it is best way to know what we really mean by the word complements.
After all, our grocery basket includes a lot of goods when we exit the store. For all the grocer knows, you will drink that bottle of wine while eating the Lean Pockets with the ketchup and mustard that you bought. Yet, it is unlikely that all of those goods are complements with one another. A clearer example is hamburger and rib steaks. I might buy both in my weekly shopping trip, but for me, they're likely to be substitutes (especially for low enough price of rib steaks).
This isn't merely a pedantic point. An economist with data on prices and quantities needs a definition of complements that can be observed in the data. The economist (like the grocer) doesn't get to see the consumer put ketchup on his Lean Pockets before he eats, but he can see what happens to Lean Pocket demand when the price of ketchup goes up.
Back to the question I posed, why are milk and coffee substitutes for Tony? As the price of milk increases, Tony will consume more coffee as a means of substituting away from milk consumption. They are substitutes that are consumed together.