Why does fiat money have value? Or as Tobin (1992) put it: &quot;How Can Money Have Positive Value in Exchange?&quot;

Money, however, is an embarrassment to value theory. According to standard theory, something can have positive value only if it generates positive marginal utility in individuals’ consumption or positive marginal productivity in the making of goods and services that do generate marginal utility. The embarrassing puzzle is sharpest for fiat money. All of its value comes from the fiat that makes it money. Fiat money has no intrinsic non-monetary source of value. It cannot be eaten or worn or be used in any other way that generates utility for consumers, except a few numismatists. Nor can it contribute to the production of things that consumers do value. It can be produced at zero social cost. Yet it is a scarce commodity for any individual agent. Why is it worth anything at all? That the institution of money is of value to the society as a whole as a public good does not automatically give it value to individuals in market exchanges.

Is there today any consensus answer to the above question?
The answer, that can be found in greater detail in the following book

Rudolf Richter, Money — Lectures on the Basis of General Equilibrium Theory and the Economics of Institutions, Springer, 1989.

is quite simple. One has to create a positive marginal utility to the user. How one can achieve this aim? One has to create a positive demand for fiat money, which can be accomplished that taxes can only be paid with fiat money. Then it has a positive marginal utility, and the trick is done.