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In Lectures on Macroeconomics by O.Blanchard and S.Fisher (1993) stated that (the emphasize is mine):

Building a model that formally explains why money is used in transactions when it is dominated as a store of value has proved to be a difficult task. Consequently, most of the research has taken a shortcut and started with the assumption that money must be used in some transactions; this constraint is known as the Clower, or cash-in-advance, constraint.

But Macroeconomics by G.Mankiw (2012) mentions neither this difficulty nor Clower constraint.

So has this difficult task been solved and the model that formally explains why money is used in transactions when it is dominated as a store of value has been created?

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