If printing trillions of dollars causes prices to go up, would taking those trillions back cause prices to drop?
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1$\begingroup$ In theory yes. In practice, the rent is increased. And we have just seen how this has lowered inflation. $\endgroup$– Jesper HybelCommented Jul 19 at 16:44
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If printing trillions of dollars causes prices to go up, would taking those trillions back cause prices to drop?
Yes prices would drop, if all other things were held constant, but they wouldn’t drop by exactly 50% because the relationship between price level and money supply is not proportional 1:1.
For example, following standard IS-LM model, the relationship between money supply and price level is given by;
$$P= \frac{M}{L(Y,i)}$$
Where $P$ is price level, $M$ money supply and $L$ money demand that depends on output $Y$ and interest rate $i$.
Depending on parameters of $L$ function the relationship won’t necessary be proportional. For example, suppose $L=aY -bi$ then;
$$dP/dM = \frac{1}{aY-bi}$$
So decrease in money supply would result in $dM \cdot \frac{1}{aY-bi}$ decrease in price level.
For example, if $a=0.01$, $Y=300$, $b=10$ and $i=0.1$ are then 50% decline in money supply would result in 25% drop in price level. Depending on parameter values the drop in prices could be more or less than 1:1 proportional.
PS: Note most money nowadays is not actually printed but created electronically.
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$\begingroup$ Hi. How can sellers/producers know that prices must increase/decrease to correspond money supply as 1:1?@1muflon1 $\endgroup$– Mike_bbCommented Jul 20 at 13:25
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$\begingroup$ As I understood you wrote that my assumption is wrong economics.stackexchange.com/a/58235/43987 but here you wrote that "the relationship between price level and money supply is proportional 1:1" @1muflon1 $\endgroup$– Mike_bbCommented Jul 20 at 13:39
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1$\begingroup$ @Mike_bb it’s a typo I meant to say is not proportional as also mentioned in later part of my answer $\endgroup$– 1muflon1 ♦Commented Jul 20 at 16:47
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1$\begingroup$ @Mike_bb u can use it, but according to modern research MV=PQ is not the best description of money market. Most economists believe that PL(y,i)=M is the more correct description of money market. Generally empirical literature with cointegration tests that tries to test whether MV=PQ which boils down to estimating cointegrated relationship like $ \ln P = \beta_1 \ln M + \beta_2 \ln V -\beta_3 \ln Q $ find that $\beta_1 \neq \beta_2 \neq \beta_3 \neq 1$ which means that empirical evidence generally rejects $MV=PQ$. There were some studies that found $\beta_1 =\beta_2 = \beta_3 =1$ but they are $\endgroup$– 1muflon1 ♦Commented Jul 20 at 21:24
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1$\begingroup$ not in majority, so the most accepted interpretation is that at best MV=PQ is a special case of PL(y,i) =M that holds occasionally when the coefficients happen to be such that you get that result. $\endgroup$– 1muflon1 ♦Commented Jul 20 at 21:25