# The science of finance/Where does the money come from?
## Money and the multiplication of goods and services

Money is a multiplier of goods and services.
Everyone is encouraged to provide goods services to earn money, and to request goods and services, as soon as we can afford them. In this way, money incentivizes everyone to provide and demand services. This incentive is permanent. Money must be destroyed, or prevented from circulating, to cancel this incentive, because as soon as money is available, people are encouraged to spend it, and therefore to circulate it.
One person's expenses make another person's income, because the goods and services purchased are always sold. So the more people spend money, the more they earn. Money stimulates economic activity by encouraging spending. The income generated by the offer of goods and services leads to demand, and therefore to offer, new goods and services, as if the goods and services already offered could be multiplied, like the multiplication of loaves.
We can measure the multiplication of goods and services by money with its speed of circulation. This speed is the number of times during a given period that a unit of currency was used to purchase a service or a new good.
When we increase the money supply, the money put into circulation encourages people to spend more. This may lead to an increase in activity, prices, or both. If there is available production capacity, producers can increase quantities without increasing prices. In this case the increase in the money supply immediately leads to an increase in activity, because the money created encourages agents to spend more. This revival by demand has a permanent effect. The increase in demand recurs in each period, as long as the money created is not destroyed, or withdrawn from circulation, and prices do not increase, because the money created always provides an incentive to spend more. The increase in prices can cancel out this revival by demand, because the money created is then used to pay more for the same quantities than before.

## Cash

Cash is notes and coins put into circulation by a central bank.
Even when their notes were convertible into gold, central banks created money by printing them, because they printed more notes than their gold reserves.
Central banks put money into circulation when they lend it and when they purchase assets.
When the notes were convertible into gold, they were like debts of the central bank, which it had to repay in gold on demand, as if the notes corresponded to gold deposits. This is why banknotes are counted as liabilities of a central bank.
As long as the notes were convertible into gold, printing more notes than the gold reserves was risky, because central banks could be exposed to massive demands for gold withdrawals that they could not honor. Gold reserves were therefore a constraint which limited monetary creation. The increase in the money supply was held back by the bridle of gold.
Banknotes are no longer convertible into gold. Everything happened as if the central banks had defaulted, as if they had definitively refused to repay their debts. The notes are still counted as their liabilities, but it is a debt that they no longer have to repay.
The abandonment of gold convertibility could have led to the abandonment of bank notes, if the agents had decided that this paper currency no longer had any value and if they had chosen another form of money. But this is not what happened, because there was no other currency capable of replacing the one proposed by the central bank.
When a central bank sells assets, or when loans are repaid to it, it withdraws money from circulation and reduces its assets and liabilities at the same time . This is why it makes sense to count notes as liabilities of the central bank, even if they are not really repayable debts, because a central bank can choose to repay its liabilities.
Proponents of cryptocurrencies claim that they could take the place of centralized currencies. According to them, we could do without central banks and pay for all our transactions in cryptos. But it's a lie. The energy cost of crypto payments is very high. All the energy resources on the entire planet would not be enough to replace currencies with cryptos. Until now we have not found anything better than the central currency and the banking system to produce all the money we need.

## The miracle of bank money

Bank accounts are money lent to banks. Since current accounts are not paid, banks borrow money without paying interest, while individuals must pay interest when they borrow. Banks make money by the interest of lending money that has been lent to them without interest.
One might believe that banks do not create money because they only lend what has been lent to them before: deposits make credits. Banks cannot lend more money than they have been given. But when they grant a new loan, they increase the borrower's current account without reducing the other current accounts: the credits make the deposits. Now the sum of all current accounts is part of the money supply. So this increases with each new bank loan. Every time a bank makes a new loan, an equal amount of money is created.
An individual can only lend money he already has. A bank can lend money it doesn't have, and receive interest for that loan, because it creates the money by lending it.
The money created by a bank loan has a counterpart: the borrower's obligation to repay. When the bank loan is repaid, the currency initially created is ultimately destroyed. We therefore do not have to fear being drowned under a disproportionate flood of new money. If there are more new bank loans than repaid loans, the money supply increases. If, on the other hand, there are fewer new loans than repaid loans, the money supply decreases.
Money creation by banks looks like dishonest privilege, because they create money every time they lend it. But we must rather see this freedom of monetary creation as a blessing. To carry out projects, we generally have to advance money. In the absence of monetary creation, we are limited by the available money supply. Money creation makes it possible to advance money to carry out projects without being limited by the money available at the start. A good banker is on the lookout for companies and good projects that deserve to be financed. Creating money to finance companies and their projects is part of the daily work of banks. This is reality, not a utopia.
If money creation leads to an increase in demand without a parallel increase in supply, it leads to inflation, it increases prices without increasing activity. But if money creation is devoted to good investments, it leads to an increase in production capacities, and producers can then increase quantities without increasing prices. It is therefore possible to create money without causing inflation, provided that the money created is used for truly productive investments.

## The origin of money creation by banks

Money in circulation can exist in several forms: cash C held by individuals or companies other than commercial banks, bank money B and reserves R of commercial banks. Public administrations, except the central bank, are considered companies.
B is the sum of all current accounts of individuals and companies in commercial banks.
R is the sum of bank cash reserves and current accounts of commercial banks at the central bank.
The central bank has no cash, no monetary reserves, because it does not need them. Why keep money in reserve when you can create it whenever you need it?
Cash reserves are similar to a bank account at the central bank, but it is the customers who counts their money, not the central bank.
M1 = C + B is the sum of monetary reserves of individuals and companies, other than commercial banks.
M0 = C + R is central money, the liability of the central bank.
M = C + B + R is the sum of all circulating monetary reserves held by individuals and companies, including commercial banks.
When an individual deposits 100 in cash in the bank, C decreases by 100 while R and B both increase by 100. M is therefore increased by 100. We create money by depositing cash in the bank, because this deposit is counted twice as a reserve, once as the bank's reserve, and a second time as the customer's reserve.
If an individual withdraws 100 in cash from his bank, C increases by 100 while R and B both decrease by 100. M is therefore reduced by 100. We destroy money when we withdraw money in cash, because reserves once present twice are now present only once.
If a bank lends 100 in cash to an individual, C increases by 100 and R decreases by 100. M is therefore not changed. Cash lending leads to monetary creation only if it is deposited in a bank. If a bank loan to an individual of 100 is repaid in cash, R increases by 100 and C decreases by 100. M is therefore not changed.
If a bank lends 100 in bank money to an individual, B increases by 100, and R is unchanged, because the decrease in the lending bank's reserves is offset by the increase in the borrower's bank's reserves. A bank loan to an individual is a creation of money if it is granted in bank money. The lending bank does not create the money it lends, because it is withdrawn from its reserves. The money created is the additional reserve of the borrower's bank.
If a bank loan to an individual of 100 is repaid in bank money, B decreases by 100 and R is not changed, because the increase in the lending bank's reserves is offset by the decrease in the bank's reserves of the borrower. Repaying a bank loan is a destruction of money if it is repaid in bank money. The lending bank does not destroy the repaid money, because it puts it in its reserves. The money destroyed is the decrease in the reserves of the borrower's bank.
If a bank buys in cash an asset from an individual at a price of 100, R decreases by 100 and C increases by 100, so M is not changed.
If a bank buys in bank money an asset from an individual at a price of 100, B increases by 100 and R is not changed, because the decrease in the purchasing bank's reserves is offset by the increase in the bank's reserves from the seller. So money is created every time a bank buys an asset and pays in bank money. The purchasing bank does not create the money with which it buys the asset, because it is withdrawn from its reserves. The money created is the seller's bank's additional reserve.
Banks can increase the money supply by purchasing assets. Why then don't they buy all the assets, since they can collectively create all the money they want to buy them?
Banks have capital requirements. When they create money by purchasing assets, they increase their assets and liabilities at the same time. A company's equity is the value of the company, the difference between its assets and its liabilities. Banks therefore cannot create money by purchasing assets unlimitedly if they meet their capital requirements.
When a bank sells in cash an asset to an individual at a price of 100, R increases by 100 and C decreases by 100, so M is not changed.
When a bank sells in bank money an asset to an individual at a price of 100, B decreases by 100 and R is not changed, because the increase in the selling bank's reserves is offset by the decrease in the bank's reserves of the buyer. So money is destroyed every time a bank sells an asset and is paid in bank money. The bank does not destroy the money it receives because it puts it in its reserves. The money destroyed is the decrease in the reserves of the buyer's bank.
Even the current expenses and revenues of commercial banks are accompanied by monetary creation or destruction, when paid in bank money. Money is created every time a bank pays its expenses in bank money. Money is destroyed every time a bank receives revenue in bank money.
Banks create money every time they spend. If all they have to do is create money to afford everything they want, why don't they spend more? Like all businesses, they have a budgetary obligation. Costs must be offset by revenues. Since the money they create by paying their costs is destroyed when they receive revenues, they cannot increase the money supply unlimitedly by increasing their spending.
If a bank pays a profit of 100 to its shareholders in bank money, B increases by 100 and R is not changed because the decrease in the reserves of the bank paying profits is offset by the increase in the reserves of the banks of the shareholders. M is therefore increased by 100. The bank does not create the money it pays to its shareholders because it is withdrawn from its reserves. The money created is the additional reserve of the shareholders' banks.

## How is money put into circulation?

The central bank puts money into circulation by lending it, buying assets, paying its current expenses and paying its profits to the State or States for the euro zone. It withdraws money from circulation when the loans it has made are repaid, when it sells assets and when it receives interest on its loans.
If the central bank lends 100 to a commercial bank, it credits it to its current account at the central bank. R is increased by 100 and therefore M too. The central bank creates the money it lends by lending it.
If the central bank buys an asset from an individual at a price of 100 in bank money, B and R are both increased by 100, because the reserves of the seller's bank increase. M is therefore increased by 200. When the central bank buys an asset it creates twice as much money as the price of the asset.
The central bank can always create as much money as it wants to lend, to buy assets, to give, or for any other expenditure.
Bank money is created when banks lend, purchase assets, pay expenses, and pay profits in bank money. It is destroyed when bank loans are repaid, when banks sell assets and when they receive income, always in bank money.
Cash is put into circulation at the request of individuals and businesses as soon as they withdraw cash from their bank. The central bank prints all the notes that are requested. The quantity of banknotes in circulation depends on demand from individuals and businesses. In particular, the central bank prints all the notes with which criminals fill suitcases, for their payments and savings.

## The momentum of money

How to inject a billion into an economy? There are two ways to do this:
* If the billion already exists and is immobilized, it is injected by putting it into circulation.
* If the billion does not already exist, it is created by putting it into circulation.
In the first case, the money supply has not changed. Only the velocity of circulation of money changes, because the billion previously immobilized is put into circulation. In the second case, the money supply is increased and the velocity of circulation has not changed. In both cases the effect is the same, because what matters for an economy is not the money supply M or the velocity V of circulation of money taken separately, but their product MV, the momentum of money.
GDP measures the production of wealth within a country during a given period. Nominal GDP is GDP valued at current prices. The velocity V of money circulation is by definition the nominal GDP divided by the money supply M:
V = GDP/M
The momentum of money, MV, is equal to the nominal GDP.

## The paradox of spending restriction

Suppose that on average agents decide to spend less money, because they have less confidence in the future and want more money in their bank account or in cash, for security. The loss of confidence in the future can also lead agents to forgo investment spending, because one must hope to invest in projects that one believes to be profitable. Since the income of some depends on the spending of others, the income of all decreases on average. Spending restriction leads to a reduction in productive activity. Moreover, agents cannot all have more money in reserve, if the money supply is constant, because the latter is the sum of all their reserves. By restricting their spending, they reduce their income and cannot achieve their objective of increasing their reserves. They obtain an effect opposite to the desired effect, an impoverishment instead of an enrichment. This is the paradox of spending restriction. It is generally called the paradox of thrift, but this could be a misleading expression, because investment expenditure can be a kind of careful spending, a good saving, and its increase does not lead to a contraction of productive activity.
When agents restrict their spending, they keep their money longer and therefore cause V to decrease. If M is constant, GDP = MV decreases by the same amount.
The loss of confidence in the future can lead agents to increase their reserves of real wealth, like a squirrel saving for the winter. This increase in savings is at the same time an increase in investment and does not lead to a contraction of activity. But fear of the future can also lead agents to restrict their spending, because they hope in vain to increase their monetary reserves, and it thus causes a contraction of activity.
The paradox of spending restriction shows that the loss of confidence in the future is enough to cause an increase in unemployment. Therefore, an economy can enter a recession for purely psychological reasons.
When money does not circulate, it has no direct effect on purchases, sales, and prices, as if it did not exist, as if it were no longer part of the money supply. But this immobile money still has an economic effect, because it influences the decisions of its owner. Agents generally want to have a minimum of monetary reserves. If their reserves decrease, they want to replenish them and are discouraged from spending. This is why even money that does not circulate can stimulate activity.
If a recession is caused by spending restrictions, in principle it is sufficient to create money to solve the problem. The money created allows agents to increase their reserves as they wish.