The previous post talked about the Inflationary gap and the Recessionary gap with respect to how Effectve Demand calculates potential real GDP. Here is the graph...
The main thing to point out here is that the inflationary gap increases to the right, but eventually hits the limit imposed by Effective demand. The vertical red line is the first limit, where Effective demand equals real GDP. The economy usually does not pass this limit. The vertical yellow line is a harsher limit, where Effective demand equals potential real GDP. The economy has never passed this limit since 1967. Thus,... and this is an important clarification...
Effective demand limits the inflationary gap.
Here is the math...
Inflationary gap = real GDP - potential real GDP
Inflationary gap = real GDP - (real GDP - $3000 billion * (cu - els)/els)
Inflationary gap = $3000 billion * (cu - els)/els)
Now, the Inflationary gap hits its limit when Effective demand = real GDP
Since, Effective demand = real GDP * els/(cu * (1-u)), we have...
real GDP * els/(cu * (1-u)) = real GDP ....
Thus...
els/(cu * (1-u)) = 1
cu = els/(1-u)
Now, to find the limit of the Inflationary gap at Effective demand, we have...
Inflationary gap at limit = $3000 billion * (cu - els)/els) * els/(cu * (1-u))
Inflationary gap at limit = $3000 billion * (els/(1-u) - els)/els) * els/(els/(1-u) * (1-u))
Simplify...
Inflationary gap at limit when equal to = $3000 billion * u/(1-u)
Thus, the Inflationary gap limit can be solely determined by the unemployment rate. When the left side of the equation equals the right side, the Inflationary gap has reached its limit. The current Inflationary gap is $165 billion. The current unemployment rate is 7.7%. So we ask the question... are we at the limit of the Inflationary gap? No...
$165 billion is not equal to $3000 billion * 7.7%/(1-7.7%) = $250 billion.
If the inflationary gap was at its limit right now, the unemployment rate would have to be 5.2%. So, we can conclude that the inflationary gap has not reached its limit yet.
