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I've been reading some explanations of inflation and I think I generally understand what it is. What I don't understand however, and I believe this should be trivial, is what a (monthly) inflation of x% actually means.
Let's say there's a product worth $10 in July and the inflation rate in August is 10%. Will it then cost $11 in August? What if the rate stays the same till the end of the year? Will each month add another 10%? Percent of what? What's the baseline here?
Let's say there's a product worth $10 in July and the inflation rate in August is 10%. Will it then cost $11 in August?
Yes. That's basically what inflation means. However. The "monthly" inflation numbers you typically see are generally a year over year inflation rate on that month. Meaning August 2017 inflation is 10% that means inflation was 10% since last July 2016, not since July 2017.
At the micro consumer level, inflation is very very very vague. Some sectors of the economy will inflate faster than the general inflation rate, others will be slower or even deflate. Sometimes a price increase comes with a value increase so it's not really inflation. And lastly, month over month inflation isn't something you will feel. Inflation is measured on the whole economy, but actual prices move in steps. A pear today might cost $1, and a pear in five years might cost $1.10. That's 10% over 5 years or about 2% per year but the actual price change might have been as abrupt as yesterday a pear was $1 and now it's $1.10. All of the prices of pears over all of the country won't be the same.
Inflation is a measure of everything in the economy roughly blended together to come up with a general value for the loss in purchasing power of a currency and is applicable over long periods. A USD inflation rate of 3% does not mean the pear you spent $1 on today will necessarily cost $1.03 next year.
As pointe out by @quid, inflation figures are almost always quoted as a comparison of prices last month, and prices a year ago last month. So 10% inflation in August means that things cost 10% more than they did in August a year ago. This can lead to some perverse conclusions.
Consider an imaginary economy where prices stay constant over years. Annualized inflation is zero.
Then something happens on January 2nd, 2018. Some crop fails, a foreign cheap source of something becomes unavailable, whatever. Prices rise, permanently, as more expensive sources are used. This is the only disruption to prices. Nothing else goes wrong.
So, in February, 2018, the authorities find that prices in January, 2018 rose by 1% over January 2017.
Inflation! Politicians pontificate, economists wring their hands, etc.
In March, again, prices for February, 2018 are found to be 1% higher than for February, 2017. More wailing...
This goes on for months. Every month, inflation (year over year) is unchanged at 1%. Everyone has a theory as to how to stop it...
Finally, in February, 2019, there's a change! Prices in January, 2019, were the same as in January 2018. Zero inflation! Everyone takes credit for bringing down inflation...
Individual product prices do not necessarily rise at inflation rates. What inflation means is that the purchasing power of one unit of currency decreases by x% in a year, which is typically measured by looking at a broad spectrum of products in an economy and extrapolating to "all products". So for all products across an economy, the aggregate price of all goods will, on average, be X% higher that they were this time last year. Some products will be cheaper, some will be more expensive, but on average their prices will rise with inflation rates.
For the other part of your question, inflation is an annualized percentage, so an inflation rate of 12% means prices are 12% higher than they were a year ago, so if you extrapolate that linear trend, prices will rise (again, on average) 1% in a month.
Inflation is an attempt to measure how much less money is worth.
It is a weighted average of some bundle of goods and services price's increase. Money's value is in what you can exchange it for, so higher prices means money is worth less.
Monthly inflation is quoted either as "a year, ending on that month" or "since the previous month". As the values differ by more than a factor of 10, you can usually tell which one is being referred to when they say "inflation in August was 0.4%, a record high" or "inflation in August was 3.6%". You do need some context of the state of the economy, and how surprised the people talking about the numbers are. Sometimes they refer to inflation since the last month, and then annualize it, which adds to the confusion.
"Consumer Inflation"'s value depends on what the basket of goods is, and what you define as the same "good". Is a computer this year the same as the last? If the computer is 10x faster, do you ignore that, or factor it in?
What basket do you use? The typical monthly consumables purchased by a middle class citizen? By a poor citizen? By a rich citizen? A mixture, and if so which mixture?
More detailed inflation figures can focus on inflation facing each quntile of the population by household income, split durable goods from non-durable goods from services, split wage from non-wage inflation, ignore volatile things like food and energy, etc.
Inflation doesn't directly cause prices to raise; instead it is a measure of how much raise in prices happened. It can easily be a self-fullfilling prophesy, as inflation expectations can lead to everyone automatically increasing the price they charge for everything (wages, goods, etc).
Inflation can be viewed as a measurement of the "cost of holding cash". At 10% inflation per year, holding a million dollars in cash for a year costs you 100,000$ in buying power. At 1% inflation it costs 10,000$. At 0.1% inflation, 1000$.
Inflation of 10% in one year, followed by 10% the next, adds up to 1.1*1.1-1 = 21% inflation over the two years. For low inflation numbers this acts a lot like adding; the further from 0% you get the more the lower-order terms make the result larger. 1% inflation for two years adds up to 2.01%, 10% over two years 21%, 100% over two years 300%, 1000% over two years 12000%, etc. (and yes, some places suffer 1000% inflation)
Inflation is a reflection on the expansion of the money supply, aka debt, being created by a central bank. Fiat currencies usually inflate, because there is no limit to the amount of debt that can be created. The consequences of reckless money supply expansion can be seen throughout history, see Zimbabwe, though there have been many others...Brazil, Argentinia, etc...
