How does an increase in USD money supply affect inflation?

Say an average american household is bringing in $50,000 a year. Between ongoing quantitative easing and the drastic stimulus packages passed in February-May 2020, the USD Money Supply increased by 25% or 16% depending on if you look at M1 or M2, respectively. (I assume M2 is more directly related to inflation, but would love if anyone can provide clarity there) Assuming 0 change in real output (not likely, but for simplicity) would the last 3 months actions to increase the money supply equate to a direct equivalent loss of value per USD? Would this average American family's \$50,000/yr income in February become equivalent to a \$42,000/yr salary(in Feb \$'s) by May?

Or are there other factors in play? (outside increasing real output)

Yes there are other factors at play. Inflation is change in a price level. The price level, according to classic textbook monetary equation, is determined as follows:

$$P = \frac{MV}{Y}$$

Where $$M$$ is the money supply, $$V$$ velocity of money (how much is one dollar used in the economy) and $$Y$$ is the real output.

So beside money supply and real output inflation depends also on velocity of money. Furthermore, the inflation also depends on peoples expectations of these quantities. That is on what people expect the money supply, real output and velocity will be (although this is not shown in the simplified textbook model above).

Would this average American family's \$50,000/yr income in February equivalent to a \$42,000/yr salary in May?

Not likely. According to the International Monetary Fund the the annual inflation forecast for USA for 2020 and 2021 is $$0.6\%$$ and $$2.2\%$$ respectively. These are mean forecasts so of course the actual realized values will not be exactly the same, but I would be surprised if even $$99\%$$ confidence interval would even include double digit inflation. The assumption that output does not change is currently also not realistic. USA lost $$6\%$$ of GDP just in 2020Q1 according to the Bureau of Economic Analysis and the fall for Q2 is projected to be even worse.

• Wouldn't the loss in GDP make it more likely that inflation reaches double digits? With such an increase in money supply, velocity stagnate (as far as I can tell), and this decrease in Y - isn't that indicative of much more than a typical years inflation? I just don't see, based on the formula you provided, where the extra value lies that keep price level near the same while money supply increases so drastically. Or is the idea GDP will rebound drastically? Why wouldn't comparisons of GDP measured in USD also be drastically skewed by the increase in USD supply? – TCooper Jun 18 '20 at 22:44
• @TCooper you are right that drop in real output would ceteris paribus lead to higher inflation - I just mentioned that as a side note not as an argument for why inflation will be low inflation - the point was that it would already mess your calculation. In addition velocity of money definitely does not stagnate. For example have a look at this Fed data on velocity of money in US it falls dramatically in last two decades ( fred.stlouisfed.org/series/M2V ). Velocity of money depends on how many transactions people make. – 1muflon1 Jun 18 '20 at 23:18
• In a recession where they are not even allowed to purchase many goods and services due to corona lockdowns it is bound to fall. Generally recessions are deflationary due to this (especially demand driven recessions are). The recent recession is both demand and supply driven but as people are not allowed to spend I would expect V to just fall further not stay stagnant. In fact currently as interest rates are at zero lower bound it is real possibility that many countries will find themselves in liquidity trap. In such situation any increase in money supply will be offset by change in V – 1muflon1 Jun 18 '20 at 23:19
• That last comment combined with a couple of the answers on the question I linked are really getting the picture completed in my mind. I appreciate you taking the time to help me understand ( also @the_rainbox ). I've never been in this SE and I see most of the questions are more involved/higher level. It was just recommended to try here when I first posted on Personal Finance. Again, really appreciate your answers and clarifications. – TCooper Jun 18 '20 at 23:26
• Got it, I definitely will. General rule on other SE's is wait 24 hours (global community and all), so I'm going to do that. – TCooper Jun 18 '20 at 23:40

The most important distinction you have to make is between real income ($$Y$$) and nominal income ($$P*Y$$);

Textbook cases imply that, for $$MV = PY$$, then $$\frac{ΔM}{M} = \frac{ΔP}{P}$$. So yes, it is expected from almost every basic model that dwells on the subject, that prices will rise for the same amount money supply does (see "Shopping-Time Model", "Baumol-Tobin Money Demand", "Friedman Money Demand").

Hence, 50,000\$will be equal to (if we accept M1 as money supply) $$50,000*1.25 = 62,500\\\$$ and not 42,000\$.

This means that the nominal income of the family will rise, but it is possible, if real income doesn't also rise for the same rate (1.25) but less (or even, if it turns to a negative growth pattern, much like we're seeing today), the real income of the household (the value of goods it can purchase) is going to go downhill.

• Absolutely. My only concern was with his 50,000/42,000 = 1.19... ratio, which doesn't add up with the 25 or 16 money supply increase, so I tried to clarify that as well, although without saying so. – S. Iason Koutsoulis Jun 18 '20 at 20:02
• I didn't make that clear, and I'm now seeing it's an odd way to look at it, but what I meant is the 50,000 per yr gives you the purchasing power of 42,000 per yr prior to the increase in money supply. So a 16% reduction in purchasing power due to a 16% increase in inflation. The velocity of money factor changes this, and setting change in output to 0 is unrealistic as well - but why did you choose to use M1 money supply over M2 for the inflation calculation? – TCooper Jun 18 '20 at 21:07
• Hello OP. Firstly, yes, purchasing power is what I assumed you were talking about, it was only a matter of clarification of an important distinction in case you missed it. Secondly, the 3 models I brought forth, all use M1 as their money supply, and I wanted to be as typical as possible; if you asked me, I'd intuitively say most people have a tendency of not estimating M2 and M3 changes as a part of money supply volatility. – S. Iason Koutsoulis Jun 18 '20 at 21:12
• I can't make the dollar sign stick to its proper place and i'm getting furious hahah – S. Iason Koutsoulis Jun 18 '20 at 21:20
• @TCooper you have to use \ in front of dollar sign, if you dont the page thinks that you are writing a mathematical expression which is always encased in two dollar signs. You will see that I edited your Q to include them – 1muflon1 Jun 18 '20 at 22:06

It seems likely there are other factors at play, that are not included in the basic model.

For example, suppose that a large portion of new money is simply gifted to a few actors. How would that affect the inflation of the prices of goods and services? What would it mean to you if your salary stayed fixed? How would it affect your life?

If those actors simply held onto the money and kept in the bank, then, largely, there may be little practical consequence to the economy as the prices of goods and services might be unchanged.

If those actors used the money for massive purchasing goods and services, the prices of those goods and services may go up, making them relatively expensive and less affordable for most people with a fixed salary.

If those actors used the money to employ people in the production of goods and services, then potentially, the cost of those goods and services could actually go down (and its surprising that governments don't directly do this as a method of stimulus).

So, inflation of prices generally, isn't a necessary logical consequence of new money. Far more important is the relationship that supply and demand has on prices. Inflation becomes an extreme concern when good and services, particularly the necessities of life (shelter, food, water, power, ... toilet paper) are in much less supply than there is demand. The supply of these items may have little to do with the total amount of available money in an economy -- rich actors with mountains of money may have little use for an extra can of beans, and their ability to pay $2000 dollars for one is unlikely to have large effects on the price of beans in a crisis. Price inflation can happen when supply chains fail and supply is reduced, driving up prices. Price inflation can happen when there is an increase in demand, and there is a fear of future supply shortages. Its important to note that the text book model is one of macroeconomics. It relates the total money to the average price of items in a closed economy. It may say little about the median prices of individual goods and services. Money velocity is a critical component than doesn't necessarily increase with money supply. Further, the text book model it a model of the fixed points of a dynamic process. These are theoretical value that do not consider the process itself to be changing. Price inflation occurs in failed economies it is sometimes as a reaction to failures in supply chains, as opposed to the release of new money. Price inflation isn't necessarily bad for people either. If we doubled the amount of money in the economy, but also doubled people's wages in consequence, it might have zero effect on most people's lives. In this scenario, the major losers might actually be people having a large amount of cash, who value has suddenly decreased. So to answer the question, to know the effect of new money on prices, you need to know the effect that money will have on the supply and demand of good and services, and their production. If the new money is given to people who cash-out-refinance their homes, and place that money in a CD, I would expect little change in the prices of most goods and services, at least in the short term, and perhaps even little change in loan prices and homes. The full answer is, its complicated, and depends a lot what the new money is used for, its consequence on behaviors, and the subsequent effect on supply and demand, particularly if were talking about the prices of individual items and not averages. • But this is already covered by the textbook equations - whether people spend money or not that’s the velocity of money. If people stuff all new money under mattresses then the velocity of money will drop. Also, the statement about if the money would be used to employ people in production of goods and services the prices would potentially go down is not correct. Increasing demand for workers and capital pushes returns to those factors up increasing costs of producing goods and services which will lead to higher prices. Moreover, also those employees are going to spend the money presumably – 1muflon1 Jun 19 '20 at 10:37 • pushing up the prices. Furthermore, it’s empirically not true that “price inflation occurs in failed economies”. US in 70s was far from failed economy yet it had relatively large inflation. “Sometimes the release of new money is the reaction to price inflation” - what source do you even get this from? I would generally like to see sources of about half of the statements you make here because they go contrary to conventional monetary theories – 1muflon1 Jun 19 '20 at 10:44 • Re velocity. Suppose that 10 trillion dollars is gifted to banks, and the those banks use it to furiously trade bitcoin back and forth, knowing that if they do so, they'll likely receive another 10 dollars (because later we find that the new money was insufficient to stimulate the economy). The velocity of that money may be high, yet the consequence on overall prices in the economy will be low. Theory that does not consider behavior is just theory. – user48956 Jun 19 '20 at 15:43 • 1. It’s not compared to individual prices or velocities but to aggregate and average prices and velocities. 2. So your whole argument is just that it would be more appropriate to use open economy model here which is essentially just based on the same fundamental relationships? Yes assuming close economy is not realistic but the point is to isolate the effects that happen within the country from outside influences as an additional ceteris paribus condition. There is nothing incorrect about doing that in fact that’s how you can gain additional insights into how the mechanisms work – 1muflon1 Jun 19 '20 at 16:07 • no I am saying that within the simple$MV=PY\$ the output determination is not fully modeled as it models only partial equilibrium on money market. However, output will be a function of prices in the short run. You can expand the monetary equation which gives you money market equilibrium into full IS-LM AS-AD model and in such mode output is function of price level in the short run. But again for the sort of question asked here resorting to general equilibrium analysis is completely unnecessary and it would not fundamentally change the message of the model. – 1muflon1 Jun 19 '20 at 16:46