In the Seven Kingdoms of Westeros, the staple food is bread, as in all the other nations in its region. Bread is widely traded across national boundaries, as is silver.
In all these nations, bread can be purchased, using raw silver, at a rate of 6 loaves per (Troy) ounce. This price is determined by international market forces, and it is not influenced by the monetary actions of any individual kingdom.
Historically, the people of the Seven Kingdoms have used coins containing silver as money.
Before its government got involved in the country's monetary system, the Seven Kingdoms had coins that were produced by private mints. Often, these mints were owned by prominent nobles. One of them was owned by Tywin Lannister, the head of House Lannister, an extremely wealthy house that dominated the western part of the Seven Kingdoms. The coins produced by this mint provided most of the currency in the westlands, and they were very commonly used elsewhere in the Seven Kingdoms.
Following traditional practice, the Lannister mint used monetary units known as "stars." Its most popular coin was a silver "dragon" whose denomination was seven stars. (Seven was an important number in Westeros: in addition to the seven kingdoms, the principal religion in Westeros featured a god with seven aspects.) These coins had a dragon engraved on one side.
The mint named and marked the coins in this way to honor House Targaryen, the house of the Lord of the Seven Kingdoms, who governed them from the Iron Throne in the city of King's Landing. The symbol of House Targaryen was a dragon.
For many years the Lannister mint bought silver and minted coins, paying for the silver in newly minted dragons (that is, dragon coins), at a mint price of 18 stars per ounce. Its mint equivalent was 21 stars per ounce. So a dragon coin, which weighed half an ounce, was not pure silver.
The price of bread in coins depended largely on the silver contents of the coins. However, because of the superior convenience of coins in exchange, a person could buy 7 loaves of bread with three dragons.
1. a.How much silver did a dragon coin contain?
b. How much silver did a star represent?
2. What was the fineness of the silver in a dragon?
Note: The fineness of a coin is the percentage of the weight of the coin that comes from its precious-metal contents - in this case, silver.
3. a. How much did six loaves of bread cost, in silver in monetary form (silver contained in coins)?
b. How much less, as a percentage, did six loaves of bread cost in monetary silver, compared to their price in raw silver?
4. How much purchasing power (in bread) would a person who brought an ounce of raw silver to the mint have gained or lost by doing so?
5. a. How many dragons would the mint have produced if a merchant had brought in a Troy pound (12 Troy ounces) of silver?
b. How many stars would it have earned, as its gross revenue from minting these dragons? How many dragons?
6. If this revenue covered the mint's costs and gave it a profit of 11 stars, then what were the mint's costs, as a percentage of the total number of stars it minted? (Note: For simplicity, round the profit percentage to the nearest percent, and use the rounded figure in subsequent calculations.)
CLASS NOTES:
In the following pages, I will build an example to illustrate how the minting process worked, and how a government could earn a large amount of revenue, from seigniorage, by debasing its coins.
I will use, as part of the example, the original English system of monetary units, which was used in England (later, Great Britain) until 1971. Under this system, the basic monetary unit was the pound (symbol £). There were 20 shillings (symbol s.) in a pound and 12 pence (symbol d.) in a
shilling, so that there were 240 pence per pound.[1],[2] Pence could be further divided into four parts, but those parts did not have an official name. Although the pound was the official English monetary unit, the shilling was widely used as a the practical unit, particularly for relatively small sums/purchases.
This system was originally created in continental western Europe by the Emperor Charlemagne, who ruled a good part of that region (the Carolingian Empire) during the eighth and ninth centuries A.D. It was adopted later by England, France and many other western European countries, although different countries used different names for the units. It was based on a Roman system of weights, whose basic weight unit was a libra that was divided into twelve unciae. In England, libra became "pound" and uncia "ounce," although the Roman/Latin origin of the system is reflected in the fact that the abbreviation for pound, as a unit of weight is "lb."
The Roman-style 12-ounce pound has been and still is used to measure weights of gold and silver for monetary purposes. It is called the Troy pound. A Troy pound actually weighs almost 20 percent less than a usual modern (avoirdupois, or a.v.) pound, but since an a.v. pound is divided into 16 ounces, a Troy ounce weighs almost 10 percent more than an a.v. ounce. For the rest of this section, when pounds and ounces are used as weight measures, they are Troy pounds and ounces.
Originally, a monetary pound was supposed to represent a pound (12 ounces) of silver, so that a shilling should have represented 12/20 = 3/5 (0.6) ounces of silver and a pence should have represented 0.6/12 = 1/20 (0.05) ounces. Whether or not there were ever coins containing these amounts of silver, by the time the national governments that eventually succeeded the Carolingian empire had fully taken over their countries' monetary systems, the coins contained much less silver. For example, in the 16th century a English "crown" coin, which had a denomination of five shillings, weighed roughly one ounce and contained even less silver, as opposed to the three ounces of silver it should have contained under the original system.
We'll imagine that initially, in England, one ounce of raw (uncoined) silver can be used to buy five loaves of bread, so that the silver price of bread is 1/5 ounce per loaf. Since England is a one country in a large region (Europe) where both raw silver and bread are traded internationally, it makes sense to assume that nothing that happens to the English monetary system can affect this price. We'll also assume that, initially, the price of bread, in silver, does not depend on whether the silver is raw, or part of a coin. (That is, we'll assume that the initial purchasing power of a coin depends entirely on its silver contents.) Finally, we'll assume that a shilling currently represents 1/5 ounce of silver. So the price of bread is one shilling per loaf, and a five-shilling coin (a crown: see above), which contains exactly one ounce of silver, can be used to purchase 5 loaves of bread.
We'll assume that the silver coins produced by the English mints have the same contents as the
silver coins currently in circulation. So the mint equivalent of silver, which is the number of monetary units (here, shillings) the government mints per weight unit (here, ounce) of silver, must be 5 shillings per ounce. We'll also assume that the mint price of silver starts out equal to its mint equivalent, so that a person who brings an ounce of silver to a mint receives 5 shillings in coins (perhaps, one crown). At this price, relatively limited amounts of silver are brought to the mints, because people who bring silver to a mint gain relatively little from doing so: silver coins obtained from a mint will not buy any more bread than the amounts of raw silver it costs to buy them. The only benefit is that using coins to make purchases may be more convenient than using raw silver.
In practice, even in normal times the mint price was at least slightly lower than the mint equivalent, so that more monetary units in coins were minted from an ounce of precious metal than were paid back to the person who sold the metal to a mint. The government retained the difference. It used some of these additional monetary units in coins to cover the mints' expenses (brassage), and it used whatever was left to finance some of its own spending (seigniorage). In what follows, I am going to ignore brassage, treating the whole difference as seigniorage.
The fact that the mint price was slightly lower than the mint equivalent meant that in normal times, when the new coins being minted had the same contents as the coins currently in circulation, a person who brought a quantity of silver to a mint received new fewer coins than the number of existing coins, of the same type, that contained that quantity of silver. So it would not have made sense for people to bring existing coins to the mint to be melted down and recoined.
But it might have made sense for some people to bring silver bullion or plate to the mint. The fact that coins were more convenient than raw silver, as money, meant that the silver price of goods was actually slightly higher, if raw silver was used, than if coins were used. If the difference between these two prices was large enough to offset the loss of silver from seigniorage, people might gain a bit of purchasing power by bringing bullion or plate to the mint. In what follows, however, I am going to ignore the "normal" difference between the mint equivalent and the mint price, in order to keep my example fairly simple.
Next, suppose the English government gets involved in a war and needs a large amount of revenue in a hurry. It increases the mint price of silver to six shillings per ounce, so that a person who brings one ounce of silver to a mint can now buy six shillings in new coins. The increase in the mint price also means that a person who brings silver to a mint can increase its value, in monetary units, by doing so. For example if, he melts down an old crown and takes the ounce of silver to the mint, he can get a new crown plus an extra shilling. This incentive should be enough to attract plenty of silver to the government mints.
At the same time, the government instructs the mint to debase new crown coins, so they only contain 5/8 ounces of silver: 1/8 ounce per shilling. Thus, the new mint equivalent is 8 shillings per ounce. The fact that the new mint equivalent for silver is higher lower than the new mint price of silver indicates that the government will now earn revenue (silver, or coins minted with
silver) by minting new silver coins. In particular, it will earn shillings for each ounce of silver brought to a mint.
Another way of reaching the same conclusion is to note that each time a new shilling is minted, the government gets 1/6 ounce of silver (because it costs the public an ounce of silver to buy six new shillings from a mint), but it only pays away 1/8 ounce of (the amount of silver in a new shilling). Thus, the government gets an ounce of silver by minting six shillings, paying away 6/8 = 3/4 ounces. So its revenue in silver is 1/4 ounce, which is just enough silver to mint two new shillings.
The seigniorage rate, which is the percentage of each new monetary unit (here, shilling) minted that is earned by the government - or, equivalently, the percentage of each ounce of precious metal (here, silver) brought to a mint that is used to mint coins for the government - can be calculated by the formula,where ME is the mint equivalent and MP is the mint price. In this example, the seigniorage rate is percent.
Again, you could calculate the same rate using the fact that the government earns 1/4 ounce of silver for each ounce brought to a mint.
The debasement rate is the percentage by which the precious metal contents of a coin decrease as a results of debasement. The debasement rate can be calculated by,where represents the new (after-debasement) mint equivalent and represents the original one. In this example, the debasement rate is percent.
If prices of goods (bread) in monetary units (shillings) don't change, the increase in the mint price means that a person can increase his purchasing power, substantially, by taking raw silver to a mint. He will still need one ounce of raw silver to buy 5 loaves of bread, but it only costs 5/6 ounces of silver to buy a new crown (5 shillings) from a mint. He can use that crown to buy the same 5 loaves, and he can use the extra 1/6 ounce of silver to buy another shilling from a mint.
Suppose people respond to this incentive by bringing 12 million ounces (one million Troy pounds, by weight) of silver to a mint. The government pays them 72 million shillings, which is £3.6 million, in newly minted crowns (14.4 million crowns). But it mints 96 million shillings, which is £4.8 million or 19.2 million crowns. So its seigniorage revenue is 24 million shillings: £1.2 million, or 4.8 million crowns. If prices have not changed, the government can use those 4.8 million crowns to buy 24 million loaves of bread, which it can use to feed its army. After it completes this operation, it returns the mint price to its original level, eliminating the extra incentive to bring silver to the mint.
Can it be true, however, that prices don't rise? After all, the new coins have substantially less silver in them. If the purchasing power of a new coin depended entirely on its silver contents, which seems to have been true when coins were privately minted, it would now take 1.6 (8/5) shillings to buy a loaf of bread, because , and a loaf of bread still costs 1/5 ounce of raw silver. Since the original price was 1 shilling per loaf, this is a 60 percent increase.
If people expected a price increase of this magnitude to happen immediately, then they wouldn't bring silver to the mint. We have seen that 1/5 ounce of raw silver will still buy a loaf of bread, so that one ounce of raw silver will buy 5 loaves. But that same ounce of silver will only buy 6 new shillings at the mint, and those shillings would only buy (3¾) loaves of bread.
Historically, however, governments usually found that people did bring large quantities of precious metal to the mint after the mint price was increased substantially. So they must not have expected prices to rise by anything like the full percentage implied by the debasement - at least, not immediately.
Governments also found that legal tender coins with the same denomination often circulated one-for-one, even if they contained different amounts of precious metal. (This is called circulation by tale.) In this example, new crowns containing 5/8 ounce of silver might trade, one-for-one, with old crowns coins containing a full ounce. And each type of coin could be used to purchase
the same amount of bread. The main alternative to circulation by tale is circulation by weight. If coins circulate by weight then their purchasing power depends on the purchasing power of their precious-metal contents, so that two coins with the same denomination, but containing different amount of precious metal, would have different values. In our example, the purchasing power of new crowns would be only 5/8ths as large as the purchasing power of old crowns.
(Money is said to be in circulation if it is being stored for use in payment in the near future. Coins and currency in people's pockets or wallets are in circulation, for example. Coins and currency being saved for long-term purposes are not considered to be in circulation; this includes coins or currency being stored as relatively long-term assets - in a chests or safes, for example - or coins or currency in the vaults of banks.)
Since the old crown coins could be melted down for one ounce of silver, which could be used to buy 5 loaves of bread, the price of bread, in these coins, could not rise above 5 loaves. Thus, if new crowns circulated with old crowns by tale, so that a new crown had the same purchasing power as an old one, the price of bread in new crowns would have to remain five shillings per loaf.
On the other hand, a basic principle of monetary theory is that, other things equal, the price level tends to rise if the quantity of money in circulation increases, and it rises by a percentage equal to the percentage increase in the quantity. We can call this the basic principle of the quantity theory of money. And it seems as though the quantity of money in circulation must have increased, in this case. The government has minted some new coins out of non-monetary silver.
And even though some new coins may have been minted using the silver from old coins, this also seems to increase the quantity of money in circulation, on net: the ounce of silver in an old crown is minted into new crowns.
In practice, however, whether prices rose, in a situation like this, may have depended on the relationship between the monetary value of the new coins minted and the monetary value of the old coins that were circulating, initially. The reason for this is that, in the case where the trade value of the silver in the old coins is equal to the monetary value of these coins, if prices of goods in these coins rise, even slightly, then people have an incentive to do one of two things with these coins:
(1) melt them down and trade the silver in them for goods, rather than using them as money, or (2) save them, rather than spending them, with the idea of melting them down later. In either case, they disappear from circulation. As long as this is happening, increases in the quantity of new coins don't increase the quantity of coins in circulation, so they don't cause prices to rise, except marginally.
If the monetary value of the new coins minted is larger than the initial quantity of old coins in circulation, however, then the quantity of coins in circulation must increase, even if all the old coins are withdrawn from circulation. At that point, prices will begin to rise, in proportion to the amount by which the quantity of coins in circulation increases.
Often, a government would begin by minting a relatively moderate amount of new, debased coins. In this case, prices might not rise, since new coins could simply replace old ones, which were melted down or saved, and the total quantity of money in circulation might not increase. Almost inevitably, however, it eventually minted more than enough new coins - including the new coins it kept for itself - to replace all the old coins. (Governments almost always underestimate the cost of wars: think of the wars in Iraq and Afghanistan.) So, sooner or later, prices began to rise.
To extend our example, suppose the initial money supply - the initial quantity of money in circulation, measured in national monetary units - was £7.5 million. This money consists of coins that contain a total of million ounces of silver. To keep things simple, we'll imagine that all the coins, old and new, were crowns (5 shillings). So there were 30 million old crowns in circulation. As we have seen, the government minted 19.2 million new crowns after it increased the mint price: it paid 14.4 million of these to people who brought silver to the mint, and it kept 4.8 million crowns as its seigniorage.
Since the monetary value of the new coins minted is smaller than the value of the old coins in circulation, prices will not rise, and there will still be 30 million crowns in circulation. Of these, 19.2 million will be new ones and million will be old. Also, 10.8 million old crowns that were formerly in circulation will have been melted down or saved.
Suppose, however, that the government finds that the war has been much more expensive than it thought. A year later, it increases the mint price to 6 shillings per ounce of silver, again, and it mints another 19.2 million crowns, keeping another 4.8 million for itself. Since there are only 10.8 million old crowns in circulation, the total quantity of coins in circulation has to rise by million coins, an increase of 28 percent. So prices eventually rise by 28 percent, also: from one shilling per loaf of bread to shillings (a bit more than 1s. 3¼ d.) per loaf.
If the government continues to rely on seigniorage for revenue, it will eventually create a situation where prices have risen so much that the smaller amount of silver in the new, debased coins will be worth as much, in trade, as the coins themselves are worth as money. (In our example, after money prices have increased by 60 percent, a new crown can only buy 5/8 loaves of bread, the same amount of bread you can buy with 5/8 ounces of silver.) Now, if the government wants to earn seigniorage again, it will have to choose a higher mint price and
debase the coins even further. Prices will stop rising, temporarily, until all the new coins have been replaced by newer coins with lower precious-metal contents.
Historically, repeated reliance on seigniorage, as a revenue source, was the first cause of inflation: a monetary phenomenon that has caused economic problems for countries for hundreds of years. It was also the cause of the tendency for coins to become more and more debased over time.
Another problem caused by seigniorage resulted from the fact that some of the old coins that were withdrawn from circulation would eventually reappear. After prices increased, the trade value of the silver in an old coin would be higher than the purchasing power of a new coin of the same type. People who had saved old coins found that they no longer traded in the market by tale. Instead, an old coin would trade at a premium: that is, at a price, in money units, higher than its denomination (also called its face value).
This price reflected the fact that its silver contents were higher than those of new coins, of the same denomination, now in circulation.[3] In our example, after prices rose by 28 percent, the premium on old coins would be 28 percent: an old silver crown could buy 1.28 new silver crowns, and it could still buy 5 loaves of bread, which was 1.28 times more than the 3.91 loaves (approximately) that a new silver crown could buy.
Once people realized that prices would eventually rise after an increase in the mint price, they had an incentive to hold on to some or all of their old coins, rather than melting them down: eventually, the old coins would be worth substantially more, in transactions, than the new ones.
As a result, after the first price increases occurred, there would be two types of coins in circulation: the new coins that had been shortweighted or debased, and old coins trading at a premium against new coins of the same type. And, after several additional episodes of seigniorage-motivated debasement (or shortweighting), there might be many different types of coins in circulation: coins that had survived several debasements, coins that had survived one or two debasements, and new coins, with all the different types of old coins trading at different premia.
All the coins of a given type might look very similar, regardless of age. But their values might be quite different: some relatively high, some relatively low, depending on their gold or silver content. Again, the difficulty of determining how much a coin was worth reduced the efficiency of the payments system.
[1] The pound is still the basic British monetary unit, but it is now divided into 100 pence; there are no more shillings, and pence are no long thought of as being divided into four parts.
[2] The abbreviation for pence was "d." partly because "pound" also begins with "p.", and partly because denarius was the Latin word for the Roman weight unit that corresponded to a pence. In France, the monetary unit that corresponded to a pence was the "denier."
[3] Typically, coins had markings that indicated when they were minted: informed people could use these markings to infer the coins' precious-metal contents. Modern U.S. coins are still marked with the year they were minted, even though their value no longer depends on their contents.