Previously in this series: Menger on Orders of Goods
Let's say you are out camping, and you would like a fried egg. The fried egg would be a consumer's good, or good of the first order. But in order to get a fried egg, you'd need the following second-order goods: a raw egg, some oil, a pan, and a fire. These second-order goods are "complementary" to each other. Since they are all needed to create the first-order good: there are "complementary goods". If any one of those complementary goods were unavailable, the other three would lose their goods-character regarding the creation of the fried egg; you'd end up with either hot oil, a charred egg stuck to the pan, completely incinerated egg and oil, or a raw egg stewing in oil. Unless there is an alternate use for these complementary goods, they would stop being goods altogether. For example, the fire and the pan might retain its goods-character if they could be used to cook other things. If there's no other food you want to fry, then the oil would lose its goods-character entirely. And course the raw egg would no longer be a good, unless you were starving (or a body builder).
As Menger puts it, "the goods-character of goods of higher order depends on our being able to command their complementary goods".
Of course, you need wood to make the fire, as well as a match (let's assume you don't know how to start a fire without one). The wood and the match, then, are goods of the third order; and they are complementary goods to each other. In the third order, just as in the second order, the two complementary goods depend on each other for their goods-character regarding the fried egg. But now there is a new type of condition. The third-order match and wood also depend on the second order pan for their goods-character regarding the fried egg. If the fried egg is the match's and the wood's economic purpose, and the fried egg is impossible for want of the pan, then the match and the wood loses all its purpose. Even though the pan is in a different order than the match and the wood, it is still a complementary good to those two.
Next in this series: Higher Ground via Higher Orders