Adam Smith in his works like Wealth of Nations (WoN) talked predominantly about public sector which is non-profit although not private non-profit. Also Smith did not written much directly applicable to business management. He was writing an economics text, some of the economic insights could be applied in operation of business but he wasn't focusing on business administration at all.
In fact most of his work focused on the public sector. WoN consists of 5 books:
Book I: Of the Causes of Improvement in the productive Powers of Labour.
Book II: Of the Nature, Accumulation, and Employment of Stock.
Book III: Of the different Progress of Opulence in different Nations.
Book IV: Of Systems of political Economy.
Book V: Of the Revenue of the Sovereign or Commonwealth.
The books I - II lay out some basic economic principles. For example, book I talks about division of labor, origin of money, determinants of wages, profits and rents in the economy. Many of the insights discussed here are applicable to any organization (e.g. private non-profits and governments benefit from division of labor, and for planning its important to understand how wages or rents are determined in the economy since they have their own employees.
In the book II Smith discusses monetary economics and discusses the role of interest rates, capital accumulation and the distinction between productive and unproductive labor. The contents of book II can be again relevant to both for profit and non-profit organizations. Both for and non-profit organization accumulate capital and use loans. The discussions of monetary economics there were relevant for government institutions like central banks.
Book III is basically discussion of long-term economic growth that is mainly relevant for the public administration.
Book IV focuses on public policy with focus on trade. Here is where Smith critiques mercantilism and offers his trade policy prescriptions. Aside from the general concept of absolute advantage, which can be useful for any organization, this chapter is primarily about public policy.
Book V focuses on fiscal policy. In book V Smith discusses issues of taxation and government debt as well as some other matters of public administration.
Consequently, most of Smith's work (by my estimation about 3/5) is primarily useful or targeted at public sector, more specifically on how government should run country. Rest of the Smith's work is laying down some general economic principles that are equally applicable to any organization (e.g. division of labor). Some of the descriptions, such as how the rate of profit is determined will be inherently mostly applicable to for profit enterprises. However, only very small portion of WoN deals with a matters that are of interest only to businesses. Hence, most of what is written in WoN is applicable to public sector (which is part of the overall non-profit sector). However, aside from some timeless insights such as why division of labor is efficient or his repudiation of mercantilism, most the description of how the economy operate is out of date so it does not have that much insights for modern organizations, neither for or non-profit.
