True or False: According to the quantity theory of money, if velocity falls so that its growth rate is negative then the Fed, to keep inflation and output growth stable, should match the decrease in velocity with an equivalent increase in the percent growth of the money stock.
This statement is true. If the velocity of money goes down, the Fed will have to increase the quantity of money in the economy if it wants to maintain the previous price level and it wants to maintain or increase total economic output.
In order to see why this is the case, let us look at the formula for the quantity theory of money. The formula is
M * V = P * Q
M is the quantity of money in the economy. V is the velocity of money. P is the price level. Q is the quantity of output.
In this equation, if V goes down, and M stays the same, the value of the left side of the equation drops. Therefore, either the price or the level of output will have to drop in order to keep the two sides of the equation balanced. Therefore, if the velocity of money drops, the Fed must either increase the money supply or it must allow either the price level or output to drop.
Thus, if the Fed wants to keep the price level from dropping and it wants to maintain or increase economic output, it must increase the money supply if the velocity of money drops.