Lost your marbles?

Ok, bear with me if you will. I’m going to present a lesson in markets in a number of parts, beginning with a simple analogy, then moving into more complex theory. It may not make much sense by the end, but I’ll begin slowly and see where the tale takes us. My intention is not to preach, but hopefully to encourage discussion and debate.

Part 1: Lost your marbles?
Picture this; we have a very small school with a total attendance of six students. For ease, let’s give this school six grades, with one student per grade. Each year, the most senior student graduates and leaves, while another student begins at the lowest grade.

Each child has a generous parent who gives them a simple allowance of ten lollies per year to take to school. Obviously, the total number of lollies in the school is 60 per year.

One day, the teacher brings a bag of marbles to the school. “Neato”, the children all think, “I’d give anything to have a marble to play with!”. The teacher would like to let the children play with the marbles every day, perhaps this will stop them from fighting, and eating the sand from the playground. However, he had to buy these marbles out of his wage, and feels he requires compensation for losing the use of his marbles.

He offers the marbles to the children in exchange for 60 lollies per marble. Obviously, none of the children has 60 lollies, so he suggests that they pay every lolly they bring to school for the year, and the same number of lollies every year until they graduate. Once and if the full amount of 60 lollies is payed, the ownership of a marble will be entirely transferred to the child who has payed their debt. The students all agree, and are soon happily playing marbles.

So, what is the total value of marbles in the school?
If you answered 360 lollies, give yourself a star. The value of the marbles was agreed through a fair exchange to be 60 lollies each.

The first point of interest in this marble market occurs at the end of the year. One student is leaving, another is enrolling. The older child no longer needs his marble, but the younger one desperately wants to fit in, and feels a marble will help his cause. However, the teacher still owns 50 lollies worth of this marble, the older student 10 lollies worth. The teacher kindly agrees to transfer the debt to the new student in exchange for the enrollee’s lolly allowance. The new student gives the teacher his entire allowance of 11 lollies, the teacher hands 16 to the graduate and the marble is exchanged.

[At this point I notice that somebody in the front row is getting excited, waving a hand in the air, and might even have done a little wee…

“What is it, Dwayne?” I ask. He points out quite correctly that this transaction involves 11 lollies rather than 10. “That is obviously because the child’s parents are flush with cash and are spoiling the little brat.” I grudgingly explain.

“But why did the graduate get so many lollies?”

“Fair question, simply answered. Sit down and listen, dammit!”]

The original agreement involved a fair value of 60 lollies, so any profit made on the sale should go deservedly to the older student. And it did. The new contract to purchase the marble over time is for 11 lollies per year, a total of 66 lollies over the 6 year attendance.

So now, what is the total value of all marbles at the school? Is it:
a) 366 lollies?
b) 396 lollies?

If you’re expecting a simple answer here, sorry. There is no right or wrong answer! On the one hand, you could consider this to be 10% inflation in the price of marbles, enabled by a 10% increase in purchasing power of the newcomer, and this certainly has merit. On the other hand, you could argue that 5 marbles are worth 60 lollies each and 1 marble is worth 66. But then again, surely each fully paid-up holder of a ’60-lolly’ marble can expect at least to get 66 lollies when they graduate and sell to the new recruit?

This perceived value of 66 lollies is clearly sustainable, regardless of your answer to the earlier question, provided everything continues as expected. One fair trade per year, and the new enrollee arriving with an 11 lolly allowance. The outcome will match the expectation.

Ok, the second spanner in the clarity-cog. To make things fair for all the kids, the other parents also decide to give their children 11 lollies per year. In fact, they go further, and decide that the lolly allowance of every child will be raised by an additional sweet every year.

Does this change things? Is the value of all marbles at this point (end yr1/start yr2) now 396 lollies? Regardless, the yearly total debt is now 61 lollies versus a yearly total allowance of 66. The remaining 5 might be consumed, traded for other knick-knacks, or saved. We’ll revisit this surplus at a later point. This ‘simple’ scenario gets interesting enough if we just ignore saving. Let’s assume they’re eaten.

Now to continue with the assumption of a stable and efficient market, where each year another student arrives, each year with an additional +1 lolly allowance. For the following few years, as each trade occurs the gap between the total perceived value and total traded value widens. This continues until 6 years has passed, at which time an oddity of mathematics (and incidentally, the most important part of the lesson) occurs.

Once each and every marble has been traded, the gap between perceived and traded value stops growing, and stays exactly the same, for as long as the trades continue in the current fashion.

[Not following? Try it in a spreadsheet.
Year___ trad__perc__gap
Year1___366__396___30
Year2___372__432___60
Year3___384__468___84
…
Year6___456__576___120
Year7___492__612___120…and so on.]

So at this point, you’re either ready to spit on me for wasting your time, or you’ve spotted the obvious implications of this simple analysis. The most important message is that the change in a small driver – in this case, inflation of lolly ‘income’ has a magnified impact on perceived value, and this magnification is not instantaneous. It grows and grows, not reaching its new equilibrium until each and every marble has been traded in this new environment. A single change, a 6 year long impact, resulting in two different measures of value.

[“Yes, moron,” screams a girl in the front row, “But what the hell has this to do with buying houses and making lots of money?”
Patiently ignoring her (as security drags her from the hall, kicking and spitting vaguely in the direction of the podium), I carry on…]

What are the drivers that might have an analogous effect on house prices?
a) Lower interest rates? – to be discussed in a future post
b) Higher wage growth? – ditto
c) Increased rental yield?
c) An increase in the money supply? – erm, yep we’ll cover that too.
d) All of the above?
e) Uh, there’s, like, two different c’s there, Mr foundation. What are you, retarded?

How long would it take for the price-perception reaction to this/these driver/s to reach ‘equilibrium’ in the housing market?
a) A year?
b) Six years?
c) Until the total number of subsequent transactions equalled the total number of houses in existence?
d) Somewhere between a) and c)?

And for 15,000 bonus points, discuss the significance and duration of the impact if one child were to save their surplus lollies and attempt to purchase an additional marble (Points deducted for answers longer than the original post)? How might this relate to the housing market, and which child is most likely to end up back eating sand?

Mmmm, food for thought. More to come, but please discuss?

Cheers, F.[cowboy2]