The wording of percentages is tricky

The wording for percentage increases is tricky.

Say the original price of a widget is $80, and a shortage pushes the price to $200. There are various ways to refer to that:

(1) The price of widgets increased by 150%.

(2) The current price of widgets is 150% higher than the old price.

(3) The current price of widgets is 250% of the old price.

(4) Widgets cost 2.5 times as much as they used to.

Note that the multiplier in the first two cases is 1.5x, but it's 2.5x in the last two cases.

Look at cases 2 and 3 closely: Case 2 refers to the amount of the *increase* in the prices, while Case 3 is comparing the prices themselves.

This article correctly refers to a 152% increase of a certain product, but this one refers to it as "a 252% price increase" (for a product that went from $37.98 to $95.98).

Discuss.

All four statements are correct, of course. I prefer the phrasing of #1.

Where things get more confusing is in the change of a percentage. For example, suppose inflation goes from 4% to 5%. I think one could correctly say either:

A) Inflation went up by 1%.
B) The rate of inflation went up by 25%.

I prefer A.

For inflation going from 4% to 5%, I think most people would call that a 1% increase. The concise way to state the increase is 1% absolute or 25% relative

Speaking of percentages, one of the most common mistakes is with capital losses. If a stock price declines by 50%, many people would say it needs to increase 50% to fully recover.

So we're all in agreement that the second source I quoted above, which referred to a 252% increase, got it wrong?

Quote: Wizard

Suppose inflation goes from 4% to 5%. I think one could correctly say...Inflation went up by 1%.

I've always considered that to be unquestionably wrong. The increase is definitely 25%, not 1%. Whether the thing that's increasing is pigs, boxes, or percentage points, when the quantity changes from 4 to 5, that's a 25% increase, definitely.

To use "1" accurately, one would have to say that inflation went up by 1 *point* (or 1 "percentage point").

Quote: Ace2

Speaking of percentages, one of the most common mistakes is with capital losses. If a stock price declines by 50%, many people would say it needs to increase 50% to fully recover.

If a store wants to raise prices by 50% then hand me a 50% off coupon, I'll take it.

As far as craps machines go, a PB 6 or 8 pays 1.1667x, but when the machine pays your bet, it may say you won 2.1667x because it adds your wager to the winning payout.

I'm wondering about currencies that lop 4 zeroes off the end. Suddenly 10,000 becomes 1. And a few months later all the zeroes came back plus a couple more.
TOP 10 - The Weakest World Currencies in 2021 https://fxssi.com/top-10-of-the-weakest-world-currencies-in-current-year

Quote: ChumpChange

As far as craps machines go, a PB 6 or 8 pays 1.1667x, but when the machine pays your bet, it may say you won 2.1667x because it adds your wager to the winning payout.

That's the difference between 7 TO 6 and 13 FOR 6.

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if inflation goes from 4 to 5% in the following year (and BTW that's very high and atypical) the rate of inflation has increased by 25%

and saying it that way makes it seem like alarms need to be sounded

but the average price increase of a typical product was only 1%

a $100 product will increase on average to $104 with 4% inflation

the following year a $100 product on average will only increase to $105 with 5% inflation

the sound of these words, IMO, more truly reflects what is actually happening

as does inflation went up by 1 percentage point





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Inflation compounds. So if you have 0.4% in one month, 0.6% the next month, and 0.8% the next month, and 1.0% the next month, and 1.2% the next month. Lemme get a calculator.
$100 to $100.40
$100.40 to $101.00
$101.00 to $101.81
$101.81 to $102.83
$102.83 to $104.06
In 5 months, you've already had 4% inflation.

So if you have 4% in one month, 6% the next month, and 8% the next month, and 10% the next month, and 12% the next month.
$100 to $104
$104 to $110.24
$110.24 to $119.06
$119.06 to $130.97
$130.97 to $146.68
In 5 months, you've already had 46.7% inflation.

So if you have 40% in one month, 60% the next month, and 80% the next month, and 100% the next month, and 120% the next month.
$100 to $140
$140 to $224
$224 to $403.20
$403.20 to $806.40
$806.40 to $1774.08
In 5 months, you've already had 1674% inflation.

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in your first example you have inflation increasing by an average of 1% in the final 3 months

that rarely happens - and when it does it's generally called hyperinflation which occurred in the 70s

inflation peaked 3 times in 1974, 1979 and 1980 and went to slightly above 12%


to put things in perspective:


the average annual inflation rate between 1990 and 2018 was 2.46%

right now our economy is facing inflation - and it is unclear how it will play out




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Past results cannot predict future conditions at this point. I'm seeing YouTube videos going crazy about inflation of certain products going up from 50% to over 100% just this year. Used cars are up 33%! We are definitely in some kind of hyperinflation right now.

Quote: ChumpChange

Past results cannot predict future conditions at this point. I'm seeing YouTube videos going crazy about inflation of certain products going up from 50% to over 100% just this year. Used cars are up 33%! We are definitely in some kind of hyperinflation right now.

the Fed Chairman Jerome Powell has indicated that he will consider raising interest rates which historically is a tool to tame inflation

unfortunately, if it doesn't work there aren't many other tools

in the 70s when inflation was considered to be out of control President Nixon enacted Wage and Price Controls

prices and wages were locked and could not increase with a few exceptions

eventually, inflation did come back down - but it took a long time





suggestion:


nothing wrong with watching YouTube vids but there are much better sources of info on this subject



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I wonder if Texas electricity goes to $9 per kwhr again this week.

Quote: MichaelBluejay

I've always considered that to be unquestionably wrong. The increase is definitely 25%, not 1%. Whether the thing that's increasing is pigs, boxes, or percentage points, when the quantity changes from 4 to 5, that's a 25% increase, definitely.

To use "1" accurately, one would have to say that inflation went up by 1 *point* (or 1 "percentage point").

I could be wrong, but I disagree with you. I think it's fine to say inflation went up by one percent, although it would be more clear, I think, to say "by one basis point."*

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Note: See correction below.

Quote: Wizard

I could be wrong, but I disagree with you. I think it's fine to say inflation went up by one percent, although it would be more clear, I think, to say "by one basis point."

I agree with your overall point but have a technical correction. A “basis point” is one hundredth of a “percentage point.”

Quote: unJon

I agree with your overall point but have a technical correction. A “basis point” is one hundredth of a “percentage point.”

Ooops. That was embarrassing.

President Ford was able to get inflation under control by distributing WIN buttons.
If everyone does their patriotic duty and wears their Whip Inflation Now lapel pins, we can turn the corner in a matter of months.

We'll see how many states "DROP DEAD" on July 1st when the new fiscal year begins. I suspect the interstate freeway rest rooms will be shutdown in a cost saving move.

Quote: MichaelBluejay

The wording for percentage increases is tricky.

Say the original price of a widget is $80, and a shortage pushes the price to $200. There are various ways to refer to that:

(1) The price of widgets increased by 150%.

(2) The current price of widgets is 150% higher than the old price.

(3) The current price of widgets is 250% of the old price.

(4) Widgets cost 2.5 times as much as they used to.

Note that the multiplier in the first two cases is 1.5x, but it's 2.5x in the last two cases.

Look at cases 2 and 3 closely: Case 2 refers to the amount of the *increase* in the prices, while Case 3 is comparing the prices themselves.

This article correctly refers to a 152% increase of a certain product, but this one refers to it as "a 252% price increase" (for a product that went from $37.98 to $95.98).

Discuss.

The wording is tricky and often requires some explanation or accompanying math for what one is trying to express, lest a reader or listener get the wrong idea. With that, let's take a look at the underlying math by which we arrive from one to another for each of your four examples:

(1) The price of widgets increased by 150%.

The price was $80 and we are saying that it increased by 150% to $200. That's a simple matter of 80 * 1.5 = 200. However, this particular means of expressing it is such that we have already arrived at the solution. Most people would not have arrived at the solution already; they would simply see that widgets were $80 and are now $200.

This phrasing would be useful if accompanied by the starting price of widgets.

(2) The current price of widgets is 150% higher than the old price.

This expression has also already arrived at a solution. This would also be useful if accompanied by the starting price of widgets.

(3) The current price of widgets is 250% of the old price.

THIS IS THE WORDING I LIKE because it tells the person the price difference and expresses it in a way that the person can look at the current price and reverse engineer what the price used to be. 200/2.5 = 80

I like this because you could look up the current price of widgets (which would be easier to find) and then use that to determine the old, and no longer practically relevant, price.

(4) Widgets cost 2.5 times as much as they used to.

Same as three, but does not express it as a percentage. You can still just divide by 2.5, but it would be an unusual way of phrasing it for a non-round percentage, "Widgets cost 2.63x more than they used to," saying, "263%," is cleaner.

I wouldn't have a problem figuring out any of these expressions based on looking at the current price of widgets, but I think a greater number of people could figure it out with the way that it is expressed in #3. You don't have to come up with anything near an algebraic formula for #3.

Quote: billryan

President Ford was able to get inflation under control by distributing WIN buttons.
If everyone does their patriotic duty and wears their Whip Inflation Now lapel pins, we can turn the corner in a matter of months.

that program was almost as successful as Nancy Reagan's program - "JUST SAY NO" to drugs


drug dealers and the cartels lost a tremendous amount of money and business because of that slogan....................NOT........................(~:\




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Quote: ChumpChange

I suspect the interstate freeway rest rooms will be shutdown in a cost saving move.

I suspect a lot more public health hazards from travellers relieving themselves on exit ramps.

I doubt we can afford to save that much.

Warning that discussion about the transportation budget violates rules against political discussion and hijacking.

I think there is a difference whether the bounds for the measure can go negative.

Take examples where the measure can cross the zero boundary.
(i) The rate of inflation went up from 2% to 4%. Widgets Corp's profit went up from 100m to 200m.
(ii) The rate of inflation went from -1% to 1%. Widgets turned a loss of 50m into a profit of 50m.
(iii) The rate of inflation went from 0.01% to 1.2%. Widgets, who broke even last year, made 75m.

Then consider price hikes (yes I know the price of a can of baked beans was -2p once in a UK supermarket ++).
Following the increases in taxes the price of a pint of beer has gone up 20p from £3.60.
The cost of fuel (petrol, gas, diesel) has dropped 5p to £1.25 / litre at the local supermarket.

With prices one can reasonably say they went up by about 5%, or down about 4%. But that doesn't work for the first example.

++ http://www.factfiend.com/time-store-paid-people-take-stuff/ (warning this page has bad language)
https://www.heraldscotland.com/news/12058680.petrol-lower-still-but-beans-make-history/ (mentions the beans as well as fuel)

I like use of the word, “By,” for percentages. It lets you know you’re comparing the increase in a percentage to some previous percentage.