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• We all hold money
 either in currency, in our pockets, or as deposits in a bank. In studying the demand for money, we try to discover why people hold money, and what determines the amount of money they hold.
• Our main goal is to find some function that tells us the amount of money people will hold for a known level of income and a known interest rate. You will recall, no doubt, that we need to know this to construct the LM curve.
• Both theory and empirical evidence suggest that an increase in people’s incomes makes them want to hold more money, and that an increase in the interest rate makes them want to hold less.
Money consists of the stock of assets held as cash, checking accounts, and other, closely related assets, not generic wealth or income. There are four different measures of the money supply: M1,
M2, M3, and L. M1 consists of those assets that are the most liquid
 most easily used to pay for goods and services. L consists of those assets that are least liquid, but which can still be converted into a form acceptable to creditors. The components of each measure of money are listed below:
M1
M2 currency, demand deposits, travelers checks, and other checkable deposits
M1 plus shares in money market mutual funds, money market deposit accounts, savings deposits, and small time deposits

M3
L
M2 plus repurchase agreements, Eurodollars, large time deposits, and institutional money market mutual fund holdings
M3 plus savings bonds, bankers acceptances, commercial paper, and short-term
Treasury securities
Money has traditionally been thought to have four functions:
A medium of exchange. Money is used to pay for goods and services, and enables us to avoid the “double coincidence of wants” required in a barter economy.
A store of value. Money retains its value over time; money we receive today can be stuck under our mattresses or placed in our checking account and used to purchase goods and services at a later date.
A unit of account. Prices are quoted in dollars and cents rather than chickens, avocados, or visits to the dentist.
A standard of deferred payment. Money is used in long-term transactions; you might borrow $100 from a friend, for example, and promise to pay him back $105 at a later date.
The most important thing to know about money is that it is whatever people generally accept as a
payment for goods and services. As such, it can take many forms.
Why would we ever choose to hold money instead of some other, interest-bearing asset? Keynes suggested three different motives:
The transactions motive. We wish to avoid having to cash in another asset every time we make a purchase. (Imagine what a nuisance that would be!)
The precautionary motive. “Just in case.” We never know our spending plans exactly; it pays to keep a little extra money around in case the urge for a hot fudge sundae hits at a time when your stockbroker is playing golf and cannot liquidate any of your assets.
The speculative motive. While money doesn’t have a very high return, it is less risky than other assets. Speculative demand for money is actually demand for a safe asset.
An increase in the rate of return on other assets reduces the demand for money, whatever one’s motive for holding it. An increase in the amount of uncertainty we have about our future spending plans increases the people’s demand for money, when that demand is based on the precautionary motive.

We model the demand for real rather than nominal money balances here ( M P rather than M) ; we assume that, because people hold money for its purchasing power, they do not care about their nominal money holdings. For this to hold, people must be free of money illusion
 the belief that changes in nominal wages and prices are meaningful.
Empirical research has settled four key points about money demand:
1) When the real interest rate increases, the demand for real money balances falls.
2) When income increases, money demand also increases.
3) It takes time for money demand to fully adjust to changes in income and the interest rate.
4) If the price level doubles, so will nominal money demand. Real money demand will be unaffected; there is no money illusion.
High inflation can also induce people to hold less money. With sufficiently high rates of inflation, people may not wish to hold financial assets at all, holding food and other goods instead. This phenomenon is known as flight out of money.
The income velocity of money is the number of times the stock of money is turned over, or reused each year to finance all of the purchases that occur. If people purchased $1,000,000 of goods and services in a particular year, and the (nominal) money supply were $1,000,000, for example, the velocity of money would be equal to 1; each dollar would be used an average of one time. If people purchased $1,000,000 of goods and services in a particular year, and the (nominal) money supply were $500,000, the velocity of money would be equal to 2; each dollar would be used an average of two times.
The income velocity of money is defined as:
V 
P  Y
M

Y
M P
The quantity theory of money uses this definition to explain how and why the price level and the money stock are connected:
M
 V  P  Y .
The classical incarnation of this theory assumes that both V and Y are fixed and, based on those assumptions, argues that any change in the money supply will cause a proportional change in the price level.

The Baumol-Tobin formula for the transactions demand for money,
M*  tcY
2i uses some basic intuition and a small bit of math to find a formula for the amount of money people want to hold for the purpose of buying goods and services.
First, notice that a person’s average balance (M) over a given period will be equal to
1 2
the amount of money they spend over that period divided by the number of times (n) they convert their other assets into money (e.g., withdraw cash from their savings account):
M 
Y
2n
Next, observe that the opportunity cost of holding money is equal to the value of the next best opportunity
 the rate of interest (i) paid by other assets. Each transfer is also assumed to cost an amount tc.
The total cost of holding average balances Y 2n , then is:

n  tc

 iY
2n
The best number of transactions is, of course, the one that minimizes this total cost. That number
(n*), it turns out, is given by the following formula:
Plugging this into our original equation M best to hold average money balances n



Y 2n iY
2tc
.
, we find that people will find it optimal, or
M*  tcY
2i
.