Powers of Ten (Dollars)

There are 10^11 stars in the galaxy. That used to be a huge number. But it's only a hundred billion. It's less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.
-Richard Feynman

Not so long ago I wrote a snarky post about economics wherein I joined the chorus of voices deriding the ludicrously horrible track record of predicting the impact of the stimulus. Well, another month another data point, overlaid on the otherwise unmodified Obama stimulus prediction:


Not only is it much worse than what the stimulus was supposed to accomplish, it's much worse than what we were told would happen if nothing were done. So what's to be done now? One suggestion is another stimulus. While I'm opposed to such a plan for both ideological and utilitarian reasons, reasonable people disagree. That's fine. What's not so fine is that a large segment of the public can't make informed judgments about the issues simply by virtue of not having an intuitive grasp on the quantities involved. I'm going to throw my hat in the ring with the help of Microsoft Excel to try to show how these large numbers compare to each other.

While a true "powers of ten" presentation would start at the single-cent level, everyone has a fairly good grasp on what fifty cents or 8 dollars or 400 dollars can buy. As such, the power of ten we'll look at first is the fourth - ie, the $10,000 range. We also won't be skipping in powers of ten as such, since I'm picking the cutoffs for each graph to hold the most "related" items in similar monetary ranges. This naturally means that my choice of cutoffs can tend to itself make a biased point - something you should always be on the lookout for, since it's easy to lie with statistics. I promise to be as fair as possible, however, by using a very vanilla bar graph with the x-axis representing $0 in all cases, the y-axis always given in USD. In each case the last thing on a given graph is the first thing on the next graph. Generally speaking I'm not including citations for sources since they're widely available public figures from official websites and the like. There are a few exceptions, I'll link the one or two more obscure numbers to their sources. On to the graphs:


Straightforward average-person-sized values. What a person at the poverty line makes, what I make, what the family right in the middle makes, what a person at the low end of "upper class" makes. In a nutshell it's the gap between rich-ish and poor-ish.


Zooming out, a house whose cost is right in the middle, the salary of the president of my university, the salary of LSU coach Les Miles. Don't construe this as an attack on Les, by the way. He makes a huge amount of money, but in total his very successful LSU Tigers are a large net source of revenue to the university - a distinction not all that many university football programs can claim.


Les Miles makes a lot, but not quite as much as it costs to build a tank. Which is itself not nearly as much as 16-year-old Miley Cyrus makes. Not that I begrudge her that salary either - can you generate Hannah Montana's kind of revenue for your company? I sure can't. We're leaving the realm of purely single-person money and starting to approach the money of large organizations. The city in which I live has a municipal budget in the low hundreds of millions.


The city's budget is half that of the college it contains, but both start to look small next to the wealth of a truly rich person like the wife of the richest senator. Though John Kerry is thought to be the richest senator, his wealth is smaller and separate from his wife. Keep in mind that the budgetary figures are annual, and so don't think it would be easy for even Teresa Kerry to support a university - it would burn through her assets in just a few years. A Nimitz-class aircraft carrier is much more expensive. Ten have been built. NASA's space operations budget is not the total NASA budget, just that which funds the Shuttle and ISS programs.


Wal-Mart's profits are enough to fund NASA and then some. Wal-Mart's actual revenues are some thirty times higher than even that, but as with most businesses the vast bulk of what's coming into the registers promptly leaves in the form of purchasing products to sell, building and maintaining stores, worker salaries, dividends, tax, etc. Bill Gates is worth considerably more. Though his position as Richest There Is comes and goes, his bar on the graph is a pretty good proxy for the most money any single person can muster. State-level expenses can easily be much greater than that every year for single budget categories. Some people who have not grasped large numbers intuitively wonder why Bill Gates can't use his money to fix X. Odds are that the answer is that X is one of those things that dwarfs even his considerable resources. The Iraq War is often used as another proxy of "Money That Could Do X", and the total 2008 appropriation for the two wars is graphed here for a sense of its magnitude. It's a lot, but we'll see that we have a few more orders of magnitude to go. The 2009 appropriation is quite a bit smaller, as Barack Obama is attempting to wind the war to a safe conclusion.


The '08 Iraq/Afghanistan cost is small compared to baseline defense spending and most of the major yearly federal budget expenses. In fact the sum total of the entire Iraq war to date is smaller than any of next year's Social Security, next year's Medicaid & Medicare, or last year's stimulus bill. If I may slide into overt editorializing, that's one reason I'm very skeptical of another stimulus. They cost an unbelievable amount of money.


Now we're into the trillions with a T. The stimulus bill - which as we said was enormously large - is itself looking pretty small next to the federal deficit. The deficit is of course what the government spends minus what it takes in (mostly via taxes). Both of those are also on the chart for comparison. I've also included the sum total of the income of every person who makes $200,000 or more, minus what they already pay in federal taxes. Since taxes on the rich and defense cuts are often suggested as a way to reduce the deficit, it's instructive to look at exactly how large the deficit is compared to defense spending (on the previous chart) and the total income the rich actually have as a group. The rich have a lot of money, but it is finite and fits on this chart.


The last chart, now reaching figures in the tens of trillions. Total government spending is federal spending plus state and local spending. I've had to use the 2007 figures for state and local spending, but given the rise in 2008 and a slight fall it 2009 the number should still be reasonably close. While the US is nominally a free-market capitalist economy, in fact government spending makes up a rather large fraction of the total economic output of the United States. Every year, the deficit piles into the debt. Currently the indebtedness of the United States government is nearly the size of a year's worth of the US economy. Increasing debt itself drives up federal expenses, as its creditors must be repaid with interest. The deficit is projected to decrease in 2010 and for a few years thereafter (though never even so far as the then-record deficit set by Bush in 2008) before ramping up again.

I don't pretend my analysis or presentation is entirely objective, but the numbers themselves are correct to the best of my ability. For better or for worse, we have to live with them.

More like this

Don't want to change the deal, but that first chart - those predictions came from the Bush Admin stimulus. That is, the one enacted last year.

great comparisons!

the one method that always shocked me was to relate the 'daily spending' of some of those bars if one were to divide it equally over the last 2009 years.

try that and the numbers are staggering when you try and think of how you would spend the amounts DAILY for over 2000 years!

Thanks for the insightful post!

This is really a very well done post. I'd have had trouble before explaining these issues to people who ask the Why Can't Bill Gates do X question. Now I'll just refer them to this post.

To Markk's comment on that first chart, I'll add that one reason the stimulus has been less than completely effective is that the forecasters probably assumed flat state spending. States are cutting back because they have to--most states, unlike the federal government, are constitutionally required to balance the budget. If federal stimulus is supposed to boost the economy via a Keynsian multiplier, then slashing state budgets will slow the economy by the same mechanism. Would the unemployment rate, sans stimulus, be higher by about as much as the difference between the two curves in the prediction? Unfortunately, there is no way to do that experiment, which is one reason why economics is so much harder than physics.

By Eric Lund (not verified) on 10 Jun 2009 #permalink

Markk, the first chart is originally from this report, released after the election but before the inauguration by the Obama team. It's about what became the American Recovery and Reinvestment Act.

Bush had some monumentally big economic packages too, which I'd have loved to put on the chart as well but things were getting cluttered as-is. In particular there was the original "mail everybody a check" stimulus, the TARP plan, and any of the various other bailouts. Those would have fit on the 10^11 chart, like the current stimulus bill.

Scary. The graph that I find most striking is the one that shows federal government income vs. spending. There must be a way to get those two bars closer to the same size, and I don't think the government is the organization to do it.

Definition for later use: "jaw boning" is when you lie about how bad it is really going to be if nothing is done so the markets don't panic and make it even worse than that despite doing everything the government can do to turn it around. You are guilty of believing that the "jaw boning" graph was an actual "prediction".

On spending, congrats on realizing the Bush tax cut and spending plan was a mistake, even if you don't actually realize it yet. The people making that argument now were shouting down anyone who made the same argument 8 years ago.

On unemployment, you are, as I pointed out the first time, ignoring the fact that the "prediction" made in January was based on bad data (surely a physicist can understand that the solution of an initial value problem requires a correct initial value) and hid (probably deliberately) the scope of what we face in the Depression (aka Great Recession) that started a year ago. I know it isn't your graph, but by republishing it you are representing it as accurate.

** The error is that the March 09 value should be plotted on the 1Q line, and the 1Q value where the two plans match up should have been where the March 09 data point is. The resulting increase in the slope between 4Q 2008 and 1Q 2009 also changes the shape of the prediction. As a physicist, you should also notice that the data are plotted incorrectly, exaggerating the slope from March (end of 1Q) to May (late 2Q) and reducing the slope from December (end of 4Q) to March.

Blaming Obama for the success of Bush's program in late 2008 at keeping unemployment under 10% (so far) just because they "jaw boned" the business world by pretending that 9% was their worst-case expectation - well, that reflects your limited life experience. This is NOT the 1975 Nixon/Ford recession or the 1983 Reagan recession, both of which went to 10%. This is an actual depression where massive spending by Bush and now Obama has a chance to keep it in check. Success will be if unemployment turns at the 10% level (like it did in those two earlier events) rather than going to 15% or more.

As for the deficits (noted by Nathan @7), this is the first time in US history that we created MASSIVE deficits when the economy was doing "well". This makes it really hard to stimulate the economy without creating UBER-massive deficits a'la what ended the Great Depression (over 50% of GDP).

The only thing worse than what you show in your graphs is what it looks like if your salary is zero, which is the likely situation if there is no stimulus money and the budget is balanced by cutting discretionary spending (NSF and NASA) as some are now arguing on the right. Do you know what TAMU would do without that stimulus money? I know what we would do, because our college planned for that eventuality. It is not pretty.

By CCPhysicist (not verified) on 10 Jun 2009 #permalink

True, another stimulus at this point is simply foolish. Freemarket supporters or not, we can't possibly begin suggesting that another stimulus is needed until we can gauge the effects of this stimulus which probably have a while to manifest. Unless of course if we had an accurate economic model for the United States economy... in theory.

CC: My job is not sacred. While I'd be heartbroken if I had to put grad school on indefinite hold if student funding evaporated and I lost my assistantship, fundamentally it is not my money. It's the money of the citizens, and it's theirs to allocate as they think necessary through their representatives.

Granting that WWII spending helped end the depression, it also happened that debt accumulated was overwhelmed by a post-WWII economic boom with the US finding itself as the world's foremost industrial power. I don't know of anyone who thinks such a boom will follow this recession, and most debt/GDP predictions are strictly monotonic increases into the indefinite future. Everyone down to the smallest business will spend into a deficit if they believe it will result in growth and profits later - but I'm not sure I can see where enough growth or profits are going to come from to pay down the debt accumulated by the treasury.

For the first graph if you'll follow the link, the person who made the graph discusses the problem of where to put the points and in fact has graphed something along the lines of your preference as well. I prefer this one, as it more closely matches the starting point on the underlying curve.

As for taking the graph's "jaw-boning" too seriously, well, I would like to think the government isn't completely talking out of its posterior when spending more than the entire cumulative Iraq war cost. I would like to think that, anyway.

If I may tie the Feynman quote to the numbers presented here.

"If the federal government sold every star in our galaxy for $1/ea on midnight Jan 1 then they'd run out cash at 3 am Jan 10."

($4T/year by 100B stars = 1/40 year = 9.125 days.)

Another way of looking at these figures is on a per capita basis. I estimate that the projected 2009 U.S. deficit is about $4000 per person, or $16000 for a family of four. I know it isn't perfect because a lot of the debt is internal but it gives some idea of the scale.

By Richard Simons (not verified) on 10 Jun 2009 #permalink

"There must be a way to get those two bars closer to the same size, and I don't think the government is the organization to do it."

Tried logarithms? :)

By Max Fagin (not verified) on 11 Jun 2009 #permalink

Now that I've got my hands on the relevant data, with the additional "stimulus" of an apparent inflection point indicated by the job-loss data, I may write something about it all later today. The main point about that graph is that the prediction of the "no stimulus" situation (the blue curve) is obviously wrong because the initial values in their model (actual Q4 values and a 10% wrong guess for Q1) mean the initial 'velocity' of their model was wrong by 75% !! and the 'acceleration' was taken to be slightly negative rather than significantly positive.

I don't think you got my point about your job. I've seen nearly 11% unemployment, and we were heading for worse if state governments would have had to cut their budgets to pre-stim levels. I'm serious about learning what TAMU's budget looks like for the coming FY.

You are quite wrong about the post-war situation. It was not pretty. Unemployment soared. (See "The Best Years of Our Lives" for a depiction of that situation.) The GI Bill was created specifically to put returning soldiers in college instead of the unemployment line. But the key to the deficit was that it had been self financed, through war bonds. Very little of the money paid to workers and soldiers by that massive deficit could be spent. There was literally nothing to buy, so they bought bonds. After the war, taxes continued high and the budget surplus was used to pay off those bonds ... putting money into people's hands that they used to buy refrigerators and tires, and then cars. That is how it worked. The difference in savings rate then and now should be obvious.

The cumulative Iraq War cost is chump change. As your graphs show, the total for six years of "war" is comparable to a single year of a typical defense budget. It was paid for out of here and there, and done totally "off budget" so it would not show up in the published deficits. It was certainly not paid for by any sacrifice by those at home. That is partly why we had such a large deficit in good times, making it hard to recover in bad.

Finally, Max @15 has a good suggestion for you, but I have a better one. Either scale the big numbers by the GDP (which is a good way to see what things cost the economy, since historically we have held taxes below 20% of GDP) or per capita (to match up your individual income and net worth numbers).

You'll have to add a new bar to the charts

134 billion: The average pocket change Japanese tourists take on trips to the Swiss Alps.

He really didn't correct it, since it still misrepresents just how bad the situation was before Obama took over and they and Congress had a chance to act.


The difference between the true "before" line (my pink line) and the blue "before" line in the transition team study is huge and shows just how a small error in one value (the guess at the Q1 average value) will result in a bad slope and worse curvature. Their model appears to have assumed we were already in recovery and that the stimulus would make the recovery more rapid.

Whether they did it on purpose or were fooled by a short-term drop in new jobless claims, their graph certainly served to hide what has been obvious to me since late last year when we learned unemployed racists were voting for Obama: that the Bush administration created a huge mess (likely the worst in my lifetime) but reacted quickly enough that it might end up being "only" a bit worse than I have seen. But, like Dean Dad and his view that the world might end in 2011 rather than 2012, I am not sanguine about a situation where local governments have to lay off employees even with the stimulus money in hand.