In a truly free market, will prices tend to go down over time?
And is that a really good thing?
Monetary Deflation: Really That Bad?
Deflation Isn't Always Dangerous (article by my professor)
Questions about Deflation
Why deflation is good?
Also, here's an abridged version of Prof. Salerno’s assessment using a specific case, and his full paper is "An Austrian Taxonomy of Deflation" (PDF) and there's also
An Austrian Taxonomy of Deflation—With Applications to the U.S. [PDF]
I think it's impossible to answer this question. There could be periods of inflation and periods of deflation. Fluctuations in the value of money, however, would be far more moderate in a free market in money production than in the current system because money production is costless in the current system. In a free market in money production, the production of money would be rationalized by prices just like production in any other sector.
One thing we can be sure of is that the supply of money would not remain fixed. As the purchasing power of money rises (deflation), the profits to be earned from money production increase and production and new investment in the money production sector must, therefore, increase. Inflation would cause the money commodity to be converted from its monetary form back into its commodity form until the supply of money is balanced with the reduced demand for money.