The fed targets a 2% inflation rate. assume the growth rate of real gdp (y) is 1.5% and the rate of change of the velocity of money (v) is constant. by how much should the fed change the money supply?

3.5%

Explanation:

The quantitative theory of money (QTM) states that MV=PT (eq.1). M is the money supply, V is the velocity of circulation, P is the price of a typical transaction and T is the total number of transactions. The velocity of circulation is the number of times that a dollar changes of holder y a period. We can also write eq.1 as MV=PY (eq.2) because the cuantitative equation assumes that the valu of transactions is equal to the GDP (Y). The QTM also has two main assumptions: V is constant in the short term and Y is given by factors and technology. If we write eq.2 in a rate of change form, then we have: ΔM+ΔV=ΔP+ΔY (eq.3).

First, ΔP represents changes in prices which is know as inflation rate (given by the problem). Second, ΔY is the growth rate of real GDP (also given by the problem). Third, ΔV is the rate of change of money velocity, but in this case, velocity does not change, which means the rate of change is 0. And, ΔM is what we have to find. According to this, we have a new equation:ΔM=ΔP+ΔY (eq.4).

Then, ΔM=2%+1.5%=3.5%. The Fed should change money supply in 3.5%

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