The demand for money and the quantity theory – Money (Senior 5 Economics) | Ganzaa

Money

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Senior 5 · Economics

Money

4 lessons

Lesson 3 of 4

The demand for money and the quantity theory

50 min

Why hold money at all?

Money in a wallet or a current account earns little or no interest. A government bond or a fixed deposit would earn more. So why does a moto-taxi rider keep cash for fuel, a family keep a balance on its phone for emergencies, and a firm keep millions in its current account? Keynes's answer is the theory of liquidity preference. Its rival, the older quantity theory, asks what happens to prices when the supply of money changes. Both are needed to understand inflation (Unit 6) and monetary policy (Unit 5).

Definition

Demand for money: the amount of their wealth that people want to hold as money (cash and current deposits) rather than in interest-earning assets such as bonds.

Liquidity preference: Keynes's name for the desire to hold wealth in its most liquid form, money. The rate of interest is the reward for giving up liquidity.

Keynes's three motives for holding money

Motive	Why money is held	Depends mainly on
Transactions motive	To pay for everyday purchases between one payday and the next: food, transport, wages of a firm's workers	Income (rises with income); also the frequency of pay and the use of credit
Precautionary motive	To meet unexpected needs: illness, accidents, a sudden business opportunity	Income, uncertainty, and access to insurance and credit
Speculative motive	To avoid losses on bonds when interest rates are expected to rise, and to be ready to buy bonds cheaply later	The rate of interest (falls as the interest rate rises)

Keynes wrote the total demand for money as $L = L_{1} (Y) + L_{2} (r)$ : the transactions and precautionary demand $L_{1}$ depends on income, and the speculative demand $L_{2}$ on the interest rate.

Why the speculative demand falls as the interest rate rises

The price of a bond moves inversely with the interest rate. A perpetual bond paying a fixed coupon $c$ a year is worth

\text{bond price} = \frac{c}{r}

Worked example 1: bond prices and interest rates

A perpetual bond pays Frw 1,000 a year (illustrative). When the market interest rate is 10%:

\text{price} = \frac{1\,000}{0.10} = 10\,000 \text{ Frw}

If the interest rate rises to 12.5%, the price falls to $\frac{1\,000}{0.125} = 8\,000$ Frw: a holder loses Frw 2,000, which wipes out two years' interest.

Interpretation. When interest rates are low, most people expect them to rise, and so expect bond prices to fall; they prefer to hold money, and speculative demand is high. When rates are high, people expect them to fall and bond prices to rise; they buy bonds, and speculative demand is low.

Equilibrium in the money market and the liquidity trap

The central bank fixes the money supply (the vertical Ms line). The interest rate settles where the demand for money equals the supply. An increase in money supply from Ms1 to Ms2 leaves people holding more money than they want, so they buy bonds; bond prices rise and the interest rate falls.

Definition

Liquidity trap: a situation, at a very low interest rate, in which people will hold any extra money rather than buy bonds, because they expect rates to rise. The demand for money is perfectly elastic, so increases in the money supply (Ms2 to Ms3) cannot push the interest rate lower, and monetary policy cannot stimulate investment.

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The quantity theory of money

The American economist Irving Fisher (1911) started from an identity: the money spent in a year must equal the value of what it buys.

M V = P T

where $M$ is the money supply, $V$ the velocity of circulation (the average number of times each franc is spent in a year), $P$ the general price level, and $T$ the volume of transactions. Economists at Cambridge (Alfred Marshall, A. C. Pigou) wrote a version based on the demand for money, $M = k P Y$ , where $k$ is the fraction of income people wish to hold as money ( $k = \frac{1}{V}$ ) and $Y$ is real output.

The theory adds two assumptions: $V$ is constant in the short run (it depends on slow-changing habits and institutions), and $T$ is constant because the economy is at full employment. Then

P = \frac{MV}{T}

and the price level changes in direct proportion to the money supply: double $M$ , double $P$ , and halve the value of money.

Worked example 2: using MV = PT

In an economy (illustrative) $M =$ Frw 2,000 billion, $V = 5$ and $T = 1\,000$ billion units of transactions.

P = \frac{2\,000 \times 5}{1\,000} = 10

(a) If M rises by 10% to 2,200 with V and T constant: $P = \frac{2\,200 \times 5}{1\,000} = 11$ , a 10% rise in prices.

(b) If M rises to 2,200 but T also rises by 10%, to 1,100: $P = \frac{2\,200 \times 5}{1\,100} = 10$ . Prices do not change: the extra money is matched by extra goods.

In growth rates, approximately: $\%\Delta M + \%\Delta V \approx \%\Delta P + \%\Delta T$ .

Criticisms of the quantity theory

It is a truism. $M V = P T$ is true by definition; it becomes a theory only through its assumptions, and these are open to doubt.
V is not constant. Velocity changes with interest rates, confidence, and new payment methods such as mobile money.
T is not constant. Economies are often below full employment, so extra money can raise output rather than prices.
It ignores the demand for money as a store of value, and the influence of the interest rate, which Keynes stressed.
Causation may run the other way. Rising prices (for example, of imported fuel) can lead banks to lend more and the money supply to grow.
Not all prices rise in proportion: wages, rents and controlled prices adjust slowly, so the effect is uneven.
It explains only demand-side inflation, not inflation caused by rising costs or poor harvests.

The theory remains useful as a long-run guide: sustained money growth far faster than output growth does lead to inflation. Unit 6 tests it on Rwanda's figures.

Warning

Keep the two theories apart. In the quantity theory, more money raises prices. In Keynes's liquidity preference theory, more money lowers the interest rate, which may raise investment and output. An answer that mixes them ("more money lowers prices through interest rates") will lose marks.

Important

Discuss. Mobile money lets people pay instantly and hold less cash. What is likely to happen to the velocity of circulation? According to $M V = P T$ , what does this mean for the money supply a central bank should aim for?

EconplusDal, "Quantity Theory of Money: Fisher Equation" (about 8 minutes). Watch how he states the assumptions about V and T, then compare his criticisms with the list above.

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Practice

Explain Keynes's three motives for holding money and what each depends on.
A perpetual bond pays Frw 600 a year. Calculate its price when the interest rate is 6% and when it is 8%.
Explain why the speculative demand for money is high when interest rates are low.
With a diagram, explain how an increase in the money supply affects the interest rate, and what happens in a liquidity trap.
State Fisher's equation of exchange and define each term.
M = 3,000, V = 4 and T = 1,500. Find P. If M rises to 3,600 and T to 1,600, find the new P and the percentage change in prices.
Explain four criticisms of the quantity theory of money.
"An increase in the money supply always causes inflation." Evaluate this statement.

Show answersHide answers

Transactions (everyday purchases; depends on income); precautionary (unexpected needs; income and uncertainty); speculative (avoiding bond losses; inversely on the interest rate).
At 6%: 600 ÷ 0.06 = Frw 10,000. At 8%: 600 ÷ 0.08 = Frw 7,500.
At low rates people expect rates to rise and bond prices to fall, so holding bonds risks a capital loss; they prefer money. The interest given up by holding money is also small.
More money supply means excess money balances; people buy bonds, bond prices rise and the interest rate falls. In the liquidity trap the demand curve is flat, so extra money is simply held and the rate does not fall.
MV = PT: M money supply, V velocity of circulation, P price level, T volume of transactions.
P = 3,000 × 4 ÷ 1,500 = 8. New P = 3,600 × 4 ÷ 1,600 = 9, a rise of 12.5%.
Any four: it is a truism; V is not constant; T is not constant (no full employment); ignores the store-of-value demand and interest; causation may be reversed; prices do not rise proportionally; ignores cost-push inflation.
For: if V and T are fixed, prices rise in proportion, and in the long run rapid money growth does cause inflation. Against: if output is growing or there are idle resources, extra money can be matched by extra goods; velocity can fall; in a liquidity trap money is hoarded. Conclusion: it depends on output growth, velocity and the state of the economy.

Sources and credits

Theory: J. M. Keynes, The General Theory of Employment, Interest and Money (1936), chapters 13 and 15; Irving Fisher, The Purchasing Power of Money (1911); explained in Ganzaa's own words.
Video: Quantity Theory of Money - Fisher Equation, EconplusDal, embedded from YouTube.

Written by Ganzaa: the text, both diagrams, the table, the worked examples and the practice items. All figures in the examples are illustrative.

1Why hold money at all?

2Keynes's three motives for holding money

Why the speculative demand falls as the interest rate rises

3Equilibrium in the money market and the liquidity trap

4The quantity theory of money

5Criticisms of the quantity theory

Why hold money at all?

Keynes's three motives for holding money

Equilibrium in the money market and the liquidity trap

The quantity theory of money

Criticisms of the quantity theory