How exactly is money supply related to the price of goods and services?

Question

I keep hearing that prices of goods and services are based on the money supply, so, for example, if there was only one good or service in the entire economy, that good or service would be worth the entire money supply. But how is this the case? Wouldn’t it make more sense for the good/service’s price to be based on what people can afford? So let’s say for example there is 100 billion dollars in an economy of 100 people. Each person has 1 billion dollars. If there’s only one good/service in the entire economy, it wouldn’t make sense to price it at 100 billion dollars since the maximum amount any given person can pay for it is 1 billion. So wouldn’t it be more accurate to say prices are based on how much money people have rather than how much the money supply is?

Answer 1

Price level in the economy is in standard New Keynesian models described as:

$$P=\frac{M}{L(Y,i)}$$

where, $P$ is price level, $M$ money supply, $L$ money demand that depends on real output $Y$ and nominal interest rate $i$. So prices do depend positively on money supply. It is not the only thing in the world that determines price level but it is one of the determinants.

Even putting theory aside it is empirically well documented that there is positive relationship between price changes and changes in money supply (e.g. see Fan et al 2016, Qayyum 2006, DeGrauwe et al 2006 or many other papers). Here is also a graph that shows how crystal clear the relationship is:

Wouldn’t it make more sense for the good/service’s price to be based on what people can afford?

Price level also depends on real output of the economy which determines what people can afford in aggregate since in aggregate what people can afford to get is the whole output of a country. $Y$ is one of the determinants of price level. This is simply just another factor that determines inflation. Same way as different factors can explain obesity (bad diet, lack of exercise, sedentary life) different factors explain changes in price level. It is completely valid to say that lack of exercise is cause of obesity even if its not only cause and it is equally valid to say that money supply change is causally linked to price changes even though there are other variables.

So wouldn’t it be more accurate to say prices are based on how much money people have rather than how much the money supply is?

It is unclear what you mean. When economists talk about money supply in relation to inflation they mean broad measures of money supply. Broad money supply is the amount of money held by individuals and businesses. If someone has 10k on their deposit account that 10k is part of M2 money supply, for example.