Lecture 3: Money and Inflation

February 9, 2009

In this lecture we analyze the money market. In most of the lecture, I willassume flexible prices and develop the so-called ”classical” theory of money andinflation. However, as I did at the end of the previous lecture, I will touch uponthe case where prices a fixed and introduce the LM curve. We call inflation theoverall increase in CPI over time. In the US, prices rose on average by 2.4%in the 1960s, 7.1% in the 1970s, 5.5% in the 1980s, and 3% in the 1990s. Wecall hyperinflation a very fast increase in the CPI. Given that CPI is a rate atwhich money is exchanged for goods and services, to understand inflation wemust understand money: its supply and demand and the role it plays in theeconomy.

1 What is Money?

1.1 Three main functions

• Store of value: money transfers purchasing power from present to future;if I earn X dollars today, I can hold the money and spend it tomorrow ora day after. Money is an imperfect store of value however because pricesrise over time and therefore the purchasing power of X dollars depreciatesover time. .

• Unit of account: money provides the terms in which prices are quoted andthe yardstick whereby to measure economic transactions.

• Medium of exchange: money is what we use to buy goods and services.The ease with which money is converted into goods is called liquidity.

• Without money, trade requires double coincidence of wants, that is: partyA selling to B must want the good sold by B. An economy without moneyis called barter economy.

1.2 Types of money

• Money that does not have intrinsic value, is called fiat money, because itsvalue relies on the government authority (decree, confidence).

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• Money that takes the form of commodity, for example gold, is called com-modity money. When people use gold or paper that is redeemable for gold,we say that the economy is on gold standard.

• Advantage of bills is that it saves on transaction costs (lighter, avoidsevaluation of gold purity problem) but it requires people’s trust that gov-ernment will redeem the bills for gold at any time....unless there is somuch trust in the government’s and country’s authority that people donot bother to redeem the bills for gold

=⇒ move from gold standards to pure fiat money.

1.3 Money supply

• In an economy that uses commodity money, money supply is quantity ofthat commodity. But in an economy with fiat money, it the governmentthat fixes money supply through how much money it decides to print.

• Monetary policy is delegated to a central bank, here the Federal Reserve.

• The Fed controls money supply through open-market operations, that isthe purchase or sells of government bonds.

1. Fed increases money supply by purchasing government bonds fromthe public with the money it has or prints; this in turn increases theamount of dollars in circulation;

2. Fed reduces money supply by selling government bonds from its ownportfolio. This takes dollars from the public and therefore reducesthe amount of dollars in circulation.

1.4 Composition of the stock of money

• 1. C for Currency (C): that is, the sum of outstanding paper moneyand coins.

2. M1 for Demand deposits: that is, the funds people hold in theirchecking accounts

3. M2: M1 plus mutual funds balances, savings deposits,..

4. M3: M2 plus large time deposits, repurchase agreements,...

2 The quantity theory of money

2.1 Quantity equation as an identity

• Quantity equation:

money × velocity = price× transactions,

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orMV = PT,

where:

1. T is the total number of transactions during a period of time, say ayear.

2. P is the typical price of a transaction=⇒ PT is the total amount of dollars exchanged in a year

3. M is the quantity of money in circulation

4. V is the transaction velocity of money, which measures the rate atwhich money circulates in the economy: number of times a dollarchanged hand during the one year period.

• The above equation is an identity because it is always true by definitionof the four variables.

• This equation is useful because it shows how the change in one variablemust be accompanied by the change in other variables

−→ e,g an increase in money supply at constant velocity, must be ac-companied either by increase in volume of transactions or by increase inprice.

2.2 From transactions to income

• From transactions to income: the volume of transaction T is hard tomeasure, so what we do is replace T by total nominal GDP Y

=⇒ but you already know that the two are not identical, in particularbecause GDP does not include used goods although they are transacted;however, it is reasonable to believe that the two variables are proportional,so that replacing one by the other boils down to redefining velocity

=⇒ in the equation

money × velocity = price× ouput,

orMV = PY,

the variable V is called income velocity of money.

2.3 Money demand for transaction

• What matters for consumers is how much a given quantity of money canbuy, i.e its purchasing power, and thus in turn is measured by

M/P

which we call real money balances.

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• Amoney demand equation is an equation that shows what determines howmuch real balances people want to hold.

• Money demand for transaction only: the simplest possible money demandequation:

(M/P )d = kY.

−→ according to this equation, the only reason people want to hold moneyis for transactions purposes

−→ if we believe in this equation, then the quantity equation tells ussomething about k in equilibrium of the money market:

(M/P )d =M/P

=⇒kY =

Y

V=⇒

k = 1/V

=⇒ the money demand parameter and the velocity of money are two sidesof the same coin.

2.4 Long run equilibrium under the quantity theory ofmoney

• The quantity theory of money is the theory that combines;

1. the assumption of constant velocity of money

2. the assumption of pure transaction money demand

• Long-run equilibrium: in the long run price are flexible and output isdetermined by the supply of capital and labor, thus:

1.Y = Y = F (K,L);

2.MsV = PY ; (1)

=⇒P =

MV

Y=

MsV

Y

=⇒ in particular any increase in money supply will translate intoinflation; the faster the government increases money supply over time,the higher the rate of inflation.−→ figures 4-1 and 4-1

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• Why would governments want to increase money supply?−→ to finance its own purchases (building roads or providing transfers)

−→ the revenue raised through printing of money is called seigniorage,from the French word ”seigneur”, as middle-age lords had the exclusiveright to coin money; today this right belongs to government or the centralbank if it is independent.

−→ in fact, when government prints money to finance expenditures, itincreases money supply and therefore inflation, thereby reducing the valueof money holdings: it thus operates a transfer of real wealth from thepublic to itself, which we call inflation tax.

3 The speculation motive for holding money

3.1 The choice of money versus bonds

• We mentioned the government’s purchase and sale of government bondsas the main instrument of monetary policy. But why would individualswant to hold bonds?

−→ because they pay interest, and the higher the nominal interest ratethe more bonds you want to hold, and therefore the lower your demandfor money (see below the relationship between nominal and real interestrates).

• Why not hold our whole wealth in the form of bonds?

−→ because we need cash for transactions, and to avoid going throughbond sales all the time; therefore the higher the volume of transactionthe higher the demand for money as in the previous transaction theory ofmoney

• Overall, money demand takes the more general form:

(M/P )d = L(i, Y ),

where∂L

∂i< 0,

∂L

∂Y> 0,

and i denotes the nominal interest rate on bonds.

3.2 Nominal versus real interest rate

• If I save one dollars today in government bond or in a savings account atthe bank, between today and tomorrow the purchasing power of my saveddollar will increase by an amount equal to the nominal interest rate on thebond minus the rate of inflation. This rate at which my purchasing powerincreases between today and tomorrow, I called the real interest rate, and

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it is nothing but the rate of interest r that influences investment demand(see previous chapter).

• Thus:r = i− πe,

or equivalentlyi = r + πe.

This latter equation is called the Fisher Equation: it shows that the nom-inal interest rate is decomposed into a real interest rate component (deter-mined in the long run by the goods market equilibrium), and the expectedinflation rate.

• Under the quantity theory of money, the inflation rate is equal to the rateof increase of money supply. Thus in this case, a one percent increasein money supply causes a one percent increase in the inflation rate andtherefore to a one percent increase in the nominal interest rate.

3.3 Equilibrium

• Under the more assumption that money demand depends on both, Y andi, the nominal interest rate is determined, together with P, by the twoequations:

Ms/P = L(i, Y )

andi = r + πe;

or equivalentlyMs/P = L(r + πe, Y ). (2)

Two remarks about this latter equation:

1. First, government bonds in fact yield real return r, whereas moneyearns rate (−πe); thus the opportunity cost of holding money is:

r − (−πe) = r + πe = i;

2. Equation (2) tells a more sophisticated story than (1). The latterequation, i.e the quantity theory of money, simply says that today’smoney supply determines today’s price level. But it does not tellthe whole story because the nominal interest rate does not remainconstant: it depends upon expected inflation which itself dependson growth in money supply. In fact what (2) says is that the pricelevel does not depend only upon today’s money supply, but also uponmoney supply expected in the future.−→ for example, announcement of future increase in money supplycauses people to expect higher inflation, which in turn raises the

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nominal interest rate and therefore reduces the demand for cash bal-ances today. This, in turn leads to an increase in the price level ifmoney supply today has remained invariant. Hence, the expectationof future increases in money supply, raises the price level today

• In the short-run, the price level is fixed and output Y is not fully deter-mined by factor supply. Then, equation (2) must be rewritten as

Ms = PL(i, Y ), (3)

which defines a relationship between Y and i which we call the LM curve.

4 Conclusion: costs and benefits of inflation• Distortion linked to the inflation cost−→ reducing the value of money holdings forces people to go to the cashmachine more often, thereby increasing transaction costs

−→ shoe-leather cost of inflation

• High inflation forces firms to change posted prices more often−→ menu costs of inflation

• Forces people to write more complicated contracts or to avoid long-termcontracts

• Higher risk if inflation is variable and partly unanticipated over time−→ all these costs are of house magnified under hyperinflation

• One potential benefit of inflation:−→ it makes labor markets work a little better, because nominal wagesare very rigid downward (it is very hard to cut nominal wage withoutemployees feeling somewhat humiliated). Then, inflation with moderatewage increase is the only way to reduce the real wage in a situation ofexcess supply of labor.

• Hyperinflation:

1. how it comes about:−→ comes about because government needs to make large spendingwhich it cannot finance through debt because of lack of credibilitynor through tax because it has inadequate tax revenues=⇒ government resorts to seigniorage and the inflation tax=⇒ inflation reduces real tax revenues, thereby forcing governmentto print even more money tomorrow, and this in turn generates in-flationary spiral

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2. solution:−→ reduce government spending and increase tax revenues in orderto reduce money supply credibly and durably.

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