The quantity theory states that the impact of money on nominal GDP can be determined without details about the aggregate demand curve, so long as the velocity of money is predictable.  What is the reasoning behind this claim?

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According to the quantity theory of money, there is a mathematical relationship between the supply of money and nominal GDP.  This relationship can be described by the equation

M* V = P* Y

when M is the money supply, V is the velocity of money, P is the price level, and Y is the quantity of output.  We also know, however, that the price level multiplied by the quantity of output gives us the nominal GDP.  Therefore, the equation can also be given as

M*V = nominal GDP.

Thus, if we know the velocity of money as the question stipulates that we do, and we know the money supply we can also know what the nominal GDP will be.  Even if we do not know the actual money supply, we will know what impact a change in the money supply will have on nominal GDP.

The reasoning behind this is that the infusion of extra money into the money supply has not changed the ability of the economy to produce goods.  All that can happen if the money supply increases is that the price level will increase as well.  This will raise nominal GDP without doing anything to actually increase the level of production in the economy. 

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