# Real income has gone down but prices have gone up - math error? **URL:** \ **Category:** Factual Questions\ **Created:** [December 1, 2015, 1:23am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084 "2015-12-01T01:23:23Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [December 1, 2015, 1:23am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/1 "2015-12-01T01:23:23Z")
I hear this a lot (and generally agreed with the hypothesis it is usually making with regards to the shrinking middle class). One example [here](http://www.motherjones.com/politics/2011/06/speedup-americans-working-harder-charts). But one particular aspect seems wrong mathematically: > [@](#): > > Increase in real value of the minimum wage since 1990: 21% > Increase in cost of living since 1990: 67% But surely they are basically counting the same (or a similar) thing twice. When you say the “real value” you mean adjusted for inflation, which should (approximately at least) reflect the cost of living. So you are comparing to values as if they were independent but to come up with that “real value” of the minimum wage from 1990 you have multiplied by 1.8ish, and that scale factor is meant to take into account the fact that the cost living has increased. The example above just states the two statistics without saying how they are linked, but often they are stated as “… has increased by … while … has increased by”. Which seems plain wrong. Or am I not getting something with economics of this. ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [December 1, 2015, 1:30am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/2 "2015-12-01T01:30:23Z")
No conflict at all if the minimum wage has not gone up as much as inflation - which it has not. Say there was no increase at all since 1990. Then the real value of the minimum wage today would have decreased since 1990. I hope that makes it clearer. ---
**Author:** ![Sage\_Rat](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/sage_rat/32/399_2.png) [@Sage\_Rat](https://boards.straightdope.com/u/Sage_Rat)\ **Post date:** [December 1, 2015, 1:43am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/3 "2015-12-01T01:43:08Z")
The minimum wage is a value set by law, not by the amount that it costs to live at minimum. It doesn’t change on its own, it only changes if your representatives get together and decide to raise it and only by the amount they decide to raise it. Technically, they could say that the “minimum wage” is $1 a year, regardless of all evidence to the contrary, since there is nothing to prevent them from doing so except common sense. Whereas, the cost of living is the cost of living (as computed by some group, based on their interpretation of what it means to live) as calculated from real world data. ---
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [December 1, 2015, 1:46am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/4 "2015-12-01T01:46:43Z")
> [@Voyager](#): > > No conflict at all if the minimum wage has not gone up as much as inflation - which it has not. Say there was no increase at all since 1990. Then the real value of the minimum wage today would have decreased since 1990. > I hope that makes it clearer. But they have factored the increase in inflation into how they state the minimum wage. In naive terms it has increased by 100% or so, but obviously that is pretty meaningless as 1990s dollars are worth more in 2015. But by doing the conversion to 2015 dollars and then comparing that to the cost of living increase that is mathematically incorrect. That cost of living increase IS what the conversion to 2015 dollars is meant to take into account. Again I am not arguing against their main hypothesis w.r.t. inequality and the shrinking middle class. And I don’t doubt there are significant differences to what you can buy with the minimum wage (or median wage, etc.). But this maths seems fishy. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 1, 2015, 1:51am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/5 "2015-12-01T01:51:45Z")
I wonder how they calculate the “cost of living”. I wonder if they assume modern cars and larger homes and gadgets. Thus, even if the real value of the minimum wage has gone up, because it can buy more stuff than before (?), it may not have gone up relative to the “cost of living” if the cost of living includes _much_ better stuff than in 1990. Which it does. I think in most cases this is a legit recalculation since you can’t even buy cars without the modern safety features, nor rely on over the air free transmission for your television. ---
**Author:** ![PastTense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pasttense/32/14550_2.png) [@PastTense](https://boards.straightdope.com/u/PastTense)\ **Post date:** [December 1, 2015, 1:53am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/6 "2015-12-01T01:53:05Z")
The minimum wage in 1990 was $3.80. The minimum wage currently is $7.25. That is an increase of $3.45 or a 90% increase. > **[Annual Federal Minimum Wage Rates, 1955-2021](https://www.infoplease.com/business/labor/annual-federal-minimum-wage-rates-1955-2021)** > > Annual federal minimum wage rates adjusted for inflation from 1955 to 2015 According to the Bureau of Labor Statistics there was an 82% increase in the cost of living from 1990 to 2015 > **[CPI Inflation Calculator](https://www.bls.gov/data/inflation_calculator.htm)** So you are right. (Note there is considerable controversy about the actual cost of living increase–many people believe it is vastly understated): [http://www.shadowstats.com/](http://www.shadowstats.com/) ---
**Author:** ![D18](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@D18](https://boards.straightdope.com/u/D18)\ **Post date:** [December 1, 2015, 2:42am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/7 "2015-12-01T02:42:33Z")
I don’t see why you think comparing the relative rise in the minimum wage and the cost of living tells you anything about the putative shrinking of the middle class. ---
**Author:** ![lance\_strongarm](https://avatars.discourse-cdn.com/v4/letter/l/87869e/32.png) [@lance\_strongarm](https://boards.straightdope.com/u/lance_strongarm)\ **Post date:** [December 1, 2015, 2:50am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/8 "2015-12-01T02:50:32Z")
> [@griffin1977](#): > > But they have factored the increase in inflation into how they state the minimum wage. I get what you mean. I think this means the increase in cost of living is more than just inflation (as I see Ludovic also pointed out). ---
**Author:** ![Peremensoe](https://avatars.discourse-cdn.com/v4/letter/p/ce7236/32.png) [@Peremensoe](https://boards.straightdope.com/u/Peremensoe)\ **Post date:** [December 1, 2015, 2:55am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/9 "2015-12-01T02:55:17Z")
Is COL not reckoned by the CPI? Is that not also the most common (though not only) way to measure worth across time? ---
**Author:** ![Voyager](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/voyager/32/133_2.png) [@Voyager](https://boards.straightdope.com/u/Voyager)\ **Post date:** [December 1, 2015, 7:31am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/10 "2015-12-01T07:31:20Z")
> [@griffin1977](#): > > But they have factored the increase in inflation into how they state the minimum wage. In naive terms it has increased by 100% or so, but obviously that is pretty meaningless as 1990s dollars are worth more in 2015. But by doing the conversion to 2015 dollars and then comparing that to the cost of living increase that is mathematically incorrect. That cost of living increase IS what the conversion to 2015 dollars is meant to take into account. > > Again I am not arguing against their main hypothesis w.r.t. inequality and the shrinking middle class. And I don’t doubt there are significant differences to what you can buy with the minimum wage (or median wage, etc.). But this maths seems fishy. My example was an extreme case to illustrate the principle. But I agree with the others - the numbers don’t mean a lot until you define cost of living and compare the minimum wage to other values. [This page](http://www.epi.org/publication/charting-wage-stagnation/) has a chart of the minimum wage over time, as well as a bunch of other information. 21% real increase is actually better than wage increases, but due only to the increase in the Obama years. So while the numbers may be right they really aren’t comparable. ---
**Author:** ![bob\_2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bob_2/32/3341_2.png) [@bob\_2](https://boards.straightdope.com/u/bob_2)\ **Post date:** [December 1, 2015, 11:23am UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/11 "2015-12-01T11:23:46Z")
I wonder what would happen if a law was passed that said all wages had to be increased annually by at least the increase in the cost of living? ---
**Author:** ![Shodan](https://avatars.discourse-cdn.com/v4/letter/s/9f8e36/32.png) [@Shodan](https://boards.straightdope.com/u/Shodan)\ **Post date:** [December 1, 2015, 12:53pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/12 "2015-12-01T12:53:36Z")
> [@bob\_2](#): > > I wonder what would happen if a law was passed that said all wages had to be increased annually by at least the increase in the cost of living? Inflation. Regards, Shodan ---
**Author:** ![boffking](https://avatars.discourse-cdn.com/v4/letter/b/858c86/32.png) [@boffking](https://boards.straightdope.com/u/boffking)\ **Post date:** [December 1, 2015, 3:45pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/13 "2015-12-01T15:45:23Z")
> [@Ludovic](#): > > nor rely on over the air free transmission for your television. Why can’t you? I use an antenna for free HD channels. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 1, 2015, 3:46pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/14 "2015-12-01T15:46:10Z")
I’ve tried multiple different antennas in multiple different places in the house in multiple different houses in Central Florida and never get more than 1 channel. ---
**Author:** ![TriPolar](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/tripolar/32/3008_2.png) [@TriPolar](https://boards.straightdope.com/u/TriPolar)\ **Post date:** [December 1, 2015, 4:03pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/15 "2015-12-01T16:03:08Z")
> [@Shodan](#): > > Inflation. > > Regards, > Shodan And if there’s no increase in minimum wage there won’t be inflation? ---
**Author:** ![lance\_strongarm](https://avatars.discourse-cdn.com/v4/letter/l/87869e/32.png) [@lance\_strongarm](https://boards.straightdope.com/u/lance_strongarm)\ **Post date:** [December 1, 2015, 4:07pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/16 "2015-12-01T16:07:35Z")
> [@Peremensoe](#): > > Is COL not reckoned by the CPI? Is that not also the most common (though not only) way to measure worth across time? [http://www.bls.gov/dolfaq/bls\_ques2.htm](http://www.bls.gov/dolfaq/bls_ques2.htm) “The CPI frequently is called a cost-of-living index, but it differs in important ways from a complete cost-of-living measure…” ---
**Author:** ![GreasyJack](https://avatars.discourse-cdn.com/v4/letter/g/df705f/32.png) [@GreasyJack](https://boards.straightdope.com/u/GreasyJack)\ **Post date:** [December 1, 2015, 7:27pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/17 "2015-12-01T19:27:55Z")
One thing that’s a bit of a wildcard in the various cost-of-living metrics is housing prices. It’s a pretty minor component of things like the CPI, but on a COL index that’s describing a more basic just-above-poverty standard of living, housing costs are huge. Over the last few decades, housing costs have increased faster than inflation so if they’re using one of those indexes it’s very possible that cost-of-living has increased in real terms. ---
**Author:** ![griffin1977](https://avatars.discourse-cdn.com/v4/letter/g/977dab/32.png) [@griffin1977](https://boards.straightdope.com/u/griffin1977)\ **Post date:** [December 1, 2015, 7:41pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/18 "2015-12-01T19:41:29Z")
> [@lance\_strongarm](#): > > I get what you mean. > > I think this means the increase in cost of living is more than just inflation (as I see Ludovic also pointed out). But those two numbers, stated like they usually are, are not showing that. The 21% vs 67% comparison is not a mathematically meaningful one. It is suggesting something that isn’t actually shown by those numbers. ---
**Author:** ![Lemur866](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lemur866/32/434_2.png) [@Lemur866](https://boards.straightdope.com/u/Lemur866)\ **Post date:** [December 1, 2015, 7:45pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/19 "2015-12-01T19:45:53Z")
> [@TriPolar](#): > > And if there’s no increase in minimum wage there won’t be inflation? He was responding to “all wages”, not “the minimum wage”. If we decree that EVERYONE must get a raise every year based on the CPI, then what happens? Since there aren’t that many people on minimum wage tying minimum wage to inflation might make sense, and if it did cause inflation it would only be by a tiny amount, and since inflation is historically low right now it shouldn’t be a problem even if it did. ---
**Author:** ![Ludovic](https://avatars.discourse-cdn.com/v4/letter/l/7ab992/32.png) [@Ludovic](https://boards.straightdope.com/u/Ludovic)\ **Post date:** [December 1, 2015, 7:52pm UTC](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084/20 "2015-12-01T19:52:22Z")
I am not sure if it would work but if it did I would expect the effect to be less than expected from a simple calculation. I don’t think there would be very much general inflation, but I would expect some medium term inflation in low end housing, since apartments can now charge more and new apartments can’t just spring up overnight like in an ideal market. Who knows if this would eat up all the increase. [Next page](https://boards.straightdope.com/t/real-income-has-gone-down-but-prices-have-gone-up-math-error/739084.md?page=2)