Suppose that instead the procedure is to posit that the government would like to purchase a certain quantity of tanks using money creation, and then describe what happens to the rate of money creation and the rate of price inflation during the adjustment process. Ignoring that the short run elasticity of supply of tanks is likely to be lower than the long run, and assuming there is already some kind of market for tanks, it would be possible to imagine that the government purchases the needed number of tanks at their current market price. Because the money is spent before it has lost any purchasing power, the government gets a bargain.
Interestingly, this traditional Austrian argument that those receiving the money relatively early, before prices have risen, benefit, can be related to a joint effect of the disequilibrium and public finance effects of inflation. If the quantity of money rises faster than prices, the real quantity of money rises. That is an increase in the base of the inflation tax. A given revenue can be generated with a lower tax rate if the base is larger. Again, leaving aside problems with short run price elasticity of supply of tanks, a smaller rate of money growth is needed to purchase the needed quantity of tanks if the expansion of the quantity of money creates an excess supply of money.
Of course, any such excess supply of money will be ephemeral. And once the real quantity of money has adjusted to the real demand to hold money, the base is smaller and so a greater rate of money growth and price inflation is needed to obtained the desired number of tanks.
But the process doesn't stop there. Price inflation makes holding real money balances more costly, and so, the demand for real money balances falls. This raises the rate of money growth and the rate of price inflation needed to obtain sufficient real revenue to purchase the desired number of tanks.
And so, we see at least two reasons why obtaining the desired number of tanks requires that the government expand the rate of money growth and so the rate of inflation. However, in the end, we are left with the same inflation calculated from the long run elasticities of supply and demand for tanks and the elasticity of demand for real money balances with respect to the inflation rate. That inflation rate and the tank purchases can persist as long as money holders/taxpayers put up with the program.
Mises on the other hand, was constantly drawn to describing a process by which the rate of money creation and price inflation must rise higher and higher until the demand for real money balances falls to zero, and money has no value. Where did he go wrong?
The "laffer curve" may be a subject of some derision, but it is an implication of basic public finance. Tax revenue is found by multiplying the tax rate by the tax base. And typically, the tax base is negatively related to the tax rate. A low rate then, allows for a high base but a low revenue. A very high rate that results in a very low base and also a low revenue. There should be some intermediate tax rate that results in some intermediate base that generates the maximum amount of revenue.
Applying this concept to the inflation tax, a low inflation rate results in a very large demand for real money balances, but the low rate and high base generates a low revenue. A very high inflation rate results in in a very low demand for real money balances. The high rate and low base also generates a low revenue. At some intermediate inflation rate and some intermediate level of real balances, the maximum revenue is generated.
Assuming that the inflation tax is earmarked to the purchase of tanks, the maximum revenue that can be generated by the inflation tax, along with the price elasticities of supply and demand determines a maximum quantity of tanks that the government can purchase from the inflation tax.
Suppose that the government decides to use the inflation tax to purchase a number of tanks that is greater than that maximum? Suppose that the government can obtain that number of tanks in the short run because of the increase in the tax base resulting from a temporary excess supply of money, or else, because the demand for real money balances only gradually responds to the higher cost of holding balances. The short run elasticity of demand for real money balance with respect of inflation becomes more elastic over time.
The rational expectations equilibrium for this scenario is that money loses all value and the government purchases absolutely no tanks using the inflation tax. However, it is possible to imagine a gradual process by which the government obtains a large amount of tanks initially, but that it as it raises the rate of money creation and inflation to try to continue this volume of purchases, inflation becomes higher and higher, and the real demand for money falls, until this futile process results in money having no value.
Mises, of course, didn't describe this in the context of the use of the inflation tax to purchase tanks. Rather, he described it in terms of the use of money creation to lower real interest rates. The reason to lower interest rates was to stimulate the production of capital goods. Or mpore precisely, to shift production of consumer goods to the more distant future. Rather than think about how a particular rate of money creation would impact the composition of demand and the allocation of resources, the assumed rate of money creation is allowed to vary to maintain the desired impact on real interest rates and the demand for capital goods.
If the only process at work is the creation of an excess supply of money, then no persistent impact is possible. But even including the public finance effect, if the initial size of the targeted change in real interest rate and the demand for capital goods is beyond what can be stimulated by subsidies funded by the maximum revenue that can be generated by the inflation tax in the long run, then a futile effort to raise the inflation rates to maintain the effect on interest rates and the demand for capital goods will eventually destroy the value of money.