How come inflation does NOT increase if the money supply increases during a liqu

Question

How come inflation does NOT increase if the money supply increases during a liquidity trap?

My guess is that if people hold more cash, they would spend more. Given that during a liquidity
trap the economy is maxed out and cannot increase output, the extra influx of spending would only serve as to increasing prices.

Apparently this is not the case. What happens to the influx of cash? Do people simply hold it?

EDIT: I found this, but it doesn't really make sense to me.

"Conventionally, the expansion of the money supply will generate inflation as more money is chasing after the same amount of goods available. During a liquidity trap, however, increases in money supply are fully absorbed by excess demand for money (liquidity); investors hoard the increased money instead of spending it because the opportunity cost of holding cash—the forgone earnings from interest—is zero when the nominal interest rate is zero. Even worse, if the increased money supply is through LSAPs on long-term debts (as is the case under QE), investors are prompted to further shift their portfolio holdings from interest-bearing assets to cash."

Explanation / Answer

The basic answer is that it depends on factors like the rate of circulation (number of times cash changes hands), the state of the economy and therefore the growth in productive capability (the long-term combination offer LRAS).

1. Growth of Real Output. Suppose the cash offer enlarged by 4WD. during a simplified model, this is able to cause a rise in combination Demand (AD) of 4WD. If AS (productive capacity) stayed static there would be no increase in Real Output, solely inflation.
However, if the rise in AD of 4WD was matched by a rise in AS of 4WD, there would be no inflation, but, simply a rise in real output.
In different words the cash offer will grow at a similar rate as real output to take care of same indicant.
However, if ceteris paribus, finances grows quicker than the speed of real output, it'll cause inflation.
But, within the planet there square measure different reasons why a rise within the finances doesn't cause a rise in inflation.

2. laborious to live finances. typically the cash offer is difficult to calculate and is consistently dynamical. giant will increase within the finances square measure typically simply because of changes within the means individuals hold cash, like increase in mastercard use might cause a rise in Broad cash M4.

3. rate of Circulation
MV=PY
The quantity theory of cash equation assumes that a rise in M causes a rise in P. However, this assumes that V and Y is constant.
V (velocity of circulation)
However, in practices it's not as easy as this equation assumes. In follow there square measure variations in rate of circulation e.t.c.

4. economic expert read – Liquidity lure
In a recession, there could also be abundant spare capability within the economy. Therefore, a rise within the finances, just helps to urge laid-off resources utilized in the final economy. Therefore, within the case of a recession, enlarged finances is unlikely to cause inflation.
In a liquidity lure, interest rates fall to zero however this doesn’t forestall individuals saving. during this state of affairs there's a fall within the rate of circulation and this will cause deflation. during this state of affairs, increasing the cash offer won't essentially cause inflation.

In traditional economic circumstances, if the cash offer grows quicker than real output it'll cause inflation.
In a depressed economy (liquidity trap) this correlation breaks down owing to a fall within the rate of circulation. {this is|this is often|this will be} why during a depressed economy Central Banks can increase the cash offer while not inflicting inflation. This occured in US between 2008-11. – giant increase in finances no inflation.
However, once the economy recovers and rate of circulation rises, enlarged finances is probably going to cause inflation.

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