One of the best things about taking physics classes is that the equations you learn are directly applicable to the real world. Every so often, while reading a book or watching a movie, I’m seized by the sudden urge to check it for plausibility. A few scratches on a piece of paper later and I will generally know one way or the other.

One of the most amusing things I’ve found doing this is that the people who come up with the statistics for Pokémon definitely don’t have any sort of education in physics.

Takes Onix. Onix is a rock/ground Pokémon renowned for its large size and sturdiness. Its physical statistics reflect this. It’s 8.8 metres (28′) long and 210kg (463lbs).

Surely such a large and tough Pokémon should be very, very dense, right? Density is such an important tactile cue for us. Don’t believe me? Pick up a large piece of solid medal. Its surprising weight will make you take it seriously.

Let’s check if Onix would be taken seriously, shall we? Density is equal to mass divided by volume. We use the symbol ρ to represent density, which gives us the following equation:

We already know Onix’s mass. Now we just need to calculate its volume. Luckily Onix is pretty cylindrical, so we can approximate it with a cylinder. The equation for the volume of a cylinder is pretty simple:

Where π is the ratio between the diameter of a circle and its circumference (approximately 3.1415…, no matter what Indiana says), r is the radius of a circle (always one half the diameter), and h is the height of the cylinder.

Given that we know Onix’s height, we just need its diameter. Luckily the Pokémon TV show gives us a sense of scale.

Judging by the image, Onix probably has an average diameter somewhere around a metre (3 feet for the Americans). This means Onix has a radius of 0.5 metres and a height of 8.8 metres. When we put these into our equation, we get:

For a volume of approximately 6.9m3. To get a comparison I turned to Wolfram Alpha which told me that this is about 40% of the volume of a gray whale or a freight container (which incidentally implies that gray whales are about the size of standard freight containers).

Armed with a volume, we can calculate a density.

Okay, so we know that Onix is 30.4 kg/m3, but what does that mean?

Well it’s currently hard to compare. I’m much more used to seeing densities of sturdy materials expressed in tonnes per cubic metre or grams per cubic centimetre than I am seeing them expressed in kilograms per cubic metre. Luckily, it’s easy to convert between these.

There are 1000 kilograms in a ton. If we divide our density by a thousand we can calculate a new density for Onix of 0.0304t/m3.

How does this fit in with common materials, like wood, Styrofoam, water, stone, and metal?

 Material Density (t/m3) Styrofoam 0.028 Onix 0.03 Balsa 0.16 Oak [1] 0.65 Water 1 Granite 2.6 Steel 7.9

From this chart, you can see that Onix’s density is eerily close to Styrofoam. Even the notoriously light balsa wood is five times denser than him. Actual rock is about 85 times denser. If Onix was made of granite, it would weigh 18 tonnes, much heavier than even Snorlax (the heaviest of the original Pokémon at 460kg).

While most people wouldn’t be able to pick Onix up (it may not be dense, but it is big), it wouldn’t be impossible to drag it. Picking up part of it would feel disconcertingly light, like picking up an aluminum ladder or carbon fibre bike, only more so.

How did the creators of Pokémon accidently bestow one of the most famous of their creations with a hilariously unrealistic density?

I have a pet theory.

I went to school for nanotechnology engineering. One of the most important things we looked into was how equations scaled with size.

Humans are really good at intuiting linear scaling. When something scales linearly, every twofold change in one quantity brings about a twofold change in another. Time and speed scale linearly (albeit inversely). Double your speed and the trip takes half the time. This is so simple that it rarely requires explanation.

Unfortunately for our intuitions, many physical quantities don’t scale linearly. These were the cases that were important for me and my classmates to learn, because until we internalized them, our intuitions were useless on the nanoscale. Many forces, for example, scale such that they become incredibly strong incredibly quickly at small distances. This leads to nanoscale systems exhibiting a stickiness that is hard on our intuitions.

It isn’t just forces that have weird scaling though. Geometry often trips people up too.

In geometry, perimeter is the only quantity I can think of that scales linearly with size. Double the length of the sides of a square and the perimeter doubles. The area, however does not. Area is quadratically related to side length. Double the length of a square and you’ll find the area quadruples. Triple the length and the area increases nine times. Area varies with the square of the length, a property that isn’t just true of squares. The area of a circle is just as tied to the square of its radius as a square is to the square of its length.

Volume is even trickier than radius. It scales with the third power of the size. Double the size of a cube and its volume increases eight-fold. Triple it, and you’ll see 27 times the volume. Volume increases with the cube (which again works for shapes other than cubes) of the length.

If you look at the weights of Pokémon, you’ll see that the ones that are the size of humans have fairly realistic weights. Sandslash is the size of a child (it stands 1m/3′ high) and weighs a fairly reasonable 29.5kg.

(This only works for Pokémon really close to human size. I’d hoped that Snorlax would be about as dense as marshmallows so I could do a fun comparison, but it turns out that marshmallows are four times as dense as Snorlax – despite marshmallows only having a density of ~0.5t/m3)

Beyond these touchstones, you’ll see that the designers of Pokémon increased their weight linearly with size. Onix is a bit more than eight times as long as Sandslash and weighs seven times as much.

Unfortunately for realism, weight is just density times volume and as I just said, volume increases with the cube of length. Onix shouldn’t weigh seven or even eight times as much as Sandslash. At a minimum, its weight should be eight times eight times eight multiples of Sandslash’s; a full 512 times more.

Scaling properties determine how much of the world is arrayed. We see extremely large animals more often in the ocean than in the land because the strength of bones scales with the square of size, while weight scales with the cube. Become too big and you can’t walk without breaking your bones. Become small and people animate kids’ movies about how strong you are. All of this stems from scaling.

These equations aren’t just important to physicists. They’re important to any science fiction or fantasy writer who wants to tell a realistic story.

Or, at least, to anyone who doesn’t want their work picked apart by physicists.

Footnotes

[1] Not the professor. His density is 0.985t/m3. ^

The Scale of Inequality

When dealing with questions of inequality, I often get boggled by the sheer size of the numbers. People aren’t very good at intuitively parsing the difference between a million and a billion. Our brains round both to “very large”. I’m actually in a position where I get reminded of this fairly often, as the difference can become stark when programming. Running a program on a million points of data takes scant seconds. Running the same set of operations on a billion data points can take more than an hour. A million seconds is eleven and a half days. A billion seconds 31 years.

Here I would like to try to give a sense of the relative scale of various concepts in inequality. Just how much wealth do the wealthiest people in the world possess compared to the rest? How much of the world’s middle class is concentrated in just a few wealthy nations? How long might it take developing nations to catch up with developed nations? How long before there exists enough wealth in the world that everyone could be rich if we just distributed it more fairly?

According to the Forbes billionaire list, there are (as of the time of writing) 2,208 billionaires in the world, who collectively control \$9.1 trillion in wealth (1 trillion seconds ago was the year 29691 BCE, contemporaneous with the oldest cave paintings in Europe). This is 3.25% of the total global wealth of \$280 trillion.

The US Federal Budget for 2019 is \$4.4 trillion. State governments and local governments each spend another \$1.9 trillion. Some \$700 billion dollars is given to those governments by the Federal government. With that subtracted, total US government spending is projected to be \$7.5 trillion next year.

Therefore, the whole world population of billionaires holds assets equivalent to 1.2 years of US government outlays. Note that US government outlays aren’t equivalent to that money being destroyed. It goes to pay salaries or buy equipment. The comparison here is simply to illustrate how private wealth stacks up against the budgets that governments control.

If we go down by a factor of 1000, there are about 15 million millionaires in the world (according to Wikipedia). Millionaires collectively hold \$37.1 trillion (13.25% of all global wealth). All of the wealth that millionaires hold would be enough to fund US government spending for five years.

When we see sensational headlines, like “Richest 1% now owns half the world’s wealth“, we tend to think that we’re talking about millionaires and billionaires. In fact, millionaires and billionaires only own about 16.5% of the world’s wealth (which is still a lot for 0.2% of the world’s population to hold). The rest is owned by less wealthy individuals. The global 1% makes \$32,400 a year or more. This is virtually identical to the median American yearly salary. This means that almost fully half of Americans are in the global 1%. Canadians now have a similar median wage, which means a similar number are in the global 1%.

To give a sense of how this distorts the global middle class, I used Povcal.net, the World Bank’s online tool for poverty measurement. I looked for the percentage of a country’s population making between 75% and 125% of the median US income (at purchasing power parity, which takes into account cheaper goods and services in developing countries), equivalent to \$64-\$107US per day (which is what you get when you divide 75% and 125% of the median US wage by 365 – as far as I can tell, this is the procedure that gives us numbers like \$1.25 per day income as the threshold for absolute poverty).

I grabbed what I thought would be an interesting set of countries: The G8, BRICS, The Next 11, Australia, Botswana, Chile, Spain, and Ukraine. These 28 countries had – in the years surveyed – a combined population of 5.3 billion people and had among them the 17 largest economies in the world (in nominal terms). You can see my spreadsheet collecting this data here.

The United States had by far the largest estimated middle class (73 million people), followed by Germany (17 million), Japan (12 million), France (12 million), and the United Kingdom (10 million). Canada came next with 8 million, beating most larger countries, including Brazil, Italy, Korea, Spain, Russia, China, and India. Iran and Mexico have largely similar middle-class sizes, despite Mexico being substantially larger. Botswana ended up having a larger middle class than the Ukraine.

This speaks to a couple of problems when looking at inequality. First, living standards (and therefore class distinctions) are incredibly variable from country to country. A standard of living that is considered middle class in North America might not be the same in Europe or Japan. In fact, I’ve frequently heard it said that the North American middle class (particularly Americans and Canadians) consume more than their equivalents in Europe. Therefore, this should be looked at as a comparison of North American equivalent middle class – who, as I’ve already said, are about 50% encompassed in the global 1%.

Second, we tend to think of countries in Europe as generally wealthier than countries in Africa. This isn’t necessarily true. Botswana’s GDP per capita is actually three times larger than Ukraine’s when unadjusted and more than twice as large at purchasing power parity (which takes into account price differences between countries). It also has a higher GDP per capita than Serbia, Albania, and Moldova (even at purchasing power parity). Botswana, Seychelles, and Gabon have per capita GDPs at purchasing power parity that aren’t dissimilar from those possessed by some less developed European countries.

Botswana, Gabon, and Seychelles have all been distinguished by relatively high rates of growth since decolonization, which has by now made them “middle income” countries. Botswana’s growth has been so powerful and sustained that in my spreadsheet, it has a marginally larger North American equivalent middle class than Nigeria, a country approximately 80 times larger than it.

Of all the listed countries, Canada had the largest middle class as a percent of its population. This no doubt comes partially from using North American middle-class standards (and perhaps also because of the omission of the small, homogenous Nordic countries), although it is also notable that Canada has the highest median income of major countries (although this might be tied with the United States) and the highest 40th percentile income. America dominates income for people in the 60th percentile and above, while Norway comes out ahead for people in the 30th percentile or below.

The total population of the (North American equivalent) middle class in these 28 countries was 170 million, which represents about 3% of their combined population.

There is a staggering difference in consumption between wealthy countries and poor countries, in part driven by the staggering difference in the size of middle (and higher classes) – people with income to spend on things beyond immediate survival. According to Trading Economics, the total disposable income of China is \$7.84 trillion (dollars are US). India has \$2.53 trillion. Canada, with a population almost 40 times smaller than either, has a total disposable income of \$0.96 trillion, while America, with a population about four times smaller than either China or India has a disposable income of \$14.79 trillion, larger than China and India put together. If China was as wealthy as Canada, its yearly disposable income would be almost \$300 trillion, approximately equivalent to the total amount of wealth in the world.

According to Wikipedia, The Central African Republic has the world’s lowest GDP per capita at purchasing power parity, making it a good candidate for the title of “world’s poorest country”. Using Povcal, I was able to estimate the median wage at \$1.33 per day (or \$485 US per year). If the Central African Republic grew at the same rate as Botswana did post-independence (approximately 8% year on year) starting in 2008 (the last year for which I had data) and these gains were seen in the median wage, it would take until 2139 for it to attain the same median wage as the US currently enjoys. This of course ignores development aid, which could speed up the process.

All of the wealth currently in the world is equivalent to \$36,000 per person (although this is misleading, because much of the world’s wealth is illiquid – it’s in houses and factories and cars). All of the wealth currently on the TSX is equivalent to about \$60,000 per Canadian. All of the wealth currently on the NYSE is equivalent to about \$65,000 per American. In just corporate shares alone, Canada and the US are almost twice as wealthy as the global average. This doesn’t even get into the cars, houses, and other resources that people own in those countries.

If total global wealth were to grow at the same rate as the market, we might expect to have approximately \$1,000,000 per person (not inflation adjusted) sometime between 2066 and 2072, depending on population growth. If we factor in inflation and want there to be approximately \$1,000,000 per person in present dollars, it will instead take until sometime between 2102 and 2111.

This assumes too much, of course. But it gives you a sense of how much we have right now and how long it will take to have – as some people incorrectly believe we already do – enough that everyone could (in a fair world) have so much they might never need to work.

This is not of course, to say, that things are fair today. It remains true that the median Canadian or American makes more money every year than 99% of the world, and that the wealth possessed by those median Canadians or Americans and those above them is equivalent to that held by the bottom 50% of the world. Many of us, very many of those reading this perhaps, are the 1%.

That’s the reality of inequality.

The Cambridge Analytica scandal has put tech companies front and centre. If the thinkpieces along the lines of “are the big tech companies good or bad for society” were coming out any faster, I might have to doubt even Google’s ability to make sense of them all.

This isn’t another one of those thinkpieces. Instead it’s an attempt at an analysis. I want to understand in monetary terms how much one tech company – Google – puts into or takes out of everyone’s pockets. This analysis is going to act as a template for some of the more detailed analyses of inequality I’d like to do later, so if you have a comment about methodology, I’m eager to hear it.

Here’s the basics: Google is a large technology company that primarily makes money off of ad revenues. Since Google is a publicly traded company, statistics are easy to come by. In 2016, Google brought in \$89.5 billion in revenue and about 89% of that was from advertising. Advertising is further broken down between advertising on Google sites (e.g. Google Search, Gmail, YouTube, Google Maps, etc.) which account for 80% of advertising revenue and advertising on partner sites, which covers the remainder. The remaining 11% is made up of a variety of smaller projects – selling corporate licenses of its GSuite office software, the Google Play Store, the Google Cloud Computing Platform, and several smaller projects.

There are two ways that we can track how Google’s existence helps or hurts you financially. First, there’s the value of the software it provides. Google’s search has become so important to our daily life that we don’t even notice it anymore – it’s like breathing. Then there’s YouTube, which has more high-quality content than anyone could watch in a lifetime. There’s Google Docs, which are almost a full (free!) replacement for Microsoft Office. There’s Gmail, which is how basically everyone I know does their email. And there’s Android, currently the only viable alternative to iOS. If you had to pay for all of this stuff, how much would you be out?

Second, we can look at how its advertising arm has changed the prices of everything we buy. If Google’s advertising system has driven an increase in spending on advertising (perhaps by starting an arms race in advertising, or by arming marketing managers with graphs, charts and metrics that they can use to trigger increased spending), then we’re all ultimately paying for Google’s software with higher prices elsewhere (we could also be paying with worse products at the same prices, as advertising takes budget that would otherwise be used on quality). On the other hand, if more targeted advertising has led to less advertising overall, then everything will be slightly less expensive (or higher quality) than the counterfactual world in which more was spent on advertising.

Once we add this all up, we’ll have some sort of answer. We’ll know if Google has made us better off, made us poorer, or if it’s been neutral. This doesn’t speak to any social benefits that Google may provide (if they exist – and one should hope they do exist if Google isn’t helping us out financially).

To estimate the value of the software Google provides, we should compare it to the most popular paid alternatives – and look into the existence of any other good free alternatives. Because of this, we can’t really evaluate Search, but because of its existence, let’s agree to break any tie in favour of Google helping us.

On the other hand, Google docs is very easy to compare with other consumer alternatives. Microsoft Office Home Edition costs \$109 yearly. Word Perfect (not that anyone uses it anymore) is \$259.99 (all prices should be assumed to be in Canadian dollars unless otherwise noted).

Free alternatives exist in the form of OpenOffice and LibreOffice, but both tend to suffer from bugs. Last time I tried to make a presentation in OpenOffice I found it crashed approximately once per slide. I had a similar experience with LibreOffice. I once installed it for a friend who was looking to save money and promptly found myself fixing problems with it whenever I visited his house.

My crude estimate is that I’d expect to spend four hours troubleshooting either free alternative per year. Weighing this time at Ontario’s minimum wage of \$14/hour and accepting that the only office suite that anyone under 70 ever actually buys is Microsoft’s offering and we see that Google saves you \$109 per year compared to Microsoft and \$56 each year compared to using free software.

With respect to email, there are numerous free alternatives to Gmail (like Microsoft’s Hotmail). In addition, many internet service providers bundle free email addresses in with their service. Taking all this into account, Gmail probably doesn’t provide much in the way of direct monetary value to consumers, compared to its competitors.

Google Maps is in a similar position. There are several alternatives that are also free, like Apple Maps, Waze (also owned by Google), Bing Maps, and even the Open Street Map project. Even if you believe that Google Maps provides more value than these alternatives, it’s hard to quantify it. What’s clear is that Google Maps isn’t so far ahead of the pack that there’s no point to using anything else. The prevalence of Google Maps might even be because of user laziness (or anticompetitive behaviour by Google). I’m not confident it’s better than everything else, because I’ve rarely used anything else.

Android is the last Google project worth analyzing and it’s an interesting one. On one hand, it looks like Apple phones tend to cost more than comparable Android phones. On the other hand, Apple is a luxury brand and it’s hard to tell how much of the added price you pay for an iPhone is attributable to that, to differing software, or to differing hardware. Comparing a few recent phones, there’s something like a \$50-\$200 gap between flagship Android phones and iPhones of the same generation. I’m going to assign a plausible sounding \$20 cost saved per phone from using Android, then multiply this by the US Android market share (53%), to get \$11 for the average consumer. The error bars are obviously rather large on this calculation.

(There may also be second order effects from increased competition here; the presence of Android could force Apple to develop more features or lower its prices slightly. This is very hard to calculate, so I’m not going to try to.)

When we add this up, we see that Google Docs save anyone who does word processing \$50-\$100 per year and Android saves the average phone buyer \$11 approximately every two years. This means the average person probably sees some slight yearly financial benefit from Google, although I’m not sure the median person does. The median person and the average person do both get some benefit from Google Search, so there’s something in the plus column here, even if it’s hard to quantify.

I’ve managed to find an assortment of sources that give a view of total advertising spending in the United States over time, as well as changes in the GDP and inflation. I’ve compiled it all in a spreadsheet with the sources listed at the bottom. Don’t just take my word for it – you can see the data yourself. Overlapping this, I’ve found data for Google’s revenue during its meteoric rise – from \$19 million in 2001 to \$110 billion in 2017.

Google ad revenue represented 0.03% of US advertising spending in 2002. By 2012, a mere 10 years later, it was equivalent to 14.7% of the total. Over that same time, overall advertising spending increased from \$237 billion in 2002 to \$297 billion in 2012 (2012 is the last date I have data for total advertising spending). Note however that this isn’t a true comparison, because some Google revenue comes from outside of America. I wasn’t able to find revenue broken down in greater depth that this, so I’m using these numbers in an illustrative manner, not an exact manner.

So, does this mean that Google’s growth drove a growth in advertising spending? Probably not. As the economy is normally growing and changing, the absolute amount of advertising spending is less important than advertising spending compared to the rest of the economy. Here we actually see the opposite of what a naïve reading of the numbers would suggest. Advertising spending grew more slowly than economic growth from 2002 to 2012. In 2002, it was 2.3% of the US economy. By 2012, it was 1.9%.

This also isn’t evidence that Google (and other targeted advertising platforms have decreased spending on advertising). Historically, advertising has represented between 1.2% of US GDP (in 1944, with the Second World War dominating the economy) and 3.0% (in 1922, during the “roaring 20s”). Since 1972, the total has been more stable, varying between 1.7% and 2.5%. A Student’s T-test confirms (P-values around 0.35 for 1919-2002 vs. 2003-2012 and 1972-2002 vs. 2003-2012) that there’s no significant difference between post-Google levels of spending and historical levels.

Even if this was lower than historical bounds, it wouldn’t necessarily prove Google (and its ilk) are causing reduced ad spending. It could be that trends would have driven advertising spending even lower, absent Google’s rise. All we can for sure is that Google hasn’t caused an ahistorically large change in advertising rates. In fact, the only thing that is clear in the advertising trends is the peak in the early 1920s that has never been recaptured and a uniquely low dip in the 1940s that seems to have obviously been caused by World War II. For all that people talk about tech disrupting advertising and ad-supported businesses, these current changes are still less drastic than changes we’ve seen in the past.

The change in advertising spending during the years Google is growing could be driven by Google and similar advertising services. But it also could be normal year to year variation, driven by trends similar to what have driven it in the past. If I had a Ph. D. in advertising history, I might be able to tell you what those trends are, but from my present position, all I can say is that the current movement doesn’t seem that weird, from a historical perspective.

In summary, it looks like the expected value for the average person from Google products is close to \$0, but leaning towards positive. It’s likely to be positive for you personally if you need a word processor or use Android phones, but the error bounds on advertising mean that it’s hard to tell. Furthermore, we can confidently say that the current disruption in the advertising space is probably less severe than the historical disruption to the field during World War II. There’s also a chance that more targeted advertising has led to less advertising spending (and this does feel more likely than it leading to more spending), but the historical variations in data are large enough that we can’t say for sure.

Whose Minimum Wage?

[Epistemic Status: I am not an economist, but…]

ETA (October 2018): Preliminary studies from Seattle make me much more pessimistic about the effects of the Ontario minimum wage hike. I’d also like to highlight the potential for problems when linking a minimum wage to inflation.

There’s something missing from the discussion about the \$15/hour minimum wage in Ontario, something basically every news organization has failed to pick up on. I’d have missed it too, except that a chance connection to a recent blog post I’d read sent me down the right rabbit hole. I’ve climbed out on the back of a mound of government statistics and I really want to share what I’ve found.

I

Reading through the coverage of the proposed \$15/hour minimum wage, I was reminded that the Ontario minimum wage is currently indexed to inflation. Before #FightFor15 really took off, indexing the minimum wage to inflation was the standard progressive minimum wage platform (as evidenced by Obama calling for it in 2013). Ontario is actually aiming for the best of both worlds; the new \$15/hour minimum wage will be indexed to inflation. The hope is that it will continue to have the same purchasing power long into the future.

In Canada, inflation is also called the “consumer price index” or CPI. The CPI is based on a standard basket of goods (i.e. a list that includes such things as “children’s sneakers” and “French fries, curly”), which Statistics Canada assesses the price of every few months. These prices are averaged, weighted, and compared to the previous year’s prices to get a single number. This number is periodically reset to 100 (most recently in 2002). The CPI for 2016 is 128.4; in 2016, it cost \$128.40 to buy a basket of goods that cost \$100.00 in 2002.

The problem with the CPI is that it’s just an average; when you look at what goes into it category by category, it becomes clear that “inflation” isn’t really a single number.

Here’s the last few years of the CPI, with some of the categories broken out:

Every row in this table that is shaded green has decreased in price since 2002. Rows that are shaded blue have increased in price, but have increased slower than the rate of inflation. Economists would say that they’ve increased in price in nominal (unadjusted for inflation) terms, but they’ve decreased in price in real (adjusted for inflation) terms. Real prices are important, because they show how prices are changing relative to other goods on the market. As the real value of goods and services change, so too does the fraction of each paycheque that people spend on them.

The red, yellow, and orange rows represent categories that have increased in price faster than the general rate of inflation. These categories of goods and services are becoming more expensive in both real and nominal terms.

There’s no other way to look at the CPI that shows variation as large as that between categories. When you break it down by major city, the CPI for 2016 varies from 120.7 (Victoria, BC) to 135.6 (Calgary, AB). When you break it down by province, you see basically the same thing, with the CPI varying from 122.4 in BC to 135.2 in Alberta.

Looking at this chart, you can see that electronics (“Home Entertainment”) have become 45% cheaper in nominal (unadjusted for inflation) terms and a whopping 58% cheaper in real (adjusted for inflation) terms. Basically, electronics have never been less expensive.

On the other hand, you have education, which has become 60.8% more expensive in nominal terms and 25% more expensive in real terms. It costing more and more to get an education, in a way that can’t just be explained by “inflation”.

Three of the four categories with the biggest increases in prices rely on the labour of responsible people. The fourth is tobacco; prices increases there are probably driven by increased taxation and its position is a bit of a red herring. It’s potentially worrying that the categories where things are getting cheaper (e.g. electronics, clothes) are in the industries that are most amenable to automation. This might imply that tasks that cannot be automated are doomed to become increasingly expensive [1].

II

I’m certainly not the first person to make the observation that “inflation” isn’t a single number. Economists have presumably known this forever, related as it is to the important economics concept of “cost disease“. More recently, you can see this point made from two different directions in Scott Alexander’s “Considerations on Cost Disease” (which tries to get to the bottom of the price increases in healthcare and education) and Andrew Potter’s “The age of anti-consumerism has passed” (which looks at the societal changes wrought by many consumer goods becoming much cheaper). As far as I know, no one has yet tied this observation to the discussion surrounding the new Ontario minimum wage.

Like I said above, the new minimum wage will still be indexed to inflation; the “\$15/hour” minimum wage won’t stay at \$15/hour. If inflation follows current trends (this is a terrible assumption but it’s all I’ve got), it will rise by about 1.5% per year. In 2020 it will be (again, bad extrapolation alert) \$15.25 and in 2021 it will be \$15.50.

Extrapolating backwards, the current Ontario minimum wage (\$11.40/hour) was equivalent to \$8.88/hour in 2002 (when the CPI was last reset). If instead of tracking inflation generally, the minimum wage had tracked electronics, it would be \$4.84 today. If it tracked education, it would be \$14.28. Next year, the minimum wage will be \$14/hour (it will take until 2019 for the \$15/hour wage to be fully phased in), which will make 2018 the first time that students working minimum wage are getting paychecks that will have increased as much as the cost of education.

This won’t last of course. The divergence in prices shows no signs of decreasing. The CPI will continue to climb upwards at a steady rate (the target is 2%, last year it only rose 1.4%), buoyed up by large increases in education costs (2.8% last year) and held down by steady decreases in the price of electronics (-1.6% last year). Imagine that the \$15/hour minimum wage allows a student to pay a year’s tuition with a summer’s worth of work. If current trends continue, in 15 years, it would only cover 75% of tuition. Fifteen years after that it would cover about 60%.

III

There’s a funny thing about these numbers. The stuff that’s getting more expensive more quickly is largely stuff that younger people have to pay for. If you’re 50, have more or less raised your kids, and own a house, then you’re golden even if you’re working a minimum wage job (although by this point, you probably aren’t). Assuming your wage has increased with inflation over your working lifetime, a lot of the things you’re looking to buy (travel, electronics, medical devices) will be getting cheaper relative to what you make. Healthcare service costs (e.g. the cost of seeing a doctor) might be increasing for you in theory, but in practice OHIP has you covered for all your doctor’s visits [2].

It’s younger people who are really shafted. First, they’re more likely to be earning minimum wage, with nearly 60% of minimum wage earners in Canada in the 15 to 24 age bracket. Second, the sorts of things that younger people need or aspire to (education, childcare, home ownership) are big ticket items that are increasing in cost above the rate of inflation. Like with the tuition example above, childcare and home ownership are going to slip out of the grasp of young workers even if you index their wage to inflation.

I happen to like the idea of a \$15/hour minimum wage. There’s a lot of disagreement among economists as to whether they’ll be ill effects, but this meta-analysis (complete with funnel plot!) has me more or less convinced that the economy will do just fine [3]. Given that Ontario will still have an economy post wage-hike, I think increasing the minimum wage will be good for workers.

But a minimum wage increase leaves the larger problem of differing rates of inflation unsolved. Even with a minimum wage indexed to inflation, we’re going to have people waking up twenty-five years from now, realizing that their minimum wage job doesn’t pay for university/food/utilities/childcare/transit the same way their parents’ minimum wage job did. This will be a problem.

I’m game to kick the can down the road for a bit if it means we can make the lives of minimum wage workers better right now. But until we’ve solved this problem for good, it will keep coming back [4].

Footnotes:

[1] I’m not sure this is exactly a bad thing, per se. Money is a means of signalling that you’d like your preferences satisfied. It becoming more expensive to pay actual humans to do things could mean that actual humans have so many good options that they’re only going to waste their time satisfying your preferences if you really make it worth their while. Looked at this way, this means we’re steadily freeing ourselves from work.

On the other hand, this seems to apply mainly to responsible/competent/intelligent people and not everyone is responsible/competent/intelligent, so this could also imply that we have a looming crisis, with a huge number of people simply becoming economically unnecessary. This is really bad, because high-quality life should be possible for everyone, not just those who’ve lucked into economically valuable traits and under capitalism it is really hard to have a high-quality life if you aren’t economically valuable. ^

[2] For readers outside of Ontario, OHIP is the Ontario Health Insurance Plan. It covers all hospital and clinic care for all legal residents of Ontario, as well as dental and ophthalmological care for minors. OHIP is a non-actuarial insurance program; premiums come from provincial income tax and payroll tax revenues, as well as transfer payments of federal tax revenues. All Ontarians enrolled in OHIP (i.e. basically all of us) have a health card which allows us to access all covered services free of charge (beyond the taxes we’ve already paid) any time we want to. ^

[3] No effect on the unemployment rate does not mean no effect on the employment of individual people. A \$15/hour minimum wage will probably tempt some people back into the labour force (I’m thinking here that this will mostly be women), while excluding others whose labour would not be valued that highly (unfortunately this will probably hit people with certain mental illnesses or disabilities the hardest). ^

[4] I think it’s especially pernicious how the difference in inflation rates between types of goods is kind of by default a source of inter-generational strife. First, it makes it more difficult for each succeeding generation to hit the same landmarks that defined adulthood and independence for the previous generation (e.g. home ownership, education, having children), with all the terrible think-pieces, conflict-ridden Thanksgiving dinners, and crushed dreams this implies. Second, it can pit the economic interests of generations against each other; healthcare for older people is subsidized by premiums from younger ones, while the increase in the cost of homes benefit existing players (who skew older) to the determinant of new market entrants (who skew younger). ^