# What constraint is there on velocity of money?

MV = PY

I am trying to develop an intuitive understanding of it. M = Money Supply, V = Number of Transactions, P = Average Prices, Y = Output/Income.

The equation seems to suggest that if money supply and output are constant, then prices will keep rising with the number of transactions in an economy. Yet, this seems odd to me.

If a society has a fixed supply of money (e.g., £1m) and a fixed supply of goods (e.g., 1m cans of coke), then the average price of cans of coke can never rise above £1 each? You can get deflation if people stop buying cans of coke. You can also get inflation, if people go from not buying any coke to suddenly buying them all. Yet won’t the maximum average price always be £1 each? No matter how many times people buy and sell the cans of coke, and no matter how high the price of certain cans become, the average price will always reach the upper limit of £1 each.

Yet, the equation seems to suggest that velocity is an independent variable that can affect prices (assuming constant output and money supply) with no upper constraint.

Note: I appreciate that the real world is more complicated than the above, but I'm trying to develop an intuition. In my mind, velocity of circulation (or number of transactions) can only increase prices beyond an upper limit if money supply is increased e.g., banks start creating more credit to enable the increased transactions or output falls.

Please feel free to send me any articles/papers that you think will be helpful. Thank you!

Velocity is not average number of transactions. Velocity is the average number of times unit of currency is used. Following, Fed:

The velocity of money is the frequency at which one unit of currency is used to purchase domestically- produced goods and services within a given time period. In other words, it is the number of times one dollar is spent to buy goods and services per unit of time.

There is a difference there because not all transactions have the same value.

MV = PY ... The equation seems to suggest that if money supply and output are constant, then prices will keep rising with the number of transactions in an economy. Yet, this seems odd to me.

That is correct. The intuition there is that higher velocity is tantamount to having higher amount of money in circulation. Having \$1 note that is used twice to purchase something, is economically equivalent to have \$2 notes that are each used only once. This why $$M$$ in the equation is also multiplied by $$V$$, you can view velocity as scalar that either increases $$M$$ if $$V>1$$ or decreases it if $$V< 1$$.

If a society has a fixed supply of money (e.g., £1m) and a fixed supply of goods (e.g., 1m cans of coke), then the average price of cans of coke can never rise above £1 each?

No this is not true, the price could go above £1 if velocity is $$V>1$$. As explained above velocity of money in essence means some money is used multiple times. For example, using your parameters if velocity is equal to 2 that would be equivalent to an economy where $$M$$ is £2m but velocity is only 1.

Yet, the equation seems to suggest that velocity is an independent variable that can affect prices (assuming constant output and money supply) with no upper constraint.

Yes that is correct. Consider an extreme but technically possible example. Suppose that in whole economy there is only 1 single dollar bill, and there is billion of apples each costing one dollar. Well a possible way how this economy could work is that I first buy an apple with 1 dollar, then person who receives the dollar buys another apple etc up until all apples are sold. In that case $$M=1$$ and $$V=1bn$$. Within the simple model $$MV=PY$$ there is no constraint on $$V$$. $$V$$ can be constrained by peoples behavior in richer models because for example in economy where there is single dollar bill but billion apples there would be too much frictions and coordination problems so many people would likely start using something else as money or barter, so that might make some values of $$V$$ extremely unlikely, but in principle any value for $$V$$ in range $$[0,\infty)$$ is a possible value.