(First post in this forum for me. So, Hi everyone! And the blog is a gold mine! Thanks! I have lots of questions. Here's the first one.)
Periodically, CPI is calculated by aggregating prices in dollars:
1 CPI(t) = A(t) + B(t) + C(t) + ..., where A(t) is prices of products/services A
1 CPI(t) = x dollars(t)
So, if for previous month I have: 1 CPI(t0) = x dollars(t0)
And for this month I have: 1 CPI(t1) = y dollars(t1)
By definition 1 CPI(t0) = 1 CPI(t1), so x dollars(t0) = y dollars(t1), then dollars(t0) = y/x dollars(t1)
(1-y/x) is inflation. Right?
But what if some businesses start to setting prices in CPI?
If the price is 0.02 CPI, and CPI(t0) = 1000 dollars(t0), I have to pay 20 dollars.
Next month, the price is still 0.02 CPI, but CPI(t1) = 1200 dollars(t0), so I have to pay 24 dollars.
It's like the Unidad de Fomento: some prices are set in UF, but I pay pesos.
But what happens if more and more prices are expressed in CPI?
1 CPI(t1) = x dollars(t1) + y CPI(t0) ?
Considering that CPI(t0) = CPI(t1), should I have:
(1-y) CPI(t1) = x dollars(t1) ?
As long as (1-y) is positive, I do not see too many problems.
But what happens if (1-y) becomes negative?
Or if x = 0?
In other words, as sellers set their prices in CPI, does dollars inflation is calculated on less and less products/services prices, or CPI prices are also taking account?
And what happens if the sellers sell for a total greater than the reference basket, knowing that their prices are expressed according to this reference basket?
I hope it's an interesting question for this forum!