Equation of Exchange MV = PQ

By Barbara Ray,2014-12-31 20:51
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Equation of Exchange MV = PQ

Equation of Exchange: MV = PQ

    M = supply of money

    V = velocity of money (number of times a year that a dollar is spent on final G & S.)

    P = price level (average price of each unit of output)

    Q = physical volume of G & S produced.

MV is the amount spent by consumers This is the same as the total C + I + G + Xn

    PQ is the amount received by sellers. This is the same as nominal GDP (current output at

    current prices)

What happens if M changes? When M increases you have to look to see if the economy is in

    full capacity. If it is not then Q increase. If it is then P increases.

One argument about V is that it is determined by peoples willingness to hold money in a non

    interest bearing form. If the interest rates go way up people are willing to hold less money. This

    means that the money they are holding must turn over quicker so V increases.

    Historically we have found that V is actually pretty stable.

Balance Sheet: a statement of assets and claims summarizing the financial position of

    a firm or bank at some point in time.

A balance sheet must always balance. Every asset is claimed by someone.

    net worth: the claims of the owners against the firms assets

liabilities: claims of the nonowners.

Assets = net worth + liabilities

In the beginning people would not want to carry around large sums of gold. They

    would therefore bring the gold to goldsmiths who would issue them receipts.

    Eventually people found it easier to trade receipts rather than gold. They knew that

    they could get the gold if they wanted to. The receipt was backed by gold.

Soon the goldsmiths saw that more gold was deposited than taken out. They decided

    to issue receipts that was not backed by gold. They did this in the form of loans.

    The fractional reserve system of banking was started. Only a fraction of the receipts were covered with gold.

The goldsmiths created money. Today the same thing occurs. Banks make loans

    based on an amount that the Federal Reserve requires them to keep in reserve.

Bank panics occur when the people want to redeem more gold (money) than the

    goldsmiths (banks) have on hand to redeem. In order to try to stop panics from

    happening the banks are required to hold a certain reserve.

Lets start a bank:

    We start by selling stock so that we can get cash. We will sell $250,000.

The cash we get is an asset. Yet we owe people for that cash. This makes stock a


    Assets Liabilities + Net Worth Cash 250,000 Capital Stock 250,000

We will now build a 220,000 dollar building and buy 20,000 in equipment. These are

    assets. Remember we must balance.

    Assets Liabilities + Net Worth Cash 10,000 Capital Stock 250,000 Property 240,000

    In order to make things easier, we will now ignore the previous transaction. As a bank we will make loans and accept deposits. Lets start by taking in $100,000 in


    Assets Liabilities and Net Worth Cash 350,000 Capital Stock 250,000

     Demand Deposits 100,000

In doing this the makeup of M1 has changed. Currency is down by 100,000 and

    Demand Deposits are up by $100,000. By definition of M1 the money in banks is not included in demand. This avoids double counting of money.

    We now have money in the form of deposits.

    legal reserve (reserve): an amount of funds equal to a specified percentage of its own

deposit liabilities which a member bank must keep on deposit with the Federal

    Reserve Bank in its district or as vault cash.

    reserve ratio: this is the specified percentage of its demand liabilities which the

    commercial bank must keep as reserves.

    Reserve ratio = banks required reserves / banks demand-deposit liabilities.

     EX: 10% = 10,000/100,000

     From here on we will for simplicity reasons assume a rate of 20%. Lets assume that the bank foresees more deposits. They do not want to keep sending

    money so they are going to send not 20,000 but 350,000 up front. (Usually they will

    hold 1 to 2% in their vaults. This vault cash would be considered part of the reserves.)

    Assets Liabilities and Net Worth Cash 0 Capital Stock 250,000 Reserves 350,000 Demand Deposits 100,000

    The amount by which the banks actual reserves exceed its required reserves is called excess reserves.

    actual reserves - required reserves = excess reserves.

     350,000 - 20,000 = 330,000

    **** You must be able to compute all of these numbers. It is the excess reserves that

    allow a bank to create money. ****

    This is called the Fractional Reserve Banking System: A system in which depository institutions hold reserves that are less than the amount of total deposits. The required reserves are not there for the banks to draw on if a run occurs. Instead

    the required reserves are their so that the Fed can control the amount of money the bank lends.

    When the bank puts its reserves in the Fed what does this represent for the Fed? What happens if one of our banks customers writes a 50,000 dollar check? This check

    will go through another bank. This bank will credit the account of the person that our

customer paid.

    The other bank will now send the check to the Fed. The Fed will take this check and

    increase the other banks reserves by 50,000. (Actually, most of this happens

    electronically now but...)

    It will then take 50,000 out of our reserves. The check will then be sent to us. We will

    then take the money out of our customers account (reducing our demand deposit by

    50,000 and reduce our reserves by the 50,000.

    Assume the person does not request any of the loan in cash. If they do it will alter the transaction.

    Assets Liabilities and Net Worth Cash 0 Capital Stock 250,000 Reserves 300,000 Demand Deposits 50,000

*** A check drawn against a bank and deposited in another bank means a loss in both

    reserves and demand deposits. This also works in the opposite. Lets assume we want to make a loan equal to 50,000. We must first look and see if we


     .20 x 50,000 = 10,000.

     Actual - Required = Excess

     300,000 - 10,000 = 290,000

    The bank will loan 50,000 and put it in the customers account.

    Assets Liabilities and Net Worth Cash 0 Capital Stock 250,000 Reserves 300,000 Demand Deposits 100,000

Loans 50,000

**** When the bank loaned the money it has created 50,000 dollars of new

    money. The demand deposits are considered money. ****

Now lets see what happens when the 50,000 is paid by check to someone else. After

    the check clears the Fed our account will look like this.

    Assets Liabilities and Net Worth Cash 0 Capital Stock 250,000 Reserves 250,000 Demand Deposits 50,000 Loans 50,000

Any one bank can only loan an amount equal to the excess reserves. A single

    commercial bank in a multi-bank system can only lend an amount equal to its initial pre-loan excess reserves.

Now lets see what happens when the loan is repaid by check. Assume a lump sum

    payment with no interest.

    Assets Liabilities and Net Worth Cash 0 Capital Stock 250,000 Reserves 250,000 Demand Deposits 0 Loans 0

We now have a situation where money has been destroyed.

If he had paid in cash we would have 50,000 in cash and 50,000 in demand deposits.

    The money has still been destroyed because cash held by banks is not considered


    If banks find their reserves to be low they can borrow from other banks reserves (the Federal funds market). This is temporary situation (overnight) and interest must be

paid equal to the Federal funds rate.

    Multiple-Deposit Expansion

We know that each individual bank can only loan money equal to its excess reserves.

    This means it can only create money equal to its excess reserves.

Yet when we combine all the banks we will see that they can create an amount in

    excess of their combined reserves.

1) assume that the reserve ratio is 20%.

    2) assume each bank exactly meets the reserve ratio. 3) assume all loans are made to one individual and that check is deposited in another


    No money is kept out. It is all left in the bank.

    Start with 100. This money is deposited it in bank A. Bank A loans out .80 or $80. This finds its way in bank B who loans out .80% ($64) and so on.

    Deposit Loans (Money Created)

    100 80

    80 64

    64 51.20

    51.20 40.96

    40.96 32.77

    32.77 26.21

    . .

    . .

    . .

    Total is $500 Total is $400

We find that the initial 80 dollars in reserves produced 400 dollars in new money.

    That is a multiple of 5 (80 X 5)..

    Remember the Keynsian Multiplier: 1/1-MPC. also 1/MPS.

    Money Multiplier (m) = 1/ Required Reserve Ration (R)

    m = 1/R tells us the amount of new money generated by the acquisition of new reserves. (NOT NEW DEPOSITS)

In this case m = 1/.20 = 5

    We can now calculate the Maximum demand-deposit expansion (D)

D = excess reserves (E) x monetary multiplier (m)

D = E x m

5 x 80 = 400 NOT 5x 100.

How much of the initial money will go to required reserves? (.20) How much to

    Excess Reserves? (Required Reserves x multiplier)


    1) Currency Drain: borrower may request part of payment in cash. Currency in

    circulation is outside the banking system and cannot be held by banks as reserves from which to make loans. The greater the amount of cash leakage, the smaller is the

    actual deposit expansion multiplier.

2) Excess reserves: Since depository institutions keep some excess reserves, deposits

    do not increase as much as the could. The greater the excess reserves, the smaller the

    actual deposit expansion multiplier. If a bank does hold money in excess you just add

    the percentage to R. This will get the new multiplier

    Real World Money Multipliers: Because of leakages, actual deposit multipliers are smaller than the maximum possible. The reserve requirement on transactions deposits

    is currently around 10 percent implying a potential deposit expansion multiplier of

    about 10. The actual M1 multiplier is between 2.5 and 3.0. The actual M2 multiplier has ranged from 6.5 in the 1960’s to over 12 in the 1990’s

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