MV=PT

where M is the total amount of money in circulation, V is the frequency with which money changes hands, P is the price level, and T is the real amount of goods and services in the economy.

During the Roman empire, the official silver coin was called the denarius, which was minted at the Temple of Juno Moneta in Rome. From the time of Nero, until the Fall of the Western Roman Empire in 476, Roman emperors defaced the currency in an attempt to increase spending. By the reign of Gallienus, the denarius had only 5 percent of its original silver content. As the currency was defaced, inflation occurred: across the Roman empire: from the 2nd to the 3rd century AD, prices rose by 20,000%.

Assume that the growth rate of V equals the growth rate of T. Using the quantity theory of money, explain clearly the relationship between Roman currency defacement and inflation