One of the reasons why Friedman defended having a central bank that controls the currency, against proponents of a gold standard, was because he saw in the gold standard a significant cost to the market in utilizing it. There are extraction costs, for instance, to take the gold out of the ground. Friedman concluded that if under a gold standard the quantity of gold will grow by approximately 3% per annum, there is no reason why we could not have something grow by a similar 3% per annum at a lower cost (like paper currency) without the gold at all.
In a 1986 paper in the Journal of Political Economy called "The Resource Cost of Irredeemable Paper Money," Friedman writes:
In earlier discussions, other monetary economists and I took it for granted that the real resource cost of producing irredeemable paper money was negligible, consisting only of the cost of paper and printing.In this manner, Friedman admits that when determining the cost of a paper standard in contrast to a commodity standard, his analysis of cost was based on solely the cost of creating the money (and in fact he is correct that printing paper is cheaper than mining gold). But what Friedman overlooked, and admits as much, were the other costs to society of using the paper rather than using the gold (this error that he made is a basic economic fallacy first explained by the economist Frederic Bastiat, called "the seen vs. the unseen"). He continues:
Experience under a universal irredeemable paper money standard makes it crystal clear that such an assumption, while it may be correct with respect to the direct cost to the government of issuing fiat outside money, is false for society as a whole and is likely to remain so unless and until a monetary structure emerges under an irredeemable paper standard that provides a high degree of long-run price-level predictability.Friedman is saying that our experience with a paper money standard has shown that the price level is far from stable and/or predictable, the way that it was for decades in the 19th century under the gold standard. As a result of this instability and unpredictability, there are costs to the economy that he did not originally consider. And since the costs to the economy of a paper money standard might be greater than those of a commodity standard, one of the main reasons why Friedman originally supported the paper money standard, vanishes.
Unlike Keynes whose refutation of his own work was never explicit, Friedman eventually realized the error of his ways. It is true that Friedman still adamantly opposed returning to a gold standard (I believe mostly for practical reasons), but at least he came to some sort of realization that the free market alternative is beneficial in ways that are not even apparent at first glance (something I might arrogantly argue he, of all people, should have realized at the outset). To that extent one could say that by the end of his career, Milton Friedman truly had a better grasp of how the free market functions than he did during the majority of his career. If only this could be said of all economists, some of whom unfortunately reveal that they can't tell the difference between a free market and a managed economy, blaming the former for a crisis that occurred as a result of the latter.