Here are a few definitions of economics (in chronological order):
Jean-Baptiste Say (1803): the science that treats the production, distribution, and consumption of wealth.
John Stuart Mill (1844): the science which traces the laws of such of the phenomena of society as arise from the combined operations of mankind for the production of wealth, in so far as those phenomena are not modified by the pursuit of any other object.
I guess following that definition the pursuit of altruism or fairness motives could not be studied in economics…unless you make them appear as a long-run income maximisation strategy.
Alfred Marshall (1890): a study of mankind in the ordinary business of life; it examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of wellbeing. . . . Thus it is on the one side a study of wealth; and on the other, and more important side, a part of the study of man.
Lionel Robbins (1932): “the science which studies human behaviour as a relationship between ends and scarce means which have alternative uses.”
Milton Friedman (1940’s): the science of how a particular society solves its economic problems, where an economic problem exists whenever scarce means are used to satisfy alternative ends”
Campbell McConnell (1960): the social science concerned with the problem of using or administering scarce resources (the means of producing) so as to attain the greatest or maximum fulfilment of our unlimited wants (the goal of producing).
Gary Becker (1976): the combined assumptions of maximizing behaviour, market equilibrium, and stable preferences, used relentlessly and unflinchingly, form the heart of the economic approach as I see it.
Ronald Coase (1977) the study of the social institutions that bind together the economic system which includes firms, input and output markets, and the banking system
(David Colander, 2006): the study of how human beings coordinate their wants and desires, given the decision-making mechanisms, social customs, and political realities of the society.
As the authors write, “at a time when economists are tackling subjects as diverse as growth, auctions, crime, and religion with a methodological toolkit that includes real analysis, econometrics, laboratory experiments, and historical case studies, and when they are debating the explanatory roles of rationality and behavioural norms, any concise definition of economics is likely to be inadequate.”