# Marginal and Average Explains Inflation Changes

One of the fundamental math lessons of economics is that when marginal exceeds average, average must be rising. When marginal is less than average, average must be falling. The inference that when marginal equals average, average must be at either a maximum or minimum follows directly.

I want to use this rule to explain what’s going on with inflation. Why does the year-over-year inflation rate continue to fall when the monthly inflation is still greater than zero? The answer is straightforward. Let’s take an example.

In November, 2022, the consumer price index (CPI) rose by 0.1% compared to October. The annual rate of 0.1% monthly inflation is 1.16% per year. This is the marginal value, the annualized month-to-month inflation rate (AMM). Compared to November, 2021, the; year-over-year (YOY) inflation rate was 7.1%. In October, 2022, the year-over-year rate was 7.8%. Marginal (AMM, 1.16%) is less than the average (YOY, 7.1%). And average fell from the previous month.

So the methodology is clear. Compare the annualized month-to-month inflation rate (AMM) with the year over year rate (YOY). If AMM is greater than YOY, marginal is greater than average. We expect the YOY rate to rise compared to the preceding month. Study this table to convince yourself that is always true.

For example, in May, 2022 (2022:05) AMM was 12.33%. YOY was 8.52%. In April, YOY was 8.22%. AMM was greater than YOY and YOY rose between April and May.

Now consider the opposite case when AMM is less than YOY. Marginal is less than average. We expect the YOY rate to fall compared to the previous month. Here’s another table to study

In July, 2022 (2022:07) AMM was -0.23%. YOY was 8.78%. In June, YOY was 9.00%. AMM was less than YOY and YOY fell between June and July.

I could go into mathematical details about why this is true, but I’m wrapping up another project and really don’t have time. But I will show you my Excel workbook that does these calculations from January, 2013 through November, 2022. Hopefully more data will be more convincing.

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