Black Monday 2: Economic Boogaloo

[publius]

Let's see. We've got a report in Spiegel that the IMF has had it with Greece and wants to cut off any further aid. Greece will run through it's current bailout funding in Sept.

And then Sicily is about to run out of money, and the Italian national govt. wants to take over. Sicily, with its history, apparently has a more autonomous govt than other regions so their is some sensitivity to Rome just taking over. But otherwise, the nearly broke national govt. must bail out the broke local govt.

And Spanish yields blew out again on Friday, with the 10 yr higher than it was before the bailout. And there's something about several of their regional govts. are about to run out of money and are begging for help. Another broke national govt. called on to bail out local govts.

[Delvo]

It doesn't say bow big or expensive the houses are, which might be interesting to know.

Well, here is something else interesting to go along with it anyway: http://online.wsj.com/article/BT-CO-...19-710275.html

So we have new construction increasing while sales of already-constructed houses decreased. To the extent that they cancel each other out, that means total purchases didn't change much but what was getting purchased did shift from already-built to getting-built-now. I'll take that as a sign that what's being built now is cheaper.

[publius]

And BTW, here's some FRED charts to show the big picture of (new -- can't seem to find existing sales and related there, but they've reorganized and there's tons of data buried everywhere) housing.

This is housing starts:




New one family house sales:

[publius]

At any rate, that is illustrative of the overall "big picture" of housing. Things are "improving", but only after a cliff dive to lows unseen since the series began. It's sort of like if you were say selling 100 units of something per unit time, dropped down to 20 units, then started bragging about a 50% increase when sales increase to 30 units.

[publius]

And back to Euroland, the Spanish 10 yr hit 7.5% I think, and the Spanish stock market has dropped 12% in two days, and Italian yields are flirting with 7% again.

Meanwhile, flight to safety has driven the US 10yr to an all time record low of below 1.4%, and the 30 yr is down below 2.5% somewhere. The 10 yr never got that low even during the Depression, or Great Depression 1.0 I should say, with us being in version 2.0 now. And German, Swiss, and Danish 2yr are all holding at negative rates. If I read it right, the Swiss 2yr is the lowest, at -0.44%.

And finally, US Debt is going to hit the $16T mark in a month or so. In deference to the "Milliard(e)" thread, that's a short scale trillion, or 10^12, which would be a billion in the long scale. It just a smidge under $15.9T now. The debt limit stands at $16.394T and we might not make to the election. The standard accounting tricks, worth $200-250B probably should be enough to get by.

Hey, I've got a solution. They can switch us over to the long scale, but leave the debt limit as it stands in trillion. Thus the limit will be $13.394*10^18. That should hold us for another 5 years or so.

[publius]

And speaking of large numbers, Japan's public debt will hit the short scale quadrillion, 10^15, mark in yen some time this fiscal year (ends in March 2013). The total derivative market sums to over a quadrillion in "notional" dollar value as well. In the long scale, a quadrillion would be a "billiard".

[HenrikOlsen]

And finally, US Debt is going to hit the $16T mark in a month or so. In deference to the "Milliard(e)" thread, that's a short scale trillion, or 10^12, which would be a billion in the long scale.

Just say it's short for terabucks, that works in both scales.

And speaking of large numbers, Japan's public debt will hit the short scale quadrillion, 10^15, mark in yen some time this fiscal year (ends in March 2013).

That would be petayen then.

[Delvo]

More housing oddness...

http://www.zerohedge.com/news/new-ho...most-20-months

New home prices & sales are down, just like used home prices. So why did construction go up?

[Ara Pacis]

More housing oddness...

http://www.zerohedge.com/news/new-ho...most-20-months

New home prices & sales are down, just like used home prices. So why did construction go up?

Remodeling? Maybe it's pend up demand, people living together finally giving up the hope that they'll ever leave and adding more room to make a proper multi-generational home. Have there been any disasters recently? Or maybe the banks that foreclosed on homes have realized they need to have them repaired before they can be sold because they let them become dilapidated?

[Ara Pacis]

Here's an interesting analysis of the job market. Apparently now compared to 1979 shows that people are making more in pay, but less have medical insurance and less have a retirement plan. It also argues against the claim by businesses that they can't find "qualified workers". And adjusted for inflation, the minumum wage is less now than then.

What's holding back the economy's ability to generate good jobs? One common explanation floated around of late points to a skills gap. We've got an 8.2% unemployment rate but companies are reporting trouble filling open positions because of a lack of qualified applicants.

Schmitt disputes that argument with simple supply-and-demand theory: "If that were true and widespread, we'd see wages of workers rising, because employers would try to steal away qualified workers from other employers. We're not seeing that in the data — we're not seeing an increase in wages relative to last year, or the year before, or before that."

He goes on to talk about workers bargaining power and unions, but I won't try to bring politics into this. It reminds me of a discussion I had elsewhere last week about H1-b visas for IT workers for the same claim of not enough qualified applicants when some believe it's actually about cost and an almost indentured nature of the positions.

[HenrikOlsen]

I have a slight quibble about this, if supply and demand considerations are correct, the drop in minimum would indicate an increase in unskilled workers, and not say anything about skilled workers with the right skills, which is what "qualified" is normally used for in this context because they won't get minimum wage.

[primummobile]

Here's an interesting analysis of the job market. Apparently now compared to 1979 shows that people are making more in pay, but less have medical insurance and less have a retirement plan. It also argues against the claim by businesses that they can't find "qualified workers". And adjusted for inflation, the minumum wage is less now than then.



He goes on to talk about workers bargaining power and unions, but I won't try to bring politics into this. It reminds me of a discussion I had elsewhere last week about H1-b visas for IT workers for the same claim of not enough qualified applicants when some believe it's actually about cost and an almost indentured nature of the positions.

I know it doesn't really prove anything either way, but my company has a horrible time trying to find qualified engineers.

[Hlafordlaes]

In the long scale, a quadrillion would be a "billiard".

I had a feeling we are about to be snookered. Thanks for the heads-up.

[publius]

The thing to keep in mind is that standard supply-and-demand analysis only holds in true free market conditions. If there are anticompetitive shenanigins and other corruption afoot, that will not hold, and things can behave just the opposite of what would be expected.

I was reading an article about this a while back about how difficult it is to prove anticompetive practices are going on from pure market data, but a failure of supply and demand to hold good is a sure sign that something hinky is going on.

For example, price controls in a free market result in shortages. However, suppose there is a monopoly afoot, or some oligopoly of collusion to set prices above the market equilibrium. If price controls are imposed there (but not below the actual market equilibrium), lowering the price below the monopoly set too-high price, there will be no shortage, and sales will increase, just the opposite of what would happen under free market conditions.

And then on the flip side, consider a monopsony (single buyer), such as a one company town, or oligopsony of collusion to set wages too low below market equilibrium. Normally, if you raise minimum wage above equilibrium, you get a surplus, which is higher unemployment.

When a monopsony is setting wages below market equilibrium, increasing the minimum wage (but not above the true market equilibrium) results in an increase in employment.

[publius]

I had a feeling we are about to be snookered. Thanks for the heads-up.

That was a good 'un, a real good 'un. Are smilies not working here in our new home? Let's see

[HenrikOlsen]

And in the Euro Zone, irony abounds.

Mr Draghi said that the high yields on some eurozone government bonds were unacceptable, adding that, "the euro is irreversible".

This speech was followed by Spain's 10-year bond going above 7% again and Italy's jumping from 5.7% before Mr Draghi spoke to 6.2% after.

When will they learn that words are not magic.

"This is a revolutionary policy, as far as the ECB is concerned. It means the ECB plans to go into the markets and buy bonds, of two to three-year durations, in very substantial quantities," said Nick Parsons at National Australia Bank.

"These are potentially unlimited and should be big enough to have the desired effect. Mr Draghi is certainly on the right track."

Sounds a bit like hidden money printing or some similar scheme.

[Ara Pacis]

That was a good 'un, a real good 'un. Are smilies not working here in our new home? Let's see

They hadn't been. I try to use non-parsing smilies by adding a nose, like this :-)

I'll hafta re-read your post a few times before I get what you're saying. It's late and it looks like math.

BTW, the article I posted was about the reduction in purchasing power due to inflation, not a real reduction in minimum wage, because that has been going up. Part of the problem may be that people have willingly dropped out of the workforce because of mental depression or because they are stuck in a location that is not close to jobs that need their skills due to mortgages or family ties which have become more important in this bad economy. It might be that some of the smart people with ambition to obtain the needed qualifications gave up and went into another field or into business for themselves instead of waiting for someone else to make a job for them.

[publius]

When will they learn that words are not magic.

Exactly. What it means is Germany is not on board (nor will it ever be) with shifting the ECB printers into turbo mode and buying up PIIGS debt to drive down yields. But Draghi thought he could get away with jawboning and make the market react as if they are going to print. The market called his bluff.

[publius]

Sorry, but I've been incognito for a bit.

If I've got it right, basically the printing presses are the only thing now keeping the Greek government afloat. Aug 20 is a drop dead date, where if Greece didn't get more funding, it would be out of cash, and the Troika and others have apparently said Nein, and it looked like Greece was really going to go under Aug 20th. And I mean really go under. No more money.

So Draghi and the ECB, not wanting to let that happen, have allowed a scheme which goes like this. Greek goverment sells bills (not bonds, mind you, but short dated bills) to their own banks. But where do their own banks get the money. Why, from the Greek central bank, which accepts the bills as collateral. But where does the Greek central bank get the real euros. Well, the ECB, even though it now rejects Greek *bonds*, will accept the short term *bills* , allowing euros to be created against them.

So that now makes the printing press the sole source of Greek government funding. The basic tenet of sound monetary policy is thou shalt not print to fund government deficits. And that's what they're doing now. That's generally the death knell for a currency, of course.

Will it happen soon? Well, Greece alone, the number of euros needed, is a small fraction of the total. So it won't be a sudden as when a government in charge of its own currency starts printing.

The nearest similiar thing for us and the dollar would be if the Fed starting printing to finance some state government. Say California ran out of money, and the federal govenment bailed them out by simply giving them the money they needed. And they get the money by selling their own Ts, which the Fed then quickly buys.

Of course, in the EMU, there is no federal govt level entity in between, but that's basically how a similiar situation would look here.

[publius]

A word we've used a lot and seen use a lot is "unsustainable". As in the phrase our current fiscal/economic trajectory is unsusustainable. But I just don't think it hits home, "clicks" in your mind, that it really is unsustainable, an if not fixed, and fixed by yesterday (or 10 years ago, really), the whole thing is going to collapse. Consider this little ditty from Bloomberg:

http://www.bloomberg.com/news/2012-0...-trillion.html

That's about what they're calling Uncle's "fiscal gap", otherwise known as unfunded liabilities or some similiar sounding term. That value currently stands at $222T, 222 terabucks, growing by $11T in the past year.

What is this fiscal gap/unfunded liability? It is the present value of the difference in what the US govt plans to spend less what it expects to receive over the next N years (N being something like 50 or 75 years).

Consider this problem. You obligate yourself to pay out $Y per year over the next N years, but only expect to make $X per year for that same N years. How much money do you need to put in the bank now (at interest), to make up the difference? That's your fiscal gap for those N years. (If the number is positive, it's a surplus, and making that result be positive is essentially the economic goal of us all, building up a nest egg of ecnomic surplus over our lives).

The result for solving that problem for the US govt is now $222T. That number is staggering. It is over 3 times the GDP of the entire world and just under 14 times US GDP.

If you can get your mind wrapped around that number and how it comes about, you'll truly appreciate "unsustainable". Imagine you do that calculation for your own finances and find the result to be 14 times you current salary. You must put 14 times that amount you make per year in the bank *now* to cover the difference. What will you do? Unless you're planning on some rich relative dying and leaving you a wad, you're up the creek and you're going to have change your ways. You will crash and burn if you do not.

Note that no individual or business would make it that far before it blew up anyway. Only governments can get that far in the hole, and it's surprising how deep we've made it at that anyway.

As I mentioned before, many people just don't understand that and go along merrily in ignorant bliss. And most of those who do understand seem to just want to cover up the ears, and shout "La, la, la! I can't hear you!"

[publius]

You know, if you want to boil this down to the mathematical essence, it is simply the fact that the difference between two exponential functions with different rates itself grows exponentially. To wit: e^(r1*t) - e^(r2*t). When r1 > r2, that difference itself grows exponentially over time. If you play around with that expression, A - B, and rearrange as something like (A/B - 1)*B you get something like (e^(r1 - r2)*t - 1)* e^(r2*t) or similiar you see the result tends to e^(r1*t) as t grow large, but starts at out at zero at t = 0.

In other, the expression A(t) - B(t) when A and B are exponentials with A growing faster than B, starts out as zero but becomes A as time goes on. If A is spending and B is income, then as time goes on, the income becomes insignificant relative to spending and the difference.

Here B = income ~ GDP, and this is just spending growing faster than GDP. No problem at the start and can be fixed easily at the start, just by making r1 <= r2. When A is small and B is small, that's relative pain free. But let it go on unchecked and get harder and harder.

We're at the really, really hard point now. We may have crossed the event horizon so to speak and collapse is inevitable no matter what we do. 10 or 20 years ago it wasn't, but now here we are.

[Hlafordlaes]

If the NPV figure is calculated as one might expect, its enormity stems mostly from extending the deficit indefinitely in time. IOW, it is extremely sensitive to future reductions or increases in the deficit, as well as the interest rate used. So it serves as a strident warning, yet not an automatic death knell.

One thing seems obvious, and that is that entitlement programs need to have some params adjusted, such as SS withholding rates, max income withholding limits, retirement age, etc. Don't have a link, but iirc that has been shown to be doable with reasonable, albeit energetic, tweaking.

That plus bring down all spending and adjust tax rates. Or are we doomed by the numbers regardless of what is done to address the problem?

[Extravoice]

One thing seems obvious, and that is that entitlement programs need to have some params adjusted, such as SS withholding rates, max income withholding limits, retirement age, etc. Don't have a link, but iirc that has been shown to be doable with reasonable, albeit energetic, tweaking.

I've heard this for years, but very little has been done. To be fair, whenever a politician (of any flavor) tries to address the issues he/she gets spanked-down by (party | lobbyists | donors | voters). Government seems to only operate in crisis mode. If it isn't a crisis, it doesn't get attention.

What was that saying about democracy being doomed because the voters eventually figure out they can vote themselves the wealth of the nation?
Don't worry, we'll just grow ourselves out of this mess. (Where is the whistle smiley when you need it?)

[Ara Pacis]

What was that saying about democracy being doomed because the voters eventually figure out they can vote themselves the wealth of the nation?
Don't worry, we'll just grow ourselves out of this mess. (Where is the whistle smiley when you need it?)

Bread and circuses? The wealth of a nation can be constrained both ways by either increasing outputs or reducing inputs. We need to work on both increasing revenue and decreasing expenditures.

[publius]

If the NPV figure is calculated as one might expect, its enormity stems mostly from extending the deficit indefinitely in time. IOW, it is extremely sensitive to future reductions or increases in the deficit, as well as the interest rate used. So it serves as a strident warning, yet not an automatic death knell.

The "fiscal gap" NPV is a complicated mess (and ultimately dependent on various assumptions about the future) actually, but can be broken down into simple pieces and we can sort of get the feel for it and that might be helpful.

At the most basic level, the PV of some amount A at some time t in the future (t = 0 is now), is simply "discounting it" by the expected interest rate r over that time t: PV = A/e^rt. Of course, that is just the elementary "time value of money" concept. If you put some PV amount of money away in the bank (or whatever investment) at interest rate, r, A is what it compounds to in the future (assuming the bank survives).

[Note to any lurkers concerned about using 'e' -- this generally just makes things simpler and slicker than using the discrete geometric form (1 + r) but they are otherwise equivalent, only difference is what 'r' is . Sometimes, though the geometric form does work out better, though. e is the limit of (1 + 1/n)^n as n goes to infinity, and that comes about from the derivatives, actually. When dA/dt/A is exactly equal to 1, then A = e^t, but I ramble...]

A zero coupon bond is the simplest example of this, of which form short term bills usually are done. The face value of the bill is A, and PV is the money raised now at the bill auction.

Anyway, given PV = A/e^rt, we see that PV decreases as t and r increase, and increases as they decrease. Thus the closer we get to D-day when we must pay A, the more we need now. And the lower the interest rate, the more we must put away. And if we start taking derivatives with respect to r and t and all that good stuff (note taking dervivatives of e^rt is very simple), we see that while PV decreases as t increase, it becomes more sensitive to changes in interest rate.

And then we can get fancy and let interest rate r itself vary with time, and e^rt becomes something more complicated. And involves some projection of the future.

Next complication is adding a series. Rather than one single lump payment at one single time in the future, we have a series of n payments, A_i, we make at a series of future times. Thus we sum up the PV for each term.

PV = A1/e^(r*t1) + A2/e^(r*t2) + ... A_n/e^(r*t_n)

The latter term contribute less and less as t_i goes further out. If that has some regular form, you can sometimes reduce that sum to some closed form expression. Bonds with a coupon are a (relatively) simple example of that -- A_n is the final principal payment, and the preceding A_i are all the regular coupon payments and you have a formula for pricing bonds given whatever r you want to make, or what the effective r is when you decided to pay something for a bond.

All these different things are just different ways of applying the time value of money concept in ways of increasing complexity.

And finally, for the US fiscal gap, our A_i series is the deficit for each year out to some N years in the future of course. From that we need projections. How much are we going to spend and how much taxes are going to collect. That depends on current rules (set in law) interacting with economic growth, the number of taxpayers, the number of people collecting various benefits, salaries, and contacts with the govt, interest rates, etc, etc, etc, etc, etc. And etc some more. In all that mess they are things you can be somewhat sure about and things you can't be.

Demographics are one thing you can be sort of sure about. As the boomers retire, we get a big bubble of people collecting SS, Medicare, and other benefits that will occur at certain time in the future. That is already baked in the caked because even if the birthrate increased now, and people started having babies like crazy, they wouldn't be at working age in time to offset that bubble. Thus the number of taxpayers relative to tax receivers starts increasing and makes A_i spike up (about 15 years or so in the future).

Remember from above, as t decreases and the closer we get to that bubble, PV increases. That's what's happening now and is the main driver of the increase. SS is bad of itself, but is fixable. It is Medicare, medical costs that are the killer. That is the one that must be addressed, and addressed yesterday or we blow up. And that is the one that is the most fraught with emotion and the likely to make people run from the room screaming and gathering with torches and pitchforks.

Also, in the A_i, we include the effects of our current debt as well in the form of the neccessary principal and coupon payments we must make on all the T bonds outstanding and that will be generated in that A_i progression.

So in the end the fiscal gap is the present value of whatever total debt will be leftover at the end of that N year progression. When that is $222T, you know the future value of that public debt will be quadrillions in the future, and that cannot happen.

Well I guess it could if you inflated the dollar down to nothing where a billion buys you a hamburger. But that won't last long either of course. In real terms, you're screwed whether you have no money or wads of worthless money.

[DoggerDan]

While the math surrounding any fiscal gap can be very complicated, the solution is simple: Ensure expenses < income. What's immediately difficult again is how to make that happen when every special interest group in the country, including its own citizenry, wants more than their fair share of the take. While the details may remain complicated, the principle is again quite simple: Discipline. Working hard, living below one's means, and saving.

Over the last 97 years, our government has proven itself incapable of fiscal discipline, but it may not have been mere fiscal discipline, but rather, a penchant for war. See graph. The Civil War, WWI, and the Great Depression all increased our Federal Deficit held by the public as a percentage of GDP roughly the same amount. WWII cost resulted in increases about double that of the other three. Vietnam? Not even a blip, but from about 1980 to 1995, there's a stead rise equivalent to the first three, and a rise of similar amount but much steeper slope (less time) since 2008, which indicates we need to act quickly, particularly as we've already eclipsed all other periods except WWII. If things continue, we'll eclipse that ratio in another 10 to 15 years.

Since the government has been unable to put itself on a proper fiscal diet, yet we know that's precisely what must happen, what is to be done? How about we put the government on a diet? It's not difficult: Vote out those who won't support fiscal conservatism and vote in those who do support it.

Without such discipline, our nation will reach economic boogaloo.

[Hlafordlaes]

The "fiscal gap" NPV is a complicated mess (and ultimately dependent on various assumptions about the future) actually, but can be broken down into simple pieces and we can sort of get the feel for it and that might be helpful.

At the most basic level, the PV of some amount A at some time t in the future (t = 0 is now), is simply "discounting it" by the expected interest rate r over that time t: PV = A/e^rt. Of course, that is just the elementary "time value of money" concept. If you put some PV amount of money away in the bank (or whatever investment) at interest rate, r, A is what it compounds to in the future (assuming the bank survives).

[Note to any lurkers concerned about using 'e' -- this generally just makes things simpler and slicker than using the discrete geometric form (1 + r) but they are otherwise equivalent, only difference is what 'r' is . Sometimes, though the geometric form does work out better, though. e is the limit of (1 + 1/n)^n as n goes to infinity, and that comes about from the derivatives, actually. When dA/dt/A is exactly equal to 1, then A = e^t, but I ramble...]

A zero coupon bond is the simplest example of this, of which form short term bills usually are done. The face value of the bill is A, and PV is the money raised now at the bill auction.

Anyway, given PV = A/e^rt, we see that PV decreases as t and r increase, and increases as they decrease. Thus the closer we get to D-day when we must pay A, the more we need now. And the lower the interest rate, the more we must put away. And if we start taking derivatives with respect to r and t and all that good stuff (note taking dervivatives of e^rt is very simple), we see that while PV decreases as t increase, it becomes more sensitive to changes in interest rate.

And then we can get fancy and let interest rate r itself vary with time, and e^rt becomes something more complicated. And involves some projection of the future.

Next complication is adding a series. Rather than one single lump payment at one single time in the future, we have a series of n payments, A_i, we make at a series of future times. Thus we sum up the PV for each term.

PV = A1/e^(r*t1) + A2/e^(r*t2) + ... A_n/e^(r*t_n) ...

Gosh, pubius. Holy smokes and golly. We are done for, and you're not going to let me lie to myself. So please lie for me and say something to give us all hope and, say, 24 hours of blissful ignorance and complacency.

Wish I were kidding and not half-kidding.

[publius]

Gosh, pubius. Holy smokes and golly. We are done for, and you're not going to let me lie to myself. So please lie for me and say something to give us all hope and, say, 24 hours of blissful ignorance and complacency.

Wish I were kidding and not half-kidding.

No, *WE* are not done for. It is the status quo that is done for. Keep that in mind. I've used this analogy before, and I'll use it again. Right now, we're like the drunk or junkie who has hit rock bottom. Or the big fat slob who just had a heart attack. The person there is not done for, but they're going to have to make some changes, some big, hard, painful changes.

It is mathematically impossible for the status quo to continue. Thus it will end and things will change. How it ends is the question, and we can affect that. Sticking one's head in the sand ensures that end is as messy as possible, of course. But it will end, one way or another. But its end does not have to mean our end. Humanity has faced bigger disasters than this, and will again in the future.

But, there were a 1000 years of darkness after Rome fell.... They chose poorly.

[publius]

You know, I've been thinking about how to explain the "mathematically impossible for the status quo to continue" bit. It boils down to the unsustainability of two diverging exponential functions. That ignores the question of how long an economic growth exponential, the base function, itself can go on -- that can't go on forever either, with finite resources. But that's not the problem. It's that our promises to spend, our desire to consume, is an exponential growing faster than our ability to produce. Thus we borrow the difference, digging a hole in the future. That hole itself is an exponential, basically growing (relative to production) at rate equal to the difference of the two.

That is the exponential that is killing us. So to explain it simply, we must explain exponential growth.

There are several parable type stories that illustrate it, but my favorite has a become a modified "rice on the chessboard" parable.

Suppose someone asks you to do something, and for payment, you say will take this: Take a chessboard and put one penny on the first square, then two on the second, doubling each square. When the chessboard is filled, you'll take that as payment.

If one was foolish enough to accept that offer, one just agreed to pay (2^64 - 1)/100 dollars -- first square is 2^0, so we count starting at zero, and the last square is 2^63 and the sum is the thus 2^64 - 1 pennies. That sum, in dollars works out to be
$184,467,440,737,095,516.15.

In (short scale) words, that is 184 quadrillion, 467 trillion, 444 billion, 737 million, 95 thousand, 516 dollars and 15 cents.

If you work it out, the first quarter of the chessboard comes to $655.35. The first third is $41,943.03 and the first half is
$42,949,672.95, roughly $43M. The second half of the chessboard is the killer.

Fun facts of exponential(geometric) growth illustrated there, each doubling step is equal to one plus the *sum of all that is accumulated before*. It starts out very tiny, but blows up at the end, and does so in spectacular fashion. Growth is not linear (duh!) -- it starts out as no problem, but overwhelms you before you know it.

The parable of the lillies in the pond illustrates this latter point. Your pond has lillies growing unchecked, such that the area is doubling every day (some lillies can get out of hand under certain conditions in certain ponds, but not this fast -- it's just a parable). Say the pond is consumed in 30 days. When did the lillies cover half the pond?

IOW, by the time you notice the lillies are covering an appreciable area of the pond, it's just about too late. You better get in there and start killing lillies like crazy, othewise your pond is screwed.

Surprisingly, they say most people will answer 15 days, erroneously assuming linear growth, even though exponential was given in the setup. The answer is on the 29th day. The latter half of the pond was consumed in just one day. On the 28th on a quarter of the pond was covered, and on the 27th only 1/8. Before that, the lillies didn't appear to be a problem, as they were barely covering the pond. But they were doubling each day.

[Ara Pacis]

So what exactly is the exponent in our situation? Are we doubling? I keep trying to read post 895 when I'm tired and my eyes glaze over.