The U.S. State Department's own inspector general appears to have called out the department for firstly, buying facebook likes through a $630,000 campaign; and secondly, getting duped by Facebook for having spent all that money when Facebook merely changed its policy so that being liked doesn't actually grant friends access to Foggy Bottom's social content feed. In essence, it may have had a communications strategy justifying the spend, but Facebook's policy change removed most of the benefits. (Thank goodness ad agencies don't have inspectors general.)
Some benchmark metrics: If you're a superpower with a two trillion dollar operating budget, you spend on average 32 cents per like. Engagement after that initial like hovered around 2 percent of "friends," making the U.S.'s cost per engaged reader about $15. After the September 2012 Facebook policy change, the State Department's social feed posts reached only a few tens of thousands of individuals without advertising, and a few hundred thousand with additional "sponsored post" advertising.