Once there are many people, exchange runs into a difficulty: if I have grain and want salt, I must find someone who happens to have salt and happens to want grain. This double coincidence of wants arises not only with goods but also with time: a young person wants to keep today's harvest for old age, but cannot find anyone able to repay him decades later. One thing that everyone accepts solves both difficulties: an exchange only has to match on one side, and saving no longer has to wait for a particular borrower. Money is at heart a record of who has given to others; its value rests on people's belief that the next person will accept it, and on discipline in issuing it.
1. With many people, wants rarely match
There are more households on the island now, and more kinds of produce: some grow grain, some dry salt, some weave cloth, some fish. I have grain and want salt; the salt-maker I meet wants cloth. An exchange can be completed directly only when the other person happens to have what I want and happens to want what I have. The more kinds of goods there are, the smaller the chance that any person one meets is a match. Jevons (1875) called this situation the double coincidence of wants and noted that it seldom occurs.
It should be said that this is a logical derivation, not history. Anthropologists point out that no society has been found that first relied on pure barter and then developed money out of it (Humphrey, 1985; Graeber, 2011); among acquaintances, keeping accounts and extending credit was more common. This is consistent with seeing money as a kind of record: money and bookkeeping were from the start two forms of the same thing.
Today's counterpart. Second-hand goods are rarely swapped directly for other goods, because it is too hard to find someone who needs exactly what the other has. Selling first and then buying uses money to split one exchange into two.
Double coincidence: the more goods, the harder to match
Drag the number of kinds of goods on the island and compare how many people one must meet, on average, to complete one exchange by direct barter and by first exchanging for money.
Barter
Via money
Illustrative: each person has one kind of good and wants another; the chance that a person met at random has what I want is 1 ÷ (number of kinds − 1). Barter also requires that the other person happen to want what I have, so the probabilities multiply. Via money, the sale and the purchase each need to match on one side only, in two steps.
2. One thing that everyone accepts
Suppose there is something that everyone is willing to accept first and then trade for what they really want. An exchange then only has to match on one side: it is enough that the other person has what I want, without also wanting what I have. No one has to designate this thing. The islanders will find that some goods change hands more easily than others: salt keeps well and divides easily, while fish rots within days. Someone who trades grain for salt knows that, even if he cannot use that much salt himself, he can later trade the salt for something else. So more and more people accept salt, and salt changes hands ever more easily. Which good wins out depends both on whether it keeps well, divides easily and is hard to counterfeit, and on whether people believe others will accept it. As long as everyone believes others will take shells, shells can circulate, even though they are of no use in themselves; once people stop believing it, shells are just shells.
Today's counterpart. The more merchants accept a payment method, the more people are willing to use it; the more people use it, the more merchants accept it.
Which good becomes money
Three goods on the island can serve as a medium of exchange. The more people accept a good, the more easily it changes hands, so more people accept it. Switch the initial beliefs and see which becomes money in the end.
Illustrative: in each round, people adjust what they are willing to accept according to the share of others who accept it and how well the good keeps. Shells keep well, divide easily and are hard to counterfeit; salt keeps but can get damp; grain rots.
3. Unit of account: a common yardstick
Money has another use: expressing the value of every good in terms of one thing. Without money, every pair of goods needs its own rate of exchange, and ten goods mean forty-five rates to remember; with money, ten prices are enough. Jevons (1875) summed up the uses of money as four: a medium of exchange, a common measure of value, a standard of deferred payment and a store of value.
Today's counterpart. Price tags, account balances and financial statements can be compared and added up only because they are all denominated in the same currency.
A common yardstick
Drag the number of kinds of goods. Without a unit of account, every pair of goods needs its own rate of exchange; with money, each good needs only one price.
No unit of account
Money as the unit
Without a unit of account, the number of rates is number of kinds × (number of kinds − 1) ÷ 2. With money as the unit, each good has one price, so the number of prices equals the number of kinds of goods (money itself not included).
4. Money is a record
Look at one exchange again: I give grain to the salt-maker, and he gives me a few shells. The shells cannot be eaten; what they record is a fact: I once gave grain to someone, and so I am entitled to take back something of equal value from someone else. Imagine the village keeps a complete ledger recording how much each person has given to others and how much each has taken from others. The salt-maker need only open the ledger and see that I have given more than I have taken, and he will be willing to give me salt. Whatever the ledger can do, shells can do; whatever shells can do, the ledger can do too. The advantage of shells is that they are cheap: no one needs to know every dealing in the village, only how many shells the other person holds.
This is the other side of the reputation for keeping one's word. Reputation is a record of whether a person keeps agreements; money is a record of how much a person has given to others. The cheaper and more reliable the record, the more exchanges can be carried out on the strength of it.
Today's counterpart. Most money today is no longer physical; it is numbers in bank accounts, that is, entries in records.
Money and the ledger: two ways of recording the same thing
Three households take turns giving to the next: the grain farmer gives grain to the salt-maker, the salt-maker gives salt to the weaver, the weaver gives cloth to the grain farmer. Click "Next step" to compare the two ways of recording.
Kocherlakota (1998) showed that where credible commitments cannot be made, any exchange arrangement that money can achieve can also be achieved with a complete ledger; money is a convenient form of record.
5. Across a lifetime: old age for the last generation
Lending requires that the borrower still have income in future, but the youngest generation cannot find anyone younger to lend to. Money can solve this problem. The young sell their harvest to the old for money; when they themselves are old, they use the money to buy grain from the next young generation. No generation has to find a particular borrower; it only has to believe that the next generation will accept money. The same result can also be achieved by an agreement, without money at all: each young generation supports the old of its day, and is in turn supported by the next generation when it grows old.
This is also where the arrangement is weak: it depends entirely on belief. If people think the next generation will not accept money, money is worthless today, and the chain unravels from its last link.
Civilization Simulator, version 4, works this chain out. I begin farming at 20, and the second person is twenty years younger than I am. With lending, the grain I have stored in old age can be lent to the second person while he is farming, and no longer spoils. But when he in turn grows old, there is no one younger on the island, and he must rely on storage that spoils. Adding a third person only pushes the problem back one generation: as long as lives are finite, there is always a generation with no one to lend to. Turn on money, with people believing the next generation will accept it, and even the youngest generation can provide for old age; turn off that belief, and everything falls back to relying on lending and storage alone.
Today's counterpart. A pay-as-you-go pension is the social agreement Samuelson described: those working today pay contributions that fund those retired today.
Civilization Simulator · Chapter 4: two generations and money
I begin farming at 20, and the second person is twenty years younger than I am. Lending can take place only among the living; turn on money and see whether the youngest generation can provide for old age without a particular borrower.
SavingSeedLendingCommitmentMoneyInsurance · Ch. 5
Illustrative model, computed by year: from age 20 to 59 each person harvests 15 portions a year net of seed; after 60 there is no harvest, and each lives to 80. Each person plans over a whole lifetime, with satisfaction measured logarithmically. Stored grain can be lent, and recovered at the agreed rate, only if a younger person is still farming when repayment is due; otherwise it can only be stored, shrinking with spoilage. With money turned on and people believing the next generation will accept it, savings can be turned into money, which does not lose value (assuming stable prices). Borrowers are assumed to produce enough with the grain or seed they borrow to repay principal and interest as agreed.
6. The cost of money: belief and discipline in issuing it
The value of money comes from people's belief that it can be exchanged for goods, and also from its limited quantity. If whoever issues it can add money at will while the island's produce does not grow to match, the same amount of money buys less: prices rise. For those holding money, rising prices are like grain rotting in the store: what they have stored is shrinking. Fisher (1911) described the relation between the quantity of money and prices with the equation of exchange: with the velocity of circulation and the volume of trade unchanged, an increase in the quantity of money raises prices in the same proportion.
Today's counterpart. Inflation erodes the purchasing power of cash; central bank independence and inflation targets both exist to maintain discipline in issuing money.
Discipline in issuing: more money, no more goods
Drag the annual rate at which new money is added and see prices, and the purchasing power of 100 units of cash, over twenty years. The island's produce grows 2% a year.
Price level (year 0 = 100)Purchasing power of 100 units of cash
Illustrative: following Fisher's (1911) equation of exchange and assuming the velocity of money is constant, the annual rate of price increase is roughly the growth rate of money minus the growth rate of produce.
7. What this step leaves open
With money, exchange and saving have become much easier, but several problems remain unsolved:
Harvests are uncertain. Money makes saving more convenient but cannot prevent crop failure; one bad year can still ruin a household.
Maturities do not match. Savers want to be able to withdraw at any time, while those clearing land or planting orchards need to borrow for many years. How are the two to be matched?
The value of money depends on belief and on the issuer. Who ensures discipline in issuing, and who ensures the ledger is not tampered with?
Who sets prices. With a common yardstick in place, prices still have to be determined jointly by the buying and selling of many people.
What this step leaves open
Four problems still unsolved once there is money. Click a problem to see the assumption it hides.
With moneyExchange, accounting and storage
8. Implications for products
Account, payment and cash-management products are all built on the mechanisms of this chapter. Three implications follow. First, the value of payments and accounts comes from the network: the more people accept them, the more useful they are, and in turn the harder they are to replace. Second, money and account balances are at heart records, and the reliability of the record determines its value; keeping records and preventing tampering is the core responsibility of such products. Third, holding money is not without risk: when issuance loses its discipline, cash shrinks like rotting grain. In arranging savings for users, purchasing power must be considered, not just the amount.
Chapter summary: money
Four conclusions, each tied to one mechanism in this chapter.
Medium of exchangeAn exchange only has to match on one side
One thing that everyone accepts frees exchange from the need for a double coincidence.
Unit of accountA common yardstick
Ten goods mean forty-five rates to remember; with money, ten prices are enough.
RecordMoney is a convenient record
It records who has given to others; the more reliable the record, the more exchanges can rest on it.
Belief and disciplineValue rests on belief and discipline in issuing
If people stop believing the next person will accept it, or issuance loses its discipline, money loses value.
References
Fisher, I. (1911). The Purchasing Power of Money. New York: Macmillan.
Graeber, D. (2011). Debt: The First 5,000 Years. Brooklyn: Melville House.
Humphrey, C. (1985). Barter and economic disintegration. Man, 20(1), 48–72.
Jevons, W. S. (1875). Money and the Mechanism of Exchange. London: Henry S. King.
Kiyotaki, N., & Wright, R. (1989). On money as a medium of exchange. Journal of Political Economy, 97(4), 927–954.
Kocherlakota, N. R. (1998). Money is memory. Journal of Economic Theory, 81(2), 232–251.
Menger, C. (1892). On the origin of money (C. A. Foley, Trans.). Economic Journal, 2(6), 239–255.
Samuelson, P. A. (1958). An exact consumption-loan model of interest with or without the social contrivance of money. Journal of Political Economy, 66(6), 467–482.