The Multiplier, Growth and Money and Banking: Question 9

Worked solution

Part (a): Money value of transactions in Year 1

The quantity theory of money states $MV = PT$, where $PT$ is the total money value of transactions in the economy. Substituting Year 1’s values:

$PT = M \times V = 800 \times 5 = 4{,}000$

So the money value of transactions in Year 1 is $\boxed{4{,}000}$, i.e. $4,000 million.

Part (b): The new value of PT and the percentage change in P

The money supply rises by 10%, so the new money supply is:

$M' = 800 \times 1.10 = 880$

With velocity unchanged at $V=5$:

$PT' = M' \times V = 880 \times 5 = 4{,}400$

Since $T$ (real output/transactions) is assumed unchanged, any change in $PT$ must be entirely a change in $P$. The percentage change in $PT$ (and so in $P$) is:

$\frac{4{,}400 - 4{,}000}{4{,}000} \times 100 = \frac{400}{4{,}000} \times 100 = 10\%$

So the price level $P$ rises by 10%, exactly matching the 10% rise in the money supply.

Part (c): Why the strict quantity theory predicts proportional inflation

The strict quantity theory of money rests on two key assumptions: the velocity of circulation $V$ is constant (households’ and firms’ payment habits do not change), and the real volume of transactions $T$ is fixed by the economy’s real productive capacity in the short run (money is “neutral”. Printing more of it does not, by itself, raise real output).

Given $MV = PT$, if $V$ and $T$ are both held constant, then the equation reduces to $M$ and $P$ being directly proportional to each other: $M$ can only rise if the right-hand side, $PT$, rises by the same percentage, and since $T$ is fixed, all of that rise must come through $P$. This is exactly what was shown numerically in (b): a 10% rise in $M$ produced a 10% rise in $P$, with nothing absorbed by $T$. This is the basis of the monetarist claim that “inflation is always and everywhere a monetary phenomenon”, growth in the money supply beyond the growth of real output feeds through directly into inflation.

Part (d): A reason the actual rise in the price level might be smaller

In reality, the assumptions behind the strict quantity theory do not always hold exactly. If the velocity of circulation $V$ falls (for example, because banks choose to hold more of the extra money as reserves, or households and firms hold onto it rather than spending or lending it at the same rate as before) then the right-hand side $PT$ rises by less than the 10% rise in $M$ alone would suggest, so $P$ rises by less than 10%.

(Alternatively, if the economy has spare capacity, an increase in the money supply might stimulate a rise in real output $T$ itself, via lower interest rates encouraging more spending and production, rather than being absorbed entirely by higher prices, again meaning the price level rises by less than the full 10%.)

Final answers

• (a) $PT =$ $4,000 million
• (b) $PT' =$ $4,400 million; price level rises by 10%
• (c) With $V$ and $T$ held constant, $MV=PT$ implies any percentage rise in $M$ must show up entirely as an equal percentage rise in $P$
• (d) A fall in the velocity of circulation (or a rise in real output $T$) would mean the price level rises by less than 10%