According to the Austrian Business Cycle Theory (ABCT), the boom-bust cycle emerges in response to a deviation in the market interest rate from the natural interest rate, or the equilibrium interest rate. It is held that the major cause for this deviation is increases in the money supply. Based on this it would appear that on a gold standard without the central bank an increase in the supply of gold is also going to set in motion boom-bust cycle.
An increase in the supply of gold is likely to result in the lowering of market interest rates. This in turn is likely to cause the market interest rates to deviate from the equilibrium interest rate. Consequently, following the ABCT an increase in the supply of gold is going to set in motion the boom-bust cycle.
According to Robert P. Murphy “More Than Quibbles: Problems with the Theory and History of Fractional Reserve Free Banking” in the QJAE Volume 22 Spring 2019, Ludwig von Mises held that an increase in the supply of gold could trigger boom-bust cycle.
Whilst suggesting that the gold standard could generate business cycles whenever an increase in the supply of gold causes the market interest rate to deviate from the natural interest rate, or the equilibrium rate, Mises however, viewed this possibility as remote.
Mises regarded the gold standard as the best monetary system as far as keeping the expansion in credit under tight control. Murphy quotes Mises on this,
Even a rapid increase in the production of the precious metals can never have the range which credit expansion can attain. The gold standard was an efficacious check upon credit expansion, as it forced the banks not to exceed certain limits in their expansionist ventures…
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