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Commodity Money

Have been out of the game for a while but I think I made a breakthrough.  I want to work up to it though by developing the paradigm that I am working in from the beginning.   This will take a few posts.  This one will describe the organic rise of commodity money in the context of a free-market economy and explain the function of real interest rates, nominal interest rates, and the rate of “inflation” (change in the value of money).  I can’t stress enough that this is a hypothetical free-market economy with no central banking.  This economy would be different in several ways from most modern economies.  Much of the confusion about monetary issues comes from not fully understanding these differences.  From this starting point, I will try to work my way up to an economy with a central bank and fiat money and contrast the two.  The next post will be a primitive model of credit.  That will be followed by a model of banking.

Commodity Pricing

A discussion of money and credit must begin with an analysis of the nature and purpose of commodity money.  I take for granted that organically occurring commodity monies have always been valued on their own before they became commonly used as a medium of exchange.  There are some who assert that even “hard” money has no value except as money.  But in order to hold this view one has to imagine that primitive people somehow thought of the idea of money suddenly out of nowhere and began searching for a suitable commodity which currently had no value but which could be given value by declaring it currency.  These people must have decided that the yellow (or silver) metal coming out of the ground that they had previously had no interest in would serve nicely and decreed that from then on they would use it to trade and somehow got everyone to go along with this.

I think the above notion is silly.  What is much more likely is that people found gold and silver and thought they looked cool and desired have them to use in crafts in order to make them look nice or something along those lines.  Because of this demand and their limited supply, these metals became valuable.  Then because of this, they acquired all of the attributes which made them ideal for use as a medium of exchange.  In order to understand how such a medium of exchange would come about and function requires a discussion about commodity pricing.

Let us start with another commodity.  Imagine a free-market economy with some existing form of money which discovers oil (or discovers a use for oil).  Assume that the quantity they initially discover is all that they will ever have and assume that many people own small quantities of it.  In this case, the market will allocate the existing supply of oil over time in the most efficient way.

If someone has oil in this economy, they must decide whether to sell it or hold it (let’s assume that they don’t want to consume it).  When considering whether to hold it, they must anticipate what the price will be in the future.  If everybody dug up their oil and sold it right away and it was all consumed, then the current price would be very low and the price in the future after it had all been used up would be very high.  This would mean that any individual would be able to make a substantial profit by holding their oil until that time when all the other oil is gone and the price is high.

And in fact, one need not be initially endowed with oil in order to make a profit in this way since one could simply purchase the oil at the current low price, hold it and sell it in the future at the higher price.  The effect of this behavior will be to increase the price and reduce consumption of the oil in the present and transfer that oil which is saved to some point in the future, thus lowering the prices in the future.

The question then is: how much will be saved/consumed and at what current and future prices.  The answer depends on the rate of interest in the economy.  Since holding oil is an investment, it must compete with other alternative investments.  The nominal interest rate represents the payment one can receive from lending money, which is an alternative investment to holding oil.  If holding oil is costless and the risk associated with it is identical to that associated with lending money to the bank at the market interest rate, then the change in the price of oil must be equal to the nominal interest rate.  This is known as the Hotelling rule after the economist of the same name.

The reason for this is fairly simple.  If the price of oil were expected to increase at a rate greater than the nominal interest rate, people would lend less money and use it to buy more oil to hold as an investment.  This would drive the current price up and the future price down just as described above which would reduce the rate of increase in the price.  Conversely, if the rate of increase in the price of oil were lower than the nominal interest rate, people would invest less in oil and simply lend their money to the bank since that would be more profitable.  This would drive the present price of oil down and the future price up which would increase the rate of change.    The only situation in which people would be happy with the exact amount of oil that they were holding for investment purposes would be when the expected increase in price were exactly equal to the nominal interest rate.

Of course, holding oil is not costless and is probably more risky than lending money to the bank so the price will likely have to increase faster than the risk-free rate to cover the cost of holding and offer some risk premium.  But the logic is the same.  We can write the portfolio-balance condition which describes the price path for the asset as follows.

%∆P=i+φ

Where i is the nominal interest rate and φ is the premium associated with that asset due to risk, cost of holding, etc.  We could break this premium up into multiple constituent parts but this is not necessary for our purposes.  In the case of oil, where the investment is costly to hold and likely more risky than a loan, φ will be positive, however, as we will see, it is possible for it to be negative as well.

Saving and Investment

Now consider a barter economy.  In this economy, people desire to store wealth.  There are many different ways to do this.  The most obvious way is to store goods but not all goods are equally desirable for this purpose.  For instance, one could store grain but grain would take up a lot of space and it eventually goes bad so it would have to be rotated out.  In addition, because it goes bad, its value will naturally decrease as it gets older since its wealth-storing ability will be diminished as it gets closer to the end of its life.

On the other hand, a commodity like gold, never deteriorates and takes up very little space.  These attributes make gold a more suitable good to use as a store of value than grain or essentially any other good.  Because of this, people will tend to hold a significant portion of wealth in the form of gold and silver, which has similar properties.  It is worth noting that people in the aggregate are limited in the total quantity of these goods that they can hold but the desirability of holding them as a store of wealth will increase their price which increases the total amount of wealth which they represent.

At this point, it is necessary to make a few remarks about the consumption of precious metals.  Recall that it must be the case that the original interest in these goods had nothing to do with transacting or storing value but was merely based on wanting to do something with them, most likely using them for decoration.  Using gold or silver for decorative purposes is a form of consumption.  Of course, this consumption is not likely to entirely use up the good in a short period of time.

If someone makes a gold necklace, they can wear the necklace for years and then melt it down and sell the gold at some point in the future.  This activity has an investment component to it.  But there is still a consumption component as well much like owning a house is part consumption and part investment.  A gold necklace is likely subject to some deterioration over time.  It is true that this will probably be minor but it will still be more than the deterioration of gold bars kept in a safe.  And recalling that the value of gold is determined in relation to demand at times far in the future, a small rate of deterioration over hundreds of years is significant.

In addition to this deterioration, some gold jewelry will be lost.  The probability of loss (or the fraction of all gold lost depending on how you wish to account for it) must be factored into the rate of consumption as well.  A gold necklace or bracelet is much more likely to be lost or destroyed than a gold bar in a safe.

Just as with oil, the competition between competing uses—consumption and investment—determines the price of gold and its evolution over time.  Since, at this point, we are in a barter economy, there is no such thing as a nominal interest rate, this rate being in terms of money which doesn’t exist yet in our economy.  But loans can still be made.  For instance, one farmer could loan a quantity of grain to another farmer in return for a promise to pay some amount of grain one year in the future.  Since grain can be planted and used to produce more grain, it is possible for the borrower to pay the lender back with more grain than he borrowed and still be compensated for the effort of planting, growing and harvesting.  The additional payment to the lender above the original principle represents the real interest rate.

The ability to lend goods today for the promise of goods in the future is a form of investment which competes with holding goods like gold.  This means that people must choose how much of their wealth to hold in the form of gold and silver and how much to hold in the form of loans.  This means that there must be some portfolio balance condition of the form:

%∆PG=r+φ                                                                                                                                                                                                        [1]

Where PG is the price of gold in terms of grain (or “other goods” somehow defined) and r is the real interest rate measured in grain/other goods.  In this case φ represents the premium which holders of gold must receive to make them indifferent between holding gold and making loans in “real goods” at the market rate r.  However, in this case gold has some advantages over lending.  For one, there is less risk associated with holding gold in your safe than lending real goods to someone else who may become unwilling or unable to repay you at the designated time.  For another, gold is most likely more liquid than an I.O.U. from someone to pay grain in the future.  So if the desire to spend some of your wealth should strike you at some time between the origination and the maturation of the loan, you would be better off having gold than the loan.

These factors most likely mean that if the real rate of return on these two assets is the same, people would prefer to hold gold to making loans.  This means that in equilibrium the real rate of return on a loan must be greater than the rate for holding gold, or in other words the φ for gold must be negative.

The above portfolio balance condition describes a path for the price of gold along with a real interest rate and a risk premium which are determined in the market such that people are indifferent between holding gold and making loans.  With this in mind, we can consider what is likely to happen if the quantity of gold unexpectedly changed.

If people suddenly found a vast supply of gold which was previously unknown, they would find themselves holding more gold than they wanted at the preexisting prices.  These prices include the current price of gold in terms of other goods as well as all future (expected) prices and the risk premium φ.  I will assume that the real interest rate r as well as output and investment are determined entirely by real factors and thus are independent of the quantity of gold.  Since gold is a consumption good in this model, this assumption may not hold but it will simplify things significantly at this point.

In this case there are three ways in which prices can adjust to bring the market into equilibrium.  The first way is for the price of gold at all points in time to fall proportionately to the increase in supply.  If this happened, people would still be holding the same value of gold, it would just take a larger quantity to comprise that value.  Since it is (most likely) the value of wealth held in gold and not the absolute quantity which determines the risk premium people are willing to pay to hold gold rather than other investments, φ will be unchanged and the portfolio balance condition will still hold.  If this happened money would be “neutral” in the classic sense meaning it would not change any “real” variables.

Whether this works out or not depends on the demand for consumption of gold relative to other goods.  In order for all markets to be brought back into equilibrium merely by a proportional decrease in the price of gold, it must be the case that the quantity of gold people are willing to consume at the new prices are at all times greater than at the old prices by the same proportion.  If this is not the case, then even though the portfolio balance condition would hold if the price of gold adjusted proportionately, the new price path would not lead to an equilibrium in the actual gold market.  If this is the case, then something else has to give.

If consumption demand for gold does not behave as described above, one of two things will happen.  Either the new equilibrium time path will have to allocate the new gold disproportionately to close time periods or it will have to allocate it disproportionately to farther periods.  In the first case, the price of gold in close periods will have to rise relative to later periods meaning that the initial rise in the price of gold will be disproportionately large compared to the increase in supply and the rate of increase will be lower.  In the latter case the opposite will be true.

If the price of gold decreases by a smaller proportion than the increase in supply in the current period then people will be holding a larger value of wealth in the form of gold.  This will mean that the premium they are willing to pay for holding it will be lower.  This will be necessary though to bring the portfolio balance condition into balance since the rate of increase in the price will also be lower (and by assumption the real rate does no change).

On the other hand, if the price decreases more than the increase in supply, people will find themselves holding a smaller amount of wealth in the form of gold and will try to increase their holdings which will bid up the premium on gold to bring the portfolio balance condition into equilibrium with a greater rate of change in prices.

So there are three possible outcomes:

  1. PG decreases proportionately to increase in supply, %ΔPG and φ are unchanged.
  2. PG decreases less than proportionately to increase in supply, %ΔPG increases and φ becomes smaller (since it is negative it is an increase in absolute value).
  3. PG decreases more than proportionately to increase in supply, %ΔPG decreases and φ becomes larger (decreases in absolute value).

Which one of these cases occurs and to what extent depends on the shape of the demand for gold in consumption relative to other goods and the demand for gold as a store of wealth/medium of exchange relative to other assets.  The latter will determine only the extent, not the qualitative outcome, as it determines only the sensitivity of the risk/liquidity premium to changes in real money balances.   It is worth noting that “money neutrality” (or non-neutrality) in this context have a somewhat different meaning than in most models since the good being used is itself also a consumption good, changes in its quantity have a direct effect on consumption both of that good and potentially of other goods.

Commodity Money

In a barter economy, people will choose to hold wealth in the form of various goods.  Some goods such as precious metals are better suited than others for this purpose and the relative desirability of a good for this purpose will be reflected in the premium one must pay to hold it in terms of the change in value over time.

It will come to pass in such an economy that most market participants will be holding some quantity of these goods as a store of wealth.  At this point, it will be more convenient in many cases to trade using these goods than other goods.  This is mainly because it avoids the commonly recognized double-coincidence-of-wants problem associated with barter.  If a butcher wants to buy bread from a baker but the baker is a vegetarian, he may not be anxious to accept meat in exchange for his bread.

It is of course, possible for the baker to accept the meat and trade it for other goods but this would have to be done very quickly or the meat would spoil.  Finding people who want to consume the meat immediately, especially if it is a large quantity, could be very inconvenient for the baker.  On the other hand, if the butcher, who is most likely holding some wealth in the form of gold, offers gold for the bread, the baker will not have to worry about consuming or trading it right away because it will be expected to hold its value well over time.

In this way goods like gold and silver become “money.”  By this I mean that they become widely used and generally accepted as a medium of exchange.  The primary factor which makes this possible is their ability to hold their value over time.  There are, of course, some other attributes which make goods particularly well suited for use in exchange which are well recognized.

Easily divisible: Diamonds don’t deteriorate over time and they are rare and nonrenewable (at least natural diamonds) so they should hold their value well.  However, they are not ideal candidates for commodity money because they cannot be easily divided into any denomination desired.  Cutting them is difficult and requires a skilled craftsman.  And once cut, they cannot be put back together which means that cutting them into smaller stones reduces their value.  On the other hand, gold and silver can be easily divided and aggregated.

High value, low weight/bulk:  Marble and granite are valuable commodities which exist in a fixed quantity but because they are relatively plentiful, the quantity of them which would be required to carry on every-day transactions would be very great and difficult to store and transport to the market, unlike gold and silver.

Uniform and easily recognizable: Land holds its value well over time but is not well suited for money because, in addition to not possessing the two characteristics mentioned above, it is not all created equal.  This means that a detailed appraisal would have to be conducted prior to each transaction.  This would be very costly.

At this point we have established two of the three functions commonly associated with money: storing value and carrying out exchange, with store of value being dependent on the demand for consumption of the good along with durability and limited supply and medium of exchange being consequent upon its ability to store value.  The third, acting as a unit of account, follows naturally from the use as a medium of exchange.  Theoretically, it would be possible to measure the value of any good in terms of any other good but if all goods are commonly trading for one good such as gold, it will be natural to measure their value in terms of this one good.

Now if we take gold to be “money,” we can see that the above portfolio balance condition is really the well-known Fisher equation.

i=r+π                                                                                                                                                                                                                       [2]

In this equation, i is the nominal rate of interest, r is the real rate, and π is the rate of inflation.  To see this note that the percentage change in the price of gold in terms of other goods is equal to the negative of the inflation rate.  Then rearrange equation 1 so that φ is on the right.

φ=-r+∆PG=-r-π=-i                                                                                                                                                                               [3]

The nominal interest rate is equal to negative φ (recall that φ above was a negative number).  In other words, the nominal interest rate represents the risk/liquidity premium on money.  To better understand this, consider three possible investments.

  1. Hold money (gold).
  2. Lend money to a farmer who will use it to buy grain, plant it, grow more grain, sell it and pay you back in money plus i% interest in the next period.
  3. Buy grain and lend it to a farmer who will plant it and pay you back in grain at rate r next period.

When financial markets are in equilibrium, people at the margin will have to be indifferent between these three investments.  For simplicity’s sake, assume that future prices are known (or at least the risk associated with the prices of grain and gold are the same).  Then there are two choices at play.  Does one prefer to hold gold or loans?  If one holds a loan, do they hold it in terms of money or grain?

First consider the choice between holding a loan or holding money.  This is the same question considered in the previous section.  Since money is more liquid—it allows for more flexibility of consumption between now and the maturation of the loan—people would prefer to just hold money if the rate of return on both were the same.  If the loan were risky, this would add to this premium but assume that this is not the case here.  This means that in equilibrium the rate of return on money, which, measured in grain, is the increase in the value of money, will have to be less than the rate of return on the loan which, measured in grain, is r.

%∆PG<r

The difference between the rate of return on money and loans when people are indifferent on the margin between holding a little more of each, is the liquidity premium φ.  This means that, by definition we have:

φ≡r-%∆PG

Now if we are considering which type of loan to make, people should be indifferent between the two.  Since both are equally liquid (and by assumption, there is no future price risk), the rate of return on both should be the same.  The rate of return measured in grain on the second loan is r.  The rate of return measured in grain on the first loan is (approximately) i+%ΔPG.

i+%∆PG=r

This can be rearranged so that:

i=r-%∆PG

The nominal interest rate is the rate measured in money which makes the real return on a loan made in money equal to the real return made in goods (r) given the change in the value of money over the course of the loan.  But this only exists because people would prefer to hold money rather than make loans if the rate of return on both were equal.  If this were not the case, the rate of return on holding money would be equal to the rate of return on loans or, in other words, the percentage change in the price of money (gold) would equal the real rate of return r and φ , by definition, would be zero.

But in that case the nominal rate which would make the rate of return equal on the two types of loan would also be zero.  Since the value of money is growing at the real interest rate, lending 1 oz. of gold today and getting 1 back in a year, would allow you to buy 1+r units of grain, the same return as if you loaned 1 unit of grain and received 1+r.  The existence of a nominal interest rate is caused by the preference for holding money relative to other investments.  (Note that this is the case in an “organic,” free-market economy.  The factors determining the nominal interest rate in a modern central-bank economy are somewhat different.)

Here is a recap of the main points so far:

  1.  Goods like gold and silver originally have value because people want to consume them in a way which is independent from their use as a store of value or medium of exchange.
  2. Because their quantities are limited and they do not deteriorate, the consumption of these goods must be allocated by the market over a very long time horizon.  This means that they hold their value well relative to other goods.
  3. Because they hold their value well relative to other goods (along with a few other characteristics) these goods are particularly suitable for carrying out exchange.
  4. The qualities which make these goods suitable for storing wealth, and therefore suitable for carrying out exchange also tend to make their value increase gradually over time (or at least cause the expected change in their value to be a gradual increase).
  5. Because they are particularly useful for carrying out exchange, these goods (which become “money”) will carry a liquidity premium which will make the return from holding them lower than holding other assets, including loans.
  6. The nominal interest rate is a reflection of that liquidity premium on money and will be equal to the negative of that premium.

Part II: Banks and Credit

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  1. November 28, 2013 at 4:40 am

    I couldn’t refrain from commenting. Very well written!

  1. February 19, 2014 at 3:06 am
  2. March 12, 2014 at 12:26 am
  3. June 7, 2014 at 8:31 am

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