It is interesting to note that Adam Smith's one explicit use of the phrase "Invisible Hand" in his Wealth of Nations is not a situation in which the competitive market equilibrium is Pareto-optimal. It is of a situation with two market failures—a home bias psychological failure among the merchants of Amsterdam, and agglomeration economies for mercantile activity in Amsterdam. And the two offset each other: if merchants were rational, the free-market equilibrium would ternate an inefficient sacrifice the agglomeration economies. If the agglomeration economies were absent, psychological home bias would lead to an inefficient concentration of activity:

Glory Liu: How the Chicago School Changed the Meaning of Adam Smith’s ‘Invisible Hand’: "For Friedman and Stigler, economics’ scientific power came from its ability to predict outcomes based on two central insights... in The Wealth of Nations... self-interest... [and,] of course, the invisible hand.... Few economists were as successful as Friedman in spreading this interpretation of Smith’s ideas to the public... populariz[ing] this interpretation of Smith’s invisible hand for an overtly conservative political agenda.... What makes the Smith of Milton Friedman and George Stigler so... problematic... is that they 'economized' Smith in a way that obscured if not precluded the relevance of his moral philosophy and political theory.... Whether his political value stems from the idea that he is an economist or moral philosopher or something else, however, is something that we—Smith’s readers—get to decide...