Injection Effects and the Quantity Theory

In response to Sumner's claim that injection effects don't matter, Nicolas Cachanosky writes:

"Homogeneous and correct expected inflation is one of the requirements. If all agents know that inflation will be 3%, then they know now much prices will rise. This is a necessary but not a sufficient condition. If I’m an entrepreneur it doesn’t help my business to increase the prices 3% today if my clients still don’t have the extra 3% of money that’s in the economy. To avoid Cantillon Effects the money helicopter is needed in addition to the correct homogeneous inflation expectations. In other words, to argue against Cantillon Effects we need to assume the helicopter. We can indeed imagine a world scenario with such characteristics, but is not one that loyally expresses the problem of monetary policy and changes in money supply".

Admittedly, I am picking on Cachanosky a bit because some of those commenting on Sumner made what I see as a fundamental error, one repeated here by Cachanosky on his blog,  Punto de Vista Economico.

Businesses won't raise their prices 3% (or any particular amount) if their clients don't have the extra 3% of money that is in the economy?

I think that this argument is not based upon any deep analysis but rather on a flawed intuition, the intuition behind the most simplistic version of the quantity theory of money.

Imagine that the existing "goods" in the economy exchange for the existing quantity of money.   If there is a single good, say wheat and there are 1000 bushels of wheat, and if there are $5000 dollars in the economy, and all the money exchanges for all the wheat, then the price of wheat must be $5 per bushel.    If the amount of money rises 10%, then there is $5500 in the economy.  If all of that money exchanges for all the wheat, then the price per bushel must be $5.50.   Inflation is "too much money chasing too few goods."

Of course, Cachonosky wouldn't be thinking there is a single good, but somehow, the variety of goods in the market economy must be exchanging for the money, and so their prices on average depend on the amount of money.   If the amount of money doesn't increase, then while some prices might increase, other prices must decrease.

But market economies aren't much like this, maybe to the point that they are nothing like this.

In some sense, the implicit assumption is that velocity is one.   Each dollar is spent on output exactly one time.   But it is really worse than that.   In reality, prices are determined by the flow of supply and demand over time, and the stock of money in existence at any point time has no simple mechanical relationship to the total amount of money spent in transactions over some period of time.

Consider a situation where velocity is .5.   The quantity of money is twice the flow of output produced, sold, bought and consumed per year.    Even if every transaction occurred at one time during the year, only half of the money would be transferred.      People would be holding large money balances that they don't spend.   They could easily pay 3% higher prices by reducing their existing money balances.  

Now, consider the situation where velocity is 4.     The quantity of money is 1/4 of the dollar value of the goods produced, sold, bought and consumed each year.   How is this possible?   How can people buy more goods per year than there is money to spend?   Well, we know that one person spends money to make a purchase, and the person receiving the money uses it to make a purchase, and that person makes a purchase.    While the dollar value of the exchanges made at any one instant can be no more than the quantity of money, the actual quantity of money is almost certainly larger than the dollar value of the transactions made at any one instant.   It is just smaller than the total amount of purchases and sales over a period of time like one year.

For example, if the quantity of money is $3 trillion and nominal GDP is $12 trillion, it would be impossible to buy $12 trillion of output all at once with only $3 trillion worth of money in existence.   But suppose spending on output is divided evenly over the year, so that there is $1 trillion spending on output per month.   The existing $3 trillion is way more than adequate to make $1 trillion of purchases per month.    If prices were to double, the $3 trillion would be enough to purchase the same goods at doubled prices--$2 trillion per month.

From an individual perspective, suppose  income is $60,000 per year paid twice each month.  That is $2500.   This person starts with $1000 money balances at the beginning of the pay period.  When paid, this rises to $3500.   Then the $2500 of income is spent at a constant rate, resulting in an average money balance of 1/2 * $2500 + $1000 or $2250.   Right before the next paycheck, money balances are back to $1000.    This individual has plenty of money to pay higher prices right away.   Instead of 3%, say it is 20%.   This would require expenditures of $3000.    The individual has $3500 to spend.

In this situation, velocity for the individual is $2500/$2250, or 1.1.   (Of course that is bimonthly.    It is closer to 27 per year. $60,000 per year divided by the average money holdings of $2,250.)

Why would anyone hold precautionary balances?   One reason is to take care of unexpected emergencies.  However, another reason is to take advantage of unexpected opportunities.   And wouldn't one such opportunity be buying more products in anticipation of future price increases?

Now, if no one has any precautionary cash balances, but rather lives pay check to pay check, spending the last penny right before the next receipt, then it is a bit more challenging to buy any more unless first one has more money.   However, it is possible to increase velocity in this simple scenario by spending money right after it is received rather than regularly over the pay period.   Instead of the average money balance being 1/2 of the amount spent over the period, it would be less.  If it is all spent in one day, it would be approximately 1/30 of the amount earned per period.  

Oddly enough, spending money "early" is exactly what is required to anticipate price increases.   Buy now to avoid having to pay more later.  And when everyone tries this, they pay more now.   Which they can actually do because velocity rises.   But, of course, this  sort of mechanical version of money demand, where people receive money and then spend it all before receiving more is unrealistic and not worth worrying about much.

The simple microeconomics is that if the price of a good is expected to rise, the supply of that good decreases and the demand for that good increases, resulting in a shortage at the existing price and a higher equilibrium price for that good.    The notion that this is impossible in aggregate because there isn't enough money is false.  The amount of money in existence is not equal to the dollar amount of transactions at each point in time.

Why do sellers reduce the supply of a good if they expect to get a higher price later?   They do so because they can make more money from the marginal unit of the product by selling it later at the higher price.  

Why do buyers increase the demand for a good if they expect to have to pay a higher price later?   They do so to avoid paying the higher price later.   Can can consume the good later while paying less for it now.

If supply falls and demand rises equal amounts, then the equilibrium price rises and the equilibrium quantity remains the same.   This implies increased spending on the particular product.   If this happens for all goods at once, it is more spending on everything.

How can people afford to spend more on everything?   Don't they have limited income?   Here we must appeal to macreconomics.   The expenditures of one is the income of another.     Of course, in this example, the quantities didn't change, so real income and real expenditure are the same.   But nominal income rises with nominal expenditure, creating enough money income to buy everything sold.

But, there is only so much money in existence.   How can there be more spending in aggregate unless there is more money?   How can higher prices be charged unless the buyers have additional money to spend?   And the answer?   Higher velocity, or equivalently, reduced money demand.   And that makes perfect sense if there is an anticipated increase in the price level.

Now, suppose the quantity of money doesn't increase after all.  Does the price level remain elevated?   No.  What happens is that real money balances are too low.   People are not expecting further increases in the price level, and so they restrain spending to rebuild their money balances.   This reduces the demands for various good and services, and results in the lower prices.

Of course, anticipating these price cuts, buyers would be motivated to reduce demand and sellers are motivated to increase supply, which results in a surplus at the current price, and so a lower equilibrium price.

None of this is meant to show that there cannot be Cantillion effects, it is just that the notion that new money has to be created before it can cause prices to rise, or more restrictively, that the "new" money must reach some particular market before prices can rise in that market, is false.   That kind of reasoning is inconsistent with basic microeconomic analysis, and as for macro, it seems most plausibly an implication of an intuition based upon the most simplistic and unrealistic quantity theory scenario--all money exchanges with all goods all at once.

From a Market Monetarist perspective, the expectations generated by a monetary regime pull nominal expenditures in a way consistent with the regime.   It is a mistake to always see money as being "injected" and pushing expenditure in some way or other.     In my view, "pushing" is a likely consequence when there is a change in the monetary regime.    I think the notion that everyone will understand the new regime is implausible.   Some pushing is likely.  

Further, when there are errors in the operation of a regime, there will also be pushing.   But it is essential to understand the pull of operation of a monetary regime on interest rates, spending, and prices.   For the monetary regime to be maintained, it is necessary for people to expect that a quantity of money consistent with the regime will be generated.    Given those expectations, the demand to hold money, or alternatively, velocity, will shift in ways that support the regime.