Money in circulation: Wikis


Note: Many of our articles have direct quotes from sources you can cite, within the Wikipedia article! This article doesn't yet, but we're working on it! See more info or our list of citable articles.


(Redirected to Money supply article)

From Wikipedia, the free encyclopedia



Financial markets

Bond market
Stock (Equities) Market
Foreign exchange market
Derivatives market
Commodity market
Money market
Spot (cash) Market
OTC market
Real Estate market
Private equity

Market participants

Institutional Investors

Corporate finance

Structured finance
Capital budgeting
Financial risk management
Mergers and Acquisitions
Financial Statements
Credit rating agency
Leveraged buyout
Venture capital

Personal finance

Credit and Debt
Employment contract
Financial planning

Public finance

Government debt
Deficit spending
Warrant (of payment)

Banks and banking

Fractional-reserve banking
Central Bank
List of banks
Money supply

Financial regulation

Finance designations
Accounting scandals


ISO 31000
International Financial Reporting

Economic history

Stock market bubble
Stock market crash
History of private equity

In economics, money supply or money stock, is the total amount of money available in an economy at a particular point in time.[1] There are several ways to define "money", but standard measures usually include currency in circulation and demand deposits.[2][3]

Money supply data are recorded and published, usually by the government or the central bank of the country. Public and private-sector analysts have long monitored changes in money supply because of its possible effects on the price level, inflation and the business cycle.[4]

That relation between money and prices is historically associated with the quantity theory of money. There is strong empirical evidence of a direct relation between long-term price inflation and money-supply growth. These underlie the current reliance on monetary policy as a means of controlling inflation.[5][6] This causal chain is however contentious, with heterodox economists arguing that the money supply is endogenous and that the sources of inflation must be found in the distributional structure of the economy.[7]


Empirical measures

Money is used in final settlement of a debt and as a ready store of value. Its different functions are associated with different empirical measures of the money supply. Since most modern economic systems are regulated by governments through monetary policy, the supply of money is broken down into types of money based on how much of an effect monetary policy can have on each. Narrow measures include those more directly affected by monetary policy, whereas broader measures are less closely related to monetary-policy actions.[6] Each measure can be classified by placing it along a spectrum between narrow and broad monetary aggregates. The different types of money are typically classified as Ms. The number of Ms usually range from M0 (narrowest) to M3 (broadest) but which Ms are actually used depends on the system. The typical layout for each of the Ms is as follows:

  • M0: Notes and coins (currency) in circulation and in bank vaults.[8] In some countries, such as the United Kingdom, M0 includes bank reserves, so M0 is referred to as the monetary base, or narrow money.[9]
  • MB: Equals M0 + reserves which commercial banks hold in their accounts with the central bank (minimum reserves and excess reserves). MB is referred to as the monetary base or total currency.[10] This is the base from which other forms of money (like checking deposits, listed below) are created and is traditionally the most liquid measure of the money supply. [11]
  • M1: M1 includes funds that are readily accessible for spending. M1 consists of: (1) currency outside Federal Reserve Banks, and the vaults of depository institutions; (2) traveler's checks of nonbank issuers; (3) demand deposits; and (4) other checkable deposits (OCDs), which consist primarily of negotiable order of withdrawal (NOW) accounts at depository institutions and credit union share draft accounts. [12] Bank reserves are not included in M1.
  • M2: Equals M1 + savings deposits, time deposits less than $100,000 and money market deposit accounts for individuals. M2 represents money and "close substitutes" for money.[13] M2 is a broader classification of money than M1. Economists use M2 when looking to quantify the amount of money in circulation and trying to explain different economic monetary conditions. M2 is a key economic indicator used to forecast inflation.[14]
  • M3: Equals M2 + large time deposits, institutional money-market funds, short-term repurchase agreements, along with other larger liquid assets.[15] M3 is no longer published or revealed to the public by the US central bank.[16] However, it is estimated by the web site Shadow Government Statistics. [17] It is also estimated on a weekly basis by the web site Now and the Future. [18]
  • MZM: Money with zero maturity. This measure equals M2 plus all money market funds, minus time deposits. It measures the supply of financial assets redeemable at par on demand.

The ratio of a pair of these measures, most often M2/M0, is called an (actual, empirical) money multiplier.


Fractional-reserve banking

The different forms of money in government money supply statistics arise from the practice of fractional-reserve banking. Whenever a bank gives out a loan in a fractional-reserve banking system, a new sum of money is created. This new type of money is what makes up the non-M0 components in the M1-M3 statistics. In short, there are two types of money in a fractional-reserve banking system[19][20]:

  1. central bank money (physical currency, government money)
  2. commercial bank money (money created through loans) - sometimes referred to as private money, or checkbook money[21]

In the money supply statistics, central bank money is M0 while the commercial bank money is divided up into the M1-M3 components. Generally, the types of commercial bank money that tend to be valued at lower amounts are classified in the narrow category of M1 while the types of commercial bank money that tend to exist in larger amounts are categorized in M2 and M3, with M3 having the largest.

Reserves are deposits that banks have received but have not loaned out. In the USA, the Federal Reserve regulates the percentage that banks must keep in their reserves before they can make new loans. This percentage is called the minimum reserve. This means that if a person makes a deposit for $1000.00 and the bank reserve mandated by the FED is 10% then the bank must increase its reserves by $100.00 and is able to loan the remaining $900.00. The maximum amount of money the banking system can legally generate with each dollar of reserves is called the (theoretical) money multiplier, and is calculated as the reciprocal of the minimum reserve. For a reserve of 10% the money multiplier, followed by the infinite geometric series formula, is the reciprocal of 10%, which is 10.


Note: The examples apply when read in sequential order.


  • Laura has ten US $100 bills, representing $1000 in the M0 supply for the United States. (M0 = $1000, M1 = $1000, M2 = $1000)
  • Laura burns one of her $100 bills. The US M0, and her personal net worth, just decreased by $100. (M0 = $900, M1 = $900, M2 = $900)


  • Laura takes the remaining nine bills and deposits them in her checking account at her bank. The bank then calculates its reserve using the minimum reserve percentage given by the Fed and loans the extra money. If the minimum reserve is 10%, this means $90 will remain in the bank's reserve, and the remaining $810 can be used by the bank as lending money. The M1 money supply increased by $810 when the loan was made (assume no further loans); money has been created. (M0 = $900, M1 = $1710, M2 = $1710)
  • Laura writes a check for $400, check number 7771. The total M1 money supply didn't change, it includes the $400 check and the $500 left in her account. (M0 = $900, M1 = $1710, M2 = $1710)
  • Laura's check number 7771 is destroyed in the laundry. M1 and her checking account still have $900 because the check is never cashed. (M0 = $900, M1 = $1710, M2 = $1710)
  • Laura writes check number 7772 for $100 to her friend Alice, and Alice deposits it into her checking account. M0 still has that $900 in it, Alice's $100 and Laura's $800. (M0 = $900, M1 = $1710, M2 = $1710)
  • The bank lends Mandy the $810 that Laura deposited on her bank. Mandy deposits the money in a checking account at another bank. The other bank must keep $81 as a reserve and has $729 available for loans. The M1 money supply is now inflated by $729 (M0 = $900, M1 = $2439, M3 = $2439)
  • Mandy's bank now lends the money to someone else who deposits it on a checking account on another bank, who again stores 10% as reserve and has 90% available for loans. This process repeats itself at the next bank and at the next bank and so on, until practically all of the $900 M0 money is in bank reserves. The money in the reserves now backs up an M1 money supply that is 10 times the M0 money, which equals $9000. (M0 = $900, M1 = $9000, M2 = $9000)


  • Laura writes check number 7774 for $1000 and brings it to the bank to start a Money Market account. M0 goes down by $1000, but M2 stayed the same, because M2 includes the Money Market account, but also everything in M1. (M0 = $4900, M1 = $6710, M2 = $6710)

Foreign Exchange

  • Laura writes check number 7776 for $200 and brings it downtown to a foreign exchange bank teller at Credit Suisse to convert it to British Pounds. On this particular day, the exchange rate is exactly USD $2.00 = GBP £1.00. The bank Credit Suisse takes her $200 check, and gives her two £50 notes (and charges her a dollar for the service fee). Meanwhile, at the Credit Suisse branch office in Hong Kong, a customer named Huang has £100 and wants $200, and the bank does that trade (charging him an extra £.50 for the service fee). US M0 still has the $900, although Huang now has $200 of it. The £50 notes Laura walks off with are part of Britain's M0 money supply that came from Huang.
  • The next day, Credit Suisse finds they have an excess of GB Pounds and a shortage of US Dollars, determined by adding up all the branch offices' supplies. They sell some of their GBP on the open FX market with Deutsche Bank, which has the opposite problem. The exchange rate stays the same.
  • The day after, both Credit Suisse and Deutsche Bank find they have too many GBP and not enough USD, along with other traders. To move their inventories, they have to sell GBP at USD $1.999, that is, 1/10 cent less than $2 per pound, and the exchange rate shifts. None of these banks has the power to increase or decrease the British M0 or the American M0; they are independent systems.

Money supplies around the world

United States

Components of US money supply (currency, M1, M2, and M3) since 1959
Year-on-year change in the components of the US money supply 1960-2007
File:Currency component of the US money supply 1959-2009.gif
Currency component of the U.S. money supply 1959-2009

The Federal Reserve previously published data on three monetary aggregates, but on 10 November 2005 announced that as of 23 March 2006, it would cease publication of M3.[16] Since the Spring of 2006, the Federal Reserve only publishes data on two of these aggregates. The first, M1, is made up of types of money commonly used for payment, basically currency (M0) and checking deposits. The second, M2, includes M1 plus balances that generally are similar to transaction accounts and that, for the most part, can be converted fairly readily to M1 with little or no loss of principal. The M2 measure is thought to be held primarily by households. The third aggregate, M3 is no longer published. Prior to this discontinuation, M3 had included M2 plus certain accounts that are held by entities other than individuals and are issued by banks and thrift institutions to augment M2-type balances in meeting credit demands; it had also included balances in money market mutual funds held by institutional investors. The aggregates have had different roles in monetary policy as their reliability as guides has changed. The following details their principal components[22]:

When the Federal Reserve announced in 2005 that they would cease publishing M3 statistics in March 2006, they explained that M3 did not convey any additional information about economic activity compared to M2, and thus, "has not played a role in the monetary policy process for many years." Therefore, the costs to collect M3 data outweighed the benefits the data provided.[16] Some politicians have spoken out against the Federal Reserve's decision to cease publishing M3 statistics and have urged the U.S. Congress to take steps requiring the Federal Reserve to do so. Congressman Ron Paul claimed that "M3 is the best description of how quickly the Fed is creating new money and credit. Common sense tells us that a government central bank creating new money out of thin air depreciates the value of each dollar in circulation."[23] Some of the data used to calculate M3 are still collected and published on a regular basis.[16] Current alternate sources of M3 data are available from the private sector[24].

As of 4 November 2009 the federal reserve reported that the U.S. dollar monetary base is $1,999,897,000,000. This is an increase of 142% in 2 years.[25] The monetary base is only one component of money supply, however. M2, the broadest measure of money supply, has increased from approximately $7.41 trillion to $8.36 trillion from November 2007 to October 2009, the latest month-data available. This is a 2-year increase in U.S. M2 of approximately 12.9%.[26]

United Kingdom

M4 money supply of the United Kingdom 1984–2007

There are just two official UK measures. M0 is referred to as the "wide monetary base" or "narrow money" and M4 is referred to as "broad money" or simply "the money supply".

  • M0: Cash outside Bank of England + Banks' operational deposits with Bank of England.
  • M4: Cash outside banks (ie. in circulation with the public and non-bank firms) + private-sector retail bank and building society deposits + Private-sector wholesale bank and building society deposits and Certificate of Deposit. [27]

There are several different definitions of money supply to reflect the differing stores of money. Due to the nature of bank deposits, especially time-restricted savings account deposits, the M4 represents the most illiquid measure of money. M0, by contrast, is the most liquid measure of the money supply.

European Union

The Euro money supply from 1998-2007.

The European Central Bank's definition of euro area monetary aggregates[28]:

  • M1: Currency in circulation + overnight deposits
  • M2: M1 + Deposits with an agreed maturity up to 2 years + Deposits redeemable at a period of notice up to 3 months
  • M3: M2 + Repurchase agreements + Money market fund (MMF) shares/units + Debt securities up to 2 years


The money supply of Australia 1984-2007

The Reserve Bank of Australia defines the monetary aggregates as[29]:

  • M1: currency bank + current deposits of the private non-bank sector
  • M3: M1 + all other bank deposits of the private non-bank sector
  • Broad Money: M3 + borrowings from the private sector by NBFIs, less the latter's holdings of currency and bank deposits
  • Money Base: holdings of notes and coins by the private sector plus deposits of banks with the Reserve Bank of Australia (RBA) and other RBA liabilities to the private non-bank sector

New Zealand

New Zealand money supply 1988-2008

The Reserve Bank of New Zealand defines the monetary aggregates as[30]:

  • M1: notes and coins held by the public plus chequeable deposits, minus inter-institutional chequeable deposits, and minus central government deposits
  • M2: M1 + all non-M1 call funding (call funding includes overnight money and funding on terms that can of right be broken without break penalties) minus inter-institutional non-M1 call funding
  • M3: the broadest monetary aggregate. It represents all New Zealand dollar funding of M3 institutions and any Reserve Bank repos with non-M3 institutions. M3 consists of notes & coin held by the public plus NZ dollar funding minus inter-M3 institutional claims and minus central government deposits


Components of the money supply of India 1970-2007

The Reserve Bank of India defines the monetary aggregates as[31]:

  • Reserve Money (M0): Currency in circulation + Bankers’ deposits with the RBI + ‘Other’ deposits with the RBI = Net RBI credit to the Government + RBI credit to the commercial sector + RBI’s claims on banks + RBI’s net foreign assets + Government’s currency liabilities to the public – RBI’s net non-monetary liabilities.
  • M1: Currency with the public + Deposit money of the public (Demand deposits with the banking system + ‘Other’ deposits with the RBI).
  • M2: M1 + Savings deposits with Post office savings banks.
  • M3: M2+ Time deposits with the banking system = Net bank credit to the Government + Bank credit to the commercial sector + Net foreign exchange assets of the banking sector + Government’s currency liabilities to the public – Net non-monetary liabilities of the banking sector (Other than Time Deposits).
  • M4: M3 + All deposits with post office savings banks (excluding National Savings Certificates).


Money supply of japan.gif

The Bank of Japan defines the monetary aggregates as[32]:

  • M1: cash currency in circulation + deposit money
  • M2 + CDs: M1 + quasi-money + CDs
  • M3 + CDs: (M2 + CDs) + deposits of post offices + other savings and deposits with financial institutions + money trusts
  • Broadly-defined liquidity: (M3 + CDs) + money market + pecuniary trusts other than money trusts + investment trusts + bank debentures + commercial paper issued by financial institutions + repurchase agreements and securities lending with cash collateral + government bonds + foreign bonds

Link with inflation

Monetary exchange equation

Money supply is important because it is linked to inflation by the equation of exchange:


  • M is the total dollars in the nation’s money supply
  • V is the number of times per year each dollar is spent
  • P is the average price of all the goods and services sold during the year
  • Q is the quantity of assets, goods and services sold during the year
U.S. M3 money supply as a proportion of gross domestic product.


  • velocity = the number of times per year that money turns over in transactions for goods and services (if it is a number it is always simply nominal GDP / money supply)
  • nominal GDP = real Gross Domestic Product × GDP deflator
  • GDP deflator = measure of inflation.

The quantity of assets goods and service sold during the year could be grossly estimated by GDP back in the 1960s. This is not the case anymore because of the rise of financial transactions relative to real transaction. Money supply may be less than or greater than the demand of money in the economy. If the money supply grows faster than its use, inflation in a class of goods or assets is likely to follow (according to Milton Friedman, "inflation is always and everywhere a monetary phenomenon"). This statement must be qualified slightly, due to changes in velocity. While the monetarists presume that velocity is relatively stable, in fact velocity exhibits variability at business-cycle frequencies, so that the velocity equation is not particularly useful as a short run tool. Moreover, in the US, velocity has grown at an average of slightly more than 1% a year between 1959 and 2005.

Economists have noted that M3 growth may not affect all assets or goods equally. For example, an almost constant rise in M3 in the 1970s, '80s and '90s produced a rise in consumer goods prices "inflation" in the seventies and a rise in the stock market in the '80s and '90s and a rise in home prices after 2001. When home prices went down, the Federal Reserve kept its loose monetary policy and lowered interest rates; the attempt to slow price declines in one asset class, e.g. real estate, may well have caused prices in other asset classes to rise, e.g. commodities.


In terms of percentage changes (to a small approximation, the percentage change in a product, say XY is equal to the sum of the percentage changes %ΔX + %ΔY). So:

%ΔP + %ΔQ = %ΔM + %ΔV

That equation rearranged gives the "basic inflation identity":

%ΔP = %ΔM + %ΔV - %ΔQ

Change in Inflation (%ΔP) is equal to the rate of money growth (%ΔM), plus the change in velocity (%ΔV), minus the rate of output growth (%ΔQ).[33]

Bank reserves at central bank

When a central bank is "easing", it triggers an increase in money supply by purchasing government securities on the open market thus increasing available funds for private banks to loan through fractional-reserve banking (the issue of new money through loans) and thus grows the money supply. When the central bank is "tightening", it slows the process of private bank issue by selling securities on the open market and pulling money (that could be loaned) out of the private banking sector. It reduces or increases the supply of short term government debt, and inversely increases or reduces the supply of lending funds and thereby the ability of private banks to issue new money through debt. Note that while the terms "easing" and "tightening" are commonly used to describe the central bank's stated interest rate policy, a central bank has the ability to influence the money supply in a much more direct fashion, as explained earlier in this paragraph.

The operative notion of easy money is that the central bank creates new bank reserves (in the US known as "federal funds"), which let the banks lend out more money. These loans get spent, and the proceeds get deposited at other banks. Whatever is not required to be held as reserves is then lent out again, and through the "multiplying" effect of the fractional-reserve system, loans and bank deposits go up by many times the initial injection of reserves.

However, in the 1970s the reserve requirements on deposits started to fall with the emergence of money funds, which require no reserves. Then in the early 1990s, reserve requirements were dropped to zero on savings deposits, CDs, and Eurodollar deposit. At present, reserve requirements apply only to "transactions deposits" – essentially checking accounts. The vast majority of funding sources used by private banks to create loans are not limited by bank reserves. Most commercial and industrial loans are financed by issuing large denomination CDs. Money market deposits are largely used to lend to corporations who issue commercial paper. Consumer loans are also made using savings deposits, which are not subject to reserve requirements. These loans can be bunched into securities and sold to somebody else, taking them off of the bank's books.

Some academics argue that the money multiplier does not exit, because this would assume that the money supply is exogenous, i.e. determined by the monetary authorities via open market operations. If we know that the Central Banks usually target the interest rates (policy instrument) then this leads of endogenous money supply (policy outcome).[34]

Neither commercial nor consumer loans are any longer limited by bank reserves. Since 1995 the amount of consumer loans has steadily increased:

Individual Consumer Loans at All Commercial Banks, 1990-2008
Net Free or Borrowed Reserves of Depository Institutions, 1990-2008

In recent years, the irrelevance of open market operations has also been argued by academic economists renowned for their work on the implications of rational expectations, including Robert Lucas, Jr., Thomas Sargent, Neil Wallace, Finn E. Kydland, Edward C. Prescott and Scott Freeman.


The main functions of the central bank are to maintain low inflation, and a low level of unemployment. The U.S. Central bank may attempt to do this by artificially stimulating demand by affecting the nation's money supply via lower (or higher) interest rates. Furthermore, deficit spending on the authorization of the U.S. Government is designed to artificially stimulate aggregate demand for products and services within an economy. Another means of stimulating demand would be changes in both consumption taxes, and personal income taxes. The argument for either, as per the efficiency to which the additional dollars are being utilized, would determine their overall effect on the GDP of a nation, and whether or not a sustainable stimulus is in effect. For example, a dollar given to a tax-payer (tax credit) for purchases of products or services (stimulating monetary velocity), versus a dollar given to an additional construction laborer - infrastructure redevelopment (for example, also stimulating monetary velocity).

The main debate amongst economists in the second half of the twentieth century concerned the central banks ability to predict how much money should be in circulation, given current employment rates, and inflation rates. Some economists like Milton Friedman believed that the central bank would always get it wrong, leading to wider swings in the economy than if it were just left alone.[35] This is why they advocated a non-interventionist approach.

Chairman of the U.S. Federal Reserve, Ben Bernanke, has suggested that over the last 10 to 15 years, many modern central banks have become relatively adept at manipulation of the money supply, leading to a smoother business cycle, with recessions tending to be smaller and less frequent than in earlier decades, a phenomenon he terms "The Great Moderation" [36] However these assumptions may very well prove ill-conceived by the global financial crisis of 2008–2009. History will judge whether or not the now classical thinking of interest, and money supply moderation, have proven effective in preventing recessions, severe or mild. Furthermore, it may be that the functions of the central bank may need to encompass more than the 'jigging' up or down of interest rates in order to influence money supply, in the sense that these tools, although valuable, do not in fact control the very volatility, nor directly the velocity, of money supply in a nation's economy.

See also


  1. ^ Paul M. Johnson. "Money stock:," A Glossary of Political Economy Terms
  2. ^ Alan Deardorff. "Money supply," Deardorff's Glossary of International Economics
  3. ^ Karl Brunner , "money supply," The New Palgrave: A Dictionary of Economics, v. 3, p. 527.
  4. ^ The Money Supply - Federal Reserve Bank of New York
  5. ^ Milton Friedman (1987). “quantity theory of money”, The New Palgrave: A Dictionary of Economics, v. 4, pp. 15-19.
  6. ^ a b "money supply Definition". Retrieved 2008-07-20.  
  7. ^ Lance Taylor: Reconstructing Macroeconomics, 2004
  8. ^
  9. ^
  10. ^
  11. ^ "M0". Investopedia. Retrieved 2008-07-20.  
  12. ^
  13. ^ "M2". Investopedia. Retrieved 2008-07-20.  
  14. ^ "M2 Definition". Retrieved 2008-07-20.  
  15. ^ "M3". Investopedia. Retrieved 2008-07-20.  
  16. ^ a b c d Discontinuance of M3, Federal Reserve, November 10, 2005, revised March 9, 2006.
  17. ^ Estimated M3, John Williams' Shadow Government Statistics:Analysis Behind and Beyond Government Economic Reporting.
  18. ^ Estimated M3, weekly since early 2006 with data back to 1867
  19. ^ Bank for International Settlements - The Role of Central Bank Money in Payment Systems. See page 9, titled, "The coexistence of central and commercial bank monies: multiple issuers, one currency": A quick quote in reference to the 2 different types of money is listed on page 3. It is the first sentence of the document:
    "Contemporary monetary systems are based on the mutually reinforcing roles of central bank money and commercial bank monies."
  20. ^ European Central Bank - Domestic payments in Euroland: commercial and central bank money: One quote from the article referencing the two types of money:
    "At the beginning of the 20th almost the totality of retail payments were made in central bank money. Over time, this monopoly came to be shared with commercial banks, when deposits and their transfer via checks and giros became widely accepted. Banknotes and commercial bank money became fully interchangeable payment media that customers could use according to their needs. While transaction costs in commercial bank money were shrinking, cashless payment instruments became increasingly used, at the expense of banknotes"
  21. ^ Chicago Fed - Our Central Bank:
    the reference is found in the "Money Manager" section:
    "the Fed works to control money at its source by affecting the ability of financial institutions to "create" checkbook money through loans or investments. The control lever that the Fed uses in this process is the "reserves" that banks and thrifts must hold."
  22. ^ ebook: The Federal Reserve - Purposes and Functions:
  23. ^ What the Price of Gold Is Telling Us
  24. ^ See, for example
  25. ^ Federal Reserve Statistics[1]
  26. ^ Federal Reserve Statistics[2]
  27. ^ Explanatory Notes - M4 retrieved August 13 2007
  28. ^ The ECB's definition of euro area monetary aggregates:
  29. ^ RBA: Glossary - Text Only Version
  30. ^ Series description – Monetary and financial statistics
  31. ^ Handbook of Statistics on Indian Economy. See the document at the bottom of the page titled, "Notes on Tables". The link to this pdf document is: The definitions are on the fourth page of the document
  32. ^ click on the link to the exms01.pdf file. They are defined in Appendix 1 which on the 11th page of the pdf.
  33. ^ "Breaking Monetary Policy into Pieces", May 24 2004,
  34. ^ Martijn Boermans & Basil Moore (2009). "Locked-in and Sticky textbooks" [3]
  35. ^ Milton Friedman (1962). Capitalism and Freedom.  
  36. ^ FRB: Speech, Bernanke-The Great Moderation-February 20, 2004

External links



Computer simulations


Got something to say? Make a comment.
Your name
Your email address