My favourite definition of economics is the following one:
“— economics is the science which studies how scarce resources are employed for the satisfaction of the needs of men living in society: on the one hand, it is interested in the essential operations of production, distribution and consumption of goods, and on the other hand, in the institutions and activities whose object it is to facilitate these operations.” (Italics in original.)
This definition comes from page 1 of Malinvaude, E. (1972), Lectures on microeconomic theory, Advanced Textbooks in Economics Volume 2, North Holland Publishing Company, Scotland(translated by Mrs. A. Silvey).
One reason that I like this definition is that, in addition to emphasising the importance of scarcity, it actually goes on to discuss the types of questions that are addressed by economists. In particular, I like the fact that it mentions institutions.
As I see it, the key components of the subject matter of economics are:
1. The presence of scarcity;
2. The behaviour of individuals who are faced with scarcity;
3. The interaction of individuals who are faced with scarcity; and
4. The existence and operation of institutions to facilitate the interaction of individuals who are faced with scarcity.
Note that the presence of scarcity is the central defining feature of the subject matter of economics. In the absence of scarcity, economics would not exist. There would be no need for it.