Following up on the answer posted by Řídící several days ago, I note that shrinkflation appears in Jan Pen, Among Economists: Reflections of a Neo-classical Post Keynesian (1984) in the following context [combined snippets]:
The forgetfulness also occurs among conservative politicians who believe that a gradual rise in P means a deadly threat to prosperity; inflation must be combated with a tight money policy. The combination of both views leads to continued wage inflation and monetary retaliation – a combination that is extremely bad for everyone's real income. In this way stagflation is promoted, and shrinkflation may be the result of it. It is this enumeration of fallacies that we, as economists, should combat. On logical grounds, but with a view to the political consequences. These consequences have manifested themselves above all in the United Kingdom, and it is therefore no wonder that concerned British economists, such as James Meade, Frank Hahn and Amartya Sen, warn against the policies that are based on a short-sighted Falsches Bewusstsein. It is going too far to regard stagflation as a consequence of false reasoning , but wrong thinking does encourage this state of affairs (2).
Here shrinkflation appears in the context of stagflation—the economic condition in which a nation's gross domestic product is stagnant while inflation reduces the value of its currency; evidently, the author views shrinkflation as the next-order problem beyond stagflation, one in which GDP actually shrinks even as the currency loses value.
A similar notion appears in Brian Domitrovic, Econoclasts: The Rebels Who Sparked the Supply-Side Movement and Restored American Prosperity (2009):
The American economy took a curious route during the first several years after 1945. Policymakers wanted to avoid a recurrence of the domestic experience of the 1930s, whatever the international monetary implications. However, for the three years following 1944, the economy shrunk by 13 percent. Accompanying this was not deflation, as in the 1930s, but the reverse. Inflation exploded. Price controls set during the war were lifted, and from 1945 to 1948 the consumer price index shot up 34 percent, a stunning total for a three-year period and exceeded ion peacetime only by the worst years of the long 1970s. Following World War II, the United States traded depression for an acute period of stagflation. Actually, it was "shrinkflation," in that the economy was contracting as prices surged.
Shrinkflation was a puzzling experience. It confounded the president, Harry Truman. And yet shrinkflation did play into the government's hands in one way. It enabled the national debt to be cut down.
Shrinkflation in the sense of making products smaller without lowering their price seems to have emerged in the middle 2010s. Philip Kotler, Gary Armstrong & Lloyd Harris, Principles of Marketing (2019) cite an article from 2015 that conveniently includes in its title a brief definition of the term as the authors use it:
Conor Pope, 'Shrinkflation: when products get smaller but the prices don't', The Irish Times, 27 April 2015
That article mentions the word twice in its main text, as follows:
While the amount of biscuit on a Brunch [ice cream bar] is, in the grand scheme of things, not the most important development in the world, it does lead us on to something more insidious, which is happening to many products beloved of Irish consumers: shrinkflation. The term describes a now common practice among big-name manufacturers to shrink the stuff they sell us while keeping the price high.
Which? [a British consumer group] is acting on behalf of British consumers. Of course, similar practices are widespread in this jurisdiction, where we deal with the same levels of shrinkflation and baffling – and sometimes misleading – offers. When price discrepancies are highlighted by Pricewatch readers, retailers usually describe them as a one-off or an error.
This occurrence of shrinkflation is about half a year younger than the one[s] in the article "Paying More for Less: Time for 'Shrinkflation'," in the [Santa Ana, California] Orange County Register (September 7, 2014), cited in toyboat's answer, but I don't have access to the content of the Orange County Register article, so I can't tell whether it treats shrinkflation as a home-grown U.S. term, a British import, or something else.
Timothy Fay, Suburban Dictionary: The Subtle, the Funny, and the Snarky: A Slang and Sarcasm User's Guide (2019) offers this appreciation of shrinkflation in the more recent sense:
shrinkflation: A mostly British term for shrinking quantities when buying items at the supermarket. Common in the US are cereal boxes with much less cereal but with a price that's the same or higher. Also common are foil bags of coffee, which have shrunk first from sixteen ounces to twelve ounces and are now sometimes ten ounces. After a period of shrinkflation, the manufacturer often reintroduces a special "maxi size" option at twice the price, which usually turns out to be the same size as the original packaging.
This seems fairly accurate to me. I became aware of this incredible-shrinking-product-for-the-same-low-price gambit in the 1960s, when candy bars got smaller without costing less (or more), followed in due course by higher-priced "extra-large" versions that were the same size as the original product. So the phenomenon is not new, although the British slang term is (relatively speaking).
Meanwhile, the original economists' sense of shrinkflation as "one step beyond stagflation in a nation's progress toward economic disaster" seems to have gone by the boards in recent years, perhaps because for several decades there was little occasion to apply it to present-day economies in English-speaking countries.