Toy model: There are 10 goods you buy. They're reasonably substitutable for one another (maybe they're different foods, or types of computer game, or something).
Every year one of these increases in price by 20%. A different one every year, cycling between them all. So every 10 years, they all increase by 20%, an effective inflation rate of about 1.8%.
We have a price index based on a basket of these goods. At the start of year 1, our basket contains equal quantities of all the goods. In year 1, the price of good #1 abruptly goes up 20%, having been stable for the last ten years. OK, we say, this is a thing that's experiencing some sort of anomalous increase in price, so we'll take it out of the basket. At the end of the year, we look at our basket of goods 2..10. The prices haven't increased at all! Zero percent inflation! Splendid.
At the start of year 2, our basket contains equal quantities of goods 2..10. In year 2, the price of good #2 abruptly goes up 20%, having been stable for the last ten years. Another anomalous increase. Better take this one out of the basket too. At the end of the year, we look at our basket of goods 3..10. The prices haven't increased at all! Zero inflation again.
At the start of year 3, our basket contains equal quantities of goods 3..10. In year 3, the price of good #3 abruptly goes up 20%, having been stable for the last ten years. Dang, better take this one out of the basket. Our basket is getting a little short of this kind of good. Hey, good 1 has been stable for a couple of years after its blip in year 1, let's put it back in. At the end of the year, we look at our basket of goods 1,4,..10. The prices haven't increased at all! Zero inflation.
And so we continue. Each year we remove an item that obviously doesn't belong in the basket because it's suffered an anomalous increase in price, so of course consumers will be switching to something else. Sometimes we put back in things that have been stable for a while. Every year we get an inflation figure of zero.
And yet, somehow, ten years after we started all the prices are 20% higher. How on earth did that happen?
Every year one of these increases in price by 20%. A different one every year, cycling between them all. So every 10 years, they all increase by 20%, an effective inflation rate of about 1.8%.
We have a price index based on a basket of these goods. At the start of year 1, our basket contains equal quantities of all the goods. In year 1, the price of good #1 abruptly goes up 20%, having been stable for the last ten years. OK, we say, this is a thing that's experiencing some sort of anomalous increase in price, so we'll take it out of the basket. At the end of the year, we look at our basket of goods 2..10. The prices haven't increased at all! Zero percent inflation! Splendid.
At the start of year 2, our basket contains equal quantities of goods 2..10. In year 2, the price of good #2 abruptly goes up 20%, having been stable for the last ten years. Another anomalous increase. Better take this one out of the basket too. At the end of the year, we look at our basket of goods 3..10. The prices haven't increased at all! Zero inflation again.
At the start of year 3, our basket contains equal quantities of goods 3..10. In year 3, the price of good #3 abruptly goes up 20%, having been stable for the last ten years. Dang, better take this one out of the basket. Our basket is getting a little short of this kind of good. Hey, good 1 has been stable for a couple of years after its blip in year 1, let's put it back in. At the end of the year, we look at our basket of goods 1,4,..10. The prices haven't increased at all! Zero inflation.
And so we continue. Each year we remove an item that obviously doesn't belong in the basket because it's suffered an anomalous increase in price, so of course consumers will be switching to something else. Sometimes we put back in things that have been stable for a while. Every year we get an inflation figure of zero.
And yet, somehow, ten years after we started all the prices are 20% higher. How on earth did that happen?