Tuesday, May 01, 2007

Do Not Pass GO, Do Not Collect $200

In thinking about the inflation debate, I thought it illustrative to give an example based on something we all know and understand: Monopoly. Yes, the board game you've been playing your entire life. Some of the traders reading this probably made their first "rip his eyes out" trade playing Monopoly, and have been in love with ripping people off every since. By the way, I thought of this over the weekend, but I'm probably not the first to think of this allegory, so my apologies in advance if it appears I'm borrowing from someone else's work.

Anyway, in this example, let's imagine we are playing a simplified version of the game. We have three players who each get the standard allotment of cash ($1,500 each). Instead of rolling around the board, each property will be put up for auction at the onset of the game. What would we suppose is the average price paid per property?

If each player spends all of his/her available cash, then the average price paid (we'll call it the price level) is $160.71 ($1,500 times 3 players divided by 28 properties.) Now, its possible that some players choose not to spend all their cash, perhaps hoping to save some money for houses and hotels. This is in essence a savings rate. So if the initial cash position (which economists usually call an endowment) is $4,500 is M and the savings rate is S, and the number of available properties is Y, then the generalized formula for the price level P is.

P = M * (1-S) / Y

Anyway, back to our game. Assume all properties are now owned and each player saved exactly 10% of his/her original endowment. They all roll around the board in the normal manner, passing GO, picking up Chance cards, paying luxury tax, paying rent on properties they land on, etc.

After playing for 1 hour, the game ends, and a new game begins. Except the players get to keep all the cash they've accumulated to that point in the game, and this money is used to bid on all 28 properties at auction for the second game.

Now the money supply has changed hasn't it? Although by what amount depends on how many times people passed GO, won 2nd prize in a beauty contest, etc. If enough people landed on Income Tax or got a Pay School Tax card, M might even be lower. For simplicity, if we assume S is zero, then the percentage change in M equals the percentage change in P.

So if we define "inflation" as the percentage change in P, we can see that there cannot be inflation from game 1 to game 2 without an increase in M. Furthermore, if we keep playing games in the same manner, there cannot be persistent inflation over several games unless M increases persistently.

Of course, this isn't how inflation is calculated in the real world. It is actually estimated by selecting a basket of goods and measuring the price change in those goods. The equivalent would be to randomly select 10 properties and measure the change in price from one game to the next of those properties. We'd expect this to do a pretty good job of estimating inflation, but there would obviously be some noise.

Consider the possibility that we take the Illinois Avenue card and throw it out. Now you can't make a monopoly out of the red properties. That dramatically reduces the value of Kentucky and Indiana. But the impact on the price level is fairly small, because Y has decreased from 28 to 27. So if we started out with Y= 4,500 and S = 0, the change in price due to the removal of Illinois would be about +3.7%.

But Kentucky might have been one of the properties in the basket of 10 used to estimate inflation. Say Kentucky declines in value by 75% and the other 9 properties rise in value by 5%. The average price has fallen by 30%! But do we really have deflation? No, because in this case we can clearly see there was a change in preferences for Kentucky Avenue which has skewed the mean price change.

Simpler things could arise which create false inflation if you will. Suppose that early in the bidding process, one player has Atlantic and Ventnor Avenues, and Marvin Gardens comes up for the bid. That player can control the yellow monopoly if s/he can secure the last property. The other players do not want to allow the player to have a monopoly. So all three players bid
aggressively, and the price of Marvin Gardens winds up being extremely high. Here again, there was a change in value of this property. If Marvin Gardens had been one of the properties in the basket of 10, we would likely calculate some degree of inflation, when in fact, there was none. Whatever extra money was spent on Marvin Gardens isn't available to be spent on other properties. So the price of at least one other property must decline to offset the increase in the price of Marvin Gardens.

In the real world, we think less of an endowment and more of income. Consumers are paid in cash and this is what they use to purchase goods and services. Furthermore, the effective money supply isn't really fixed. Goods and services (as well as capital goods) can be bought on credit which has the effect of allowing for more transactions than what a strictly cash-based system would allow. So there is more that impacts the money supply than just how much cash the Fed is printing. But unless there is an increase in the money supply, there can't be generalized inflation.

Let's take the example of oil. Oil is a direct or indirect input in many consumer and producer goods. And virtually all consumers must regularly fill up their gas tanks. But how would an exogenous increase in oil prices affect inflation? Without an increase in the money supply, there can be no net impact. Let's go back to our Monopoly example. Say the first of the Railroads to come up for bid was Reading. And for whatever reason, Reading was bid more aggressively that in previous games. Does the price of Reading mean anything for the price of the other Railroads? Probably, because the players will have seen how aggressive the bidding was for one railroad and bid the others more aggressively as well. Here the Railroads are a bit like inputs into a finished good, because owning multiple railroads is more valuable than owning one. So the price of one impacts the price of others. Similar to how the price of oil impacts the price of finished goods that involve oil, such as gasoline, or services such as shipping or air travel.

But ultimately if there is no more money in the system, there can't be generalized inflation. If Monopoly players bid up the Railroads, they must bid less for other stuff. And if consumers spend more on air travel, they must spend less on something else.

The real debate should be how we can measure the money supply, and what economic events result in a change in the money supply. Now, what do I hear for New York Avenue?


Anonymous said...

I take out a 100% LTV mortgage on a house I purchase for $300,000.

Doesn't work. I jingle mail the keys to the bank, and the bank ends up selling the house for $150,000.

Question: it would seem to me that $150,000 just disappeared, never to be heard from again. Is that correct?

In other words, if a huge equity piece of the economy suddenly shrinks in value, we get deflation.


Anonymous said...

The way I learned it Anon, inflation is just the opposite of that: Your 300K loan was created from thin air and the Fed prints money to match it (M increases); i.e., M is still $150K higher after you mail your keys to the bank.

Confusing stuff, eh?

Will said...

Lately I have begun to rethink the monetarist explanation for rising prices.

At its core, money is just a medium of exchange. If there is more demand for money, the money supply will increase -- whether it is done by the government or the private sector. The private sector can increase the money supply by simply trading more -- even during "ancient" times, credit instruments, commodities, etc., were used to facilitate the exchange of goods.

Therefore, given the choice, I think that inflation is caused by supply and demand for goods and services as opposed to supply and demand for money.

Accrued Interest said...

The difference between Anon's point and RW's point is just from when you measure it. Bottom line is that the money supply didn't decrease in all that, it just didn't increase by as much.


In theory, interest rates are the price of money. In order to facilitate current consumption beyond current income, you have to "buy" more money by borrowing it. If there is more demand than supply the price (interest rate) should go up.

But the private supply of borrowable funds still have to come from someplace. Assume the Fed never prints money. Banks can lend out all but a small percentage of their deposits. Let's say that reserve requirement is 2% to make the math easy. So a bank with $100 million in deposits makes $98 million in loans. But see, that $98 million in loans came from depositors, not from thin air. If you will remember Macroeconomics 101, this is why Savings=Investment. Because in order for banks to loan the money, someone has to be putting the money in the bank to begin with.

Back to the real world, the Fed allows banks to borrow money to make their reserve requirement. So in essense, to the extend the Fed wants to increase the money supply, it prints money and lends it to banks. In essense, the Fed has become a depositor at that bank: they put in money and get back interest, just like Mrs. Smith's savings account.

I think Will's idea would stand if we went to a completely private money supply, where we used bank notes instead of Federal Reserve notes. I think all but the most hard core libertarians/conspiracy theorists agree that fiat money is superior to private money because of decreased transaction costs of assuring we have "good" money. That debate is interesting, but entirely academic, since we aren't going to private money any time soon.

GS751 said...

I am a freshman econ major. This is by far one of the best blog posts I have ever read. I have it bookmarked and go back and read it multiple times. Thanks.

Kaushal Trivedi said...

I am learning - and this post was a great thought provoker. Thanks.

Duane said...

Let's try an even simpler Monopoly game example. I see it as more real-world, easy for anyone to get their head around example.

4 players. Regular game. All properties have been bought through regular play. Everyone is more or less even. Then player 'Bob' is handed an additional 10 $500 ($5000) Monopoly money. Bob is owner of a large construction company that just won a contract for 10 prisons. Bob has the additional money - which was *added* to the economy, not borrowed from the other players; the other players didn't get a contract.

Bob goes to work, starting by buying up properties from the most hard up player. After a bit of time, Bob has many additional properties; the other players have fewer. The average sales price of the properties has increased by ($5k / 23? properties).

Bob got the money first, so he was able to take advantage of pre-inflation prices. Chances are someone has few properties and therefore income potential. Properties now cost a lot more for everyone. Bob doesn't care; he just got another contract to help rebuild Iraq (due to college connections that have made their way into power). Bob just got an injection of $20k (again, non-borrowed) this time around...

Welcome to the real world.