Consider a financial crisis where people stop spending money and hence velocity falls. In particular, suppose velocity falls by a factor of 1/2, i.e., . Suppose potential GDP is growing at 2% per year. If the central bank wants 2% inflation in the long run, by how much should it expand the money supply in this financial crisis?

Question

Consider a financial crisis where people stop spending money and hence velocity falls. In particular, suppose velocity falls by a factor of 1/2, i.e.,  . Suppose potential GDP is growing at 2% per year. If the central bank wants 2% inflation in the long run, by how much should it expand the money supply in this financial crisis?

BlackTom AI · Accepted Answer

We start from the most basic relationship that ties money, velocity, and nominal output: the quantity equation MV = PY. In growth terms, the growth rate of M plus the growth rate of V equals the growth rate of nominal output (which is P times Y).

Step 1: Identify the target nominal growth. If potential GDP (Y) is growing at 2% per year and the central bank aims for 2% inflation in the long run, then nominal GDP (P·Y) must grow by approximately 2% + 2% = 4% per year. This is the desired growth rate of nominal output in the long run.

Step 2: account for the fall in velocity. The problem states velocity falls by a factor of 1/2, i.e., V is reduced by 50%. This corresponds to a change in velocity growth rate, ΔV, of −50% in the relevant period. In growth terms, we use %ΔV = −50%.

Step 3: apply the quantity equation in growth form. We need %ΔM + %ΔV ≈ %Δ(PY) = 4%. Substituting %ΔV = −50%, we get %ΔM − 50% ≈ 4%.

Step 4: solve for %ΔM. Rearranging gives %ΔM ≈ 4% + 50% = 54%.

Conclusion (numerical result): To achieve a 2% inflation long run target given a 50% drop in velocity and 2% potential GDP growth, the central bank should expand the money supply by about 54% in the crisis period. (Thus the required monetary expansion is 54%.)

类似问题

If the real GDP per capita growth is 2.1 percent per year, the population growth rate is 3.2 percent per year, the money growth rate is 4.7 percent per year, and velocity is constant then, according to the quantity theory of money, the inflation rate is ________ percent in the long run.

According to the assumptions of the quantity theory of money, if the money supply increases by 5 percent, then[Fill in the blank]

If the growth rate of real GDP is 3.5 percent per year, the money supply grows at a rate of 7 percent, and the velocity is constant, using the quantity theory, the inflation rate is ______ percent. Round your answer to the nearest hundredth of a percent.

更多留学生实用工具

智能学习助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

学校历年真题

智能刷题助手

智能匹配练习

希望你的学习变得更简单