Suppose that the Fed's inflation target is 2%, potential output growth is 3.5%, and velocity is a function of how much the interest rate differs from 5%: % triangle v=0.5 x (i-5)
Suppose that a model of the economy suggests that the real interest rate is determined by the equation:
r =8.5-% triangle Y
where Y is the level of output, so %triangle Y is the growth rate of output. Suppose that people expect the Fed to hit its inflation target.
A: Calculate the optimal money growth rate needed for the Fed to hit its inflation target in the long run.
B: In the short run, if output growth is just 2% for two years and the equation determining the real interest rate changes to r = 4.5- %triangle Y, what money growth rate should the Fed aim for to hit its inflation target in that period?
C: If the Fed instead maintained the money growth rate from part A, what is likely to happen to inflation?
D: Which policy do you think is better in the short run? Which is better in the long run?
To answer these questions, we need to use the equation of exchange, which states that MV = PY, where M is the money supply, V is the velocity of money, P is the price level, and Y is the level of output or national income.
A: Calculate the optimal money growth rate needed for the Fed to hit its inflation target in the long run.
To achieve the inflation target of 2% in the long run, we need the growth rate of nominal GDP (PY) to equal 2% as well. Since potential output growth is given as 3.5%, we know that the long-run growth rate of output (Y) is also 3.5%.
Let's denote the optimal money growth rate as %triangle M.
Using the equation of exchange, we can rewrite it as:
%triangle M + %triangle V = %triangle Y + %triangle P
Given that %triangle V = 0.5 x (i - 5), and %triangle Y = 3.5%, and assuming %triangle P = 2% (inflation target), we can solve for %triangle M:
%triangle M + 0.5 x (i - 5) = 3.5% + 2%
%triangle M + 0.5i - 2.5 = 5.5%
Simplifying the equation, we get:
%triangle M = 5.5% - 0.5i + 2.5
So, the optimal money growth rate needed for the Fed to hit its inflation target in the long run depends on the interest rate (i).
B: In the short run, if output growth is just 2% for two years and the equation determining the real interest rate changes to r = 4.5 - %triangle Y, what money growth rate should the Fed aim for to hit its inflation target in that period?
In the short run, we are given that output growth (%triangle Y) is 2% for two years. The equation determining the real interest rate (r) is also given as r = 4.5 - %triangle Y.
To hit the inflation target in the short run, we need the growth rate of nominal GDP (PY) to equal 2% as well.
Using the equation of exchange, we can rewrite it as:
%triangle M + %triangle V = %triangle Y + %triangle P
Given that %triangle V = 0.5 x (i - 5), and %triangle Y = 2%, and assuming %triangle P = 2% (inflation target), we can substitute the new equation for r:
%triangle M + 0.5 x (4.5 - %triangle Y - 5) = 2% + 2%
%triangle M + 0.5 x (4.5 - 2 - 5) = 4%
Simplifying the equation, we get:
%triangle M + 0.5 x (-2.5) = 4%
%triangle M - 1.25 = 4%
%triangle M = 5.25%
So, the money growth rate the Fed should aim for in the short run is 5.25% to hit its inflation target.
C: If the Fed instead maintained the money growth rate from part A, what is likely to happen to inflation?
In part A, we determined that the optimal money growth rate for the Fed to hit its inflation target in the long run depends on the interest rate (i).
If the Fed maintains the money growth rate from part A, which is %triangle M = 5.5% - 0.5i + 2.5, then the change in inflation (%triangle P) will depend on the other factors in the equation of exchange (%triangle M + %triangle V = %triangle Y + %triangle P).
Without knowing the values of %triangle V and %triangle Y, we cannot determine the exact change in inflation. However, we can say that if the other factors remain constant, maintaining the money growth rate from part A would likely result in the expected inflation target of 2% being achieved.
D: Which policy do you think is better in the short run? Which is better in the long run?
In the short run, the better policy depends on the specific economic conditions and the goals of the central bank. If the goal is to quickly stimulate economic growth, a higher money growth rate (%triangle M) can help achieve that. However, it might also lead to higher inflation in the short term. Conversely, a lower money growth rate may help control inflation but could potentially restrict economic growth.
In the long run, the optimal policy is to aim for the money growth rate that aligns with the long-run growth rate of potential output (%triangle Y). This helps maintain stable and sustainable economic growth while keeping inflation in check. In this case, the optimal money growth rate was calculated in part A as %triangle M = 5.5% - 0.5i + 2.5. This policy aims to achieve the inflation target of 2%.
It's important to note that the choice of policy depends on various factors such as the current state of the economy, the central bank's objectives, and the desired trade-offs between inflation and economic growth.