ECON 100 Tutorial: Week 21
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Question 1(a): MV ≡ PQ.
If M were to rise by 6 percent, Q by 4 percent while
V is unchanged, by what percentage would P
increase?
First, we can normalize everything to 1 so that:
M = V = P = Q = 1 at the beginning.
Then we can re-write the problem: If M = 1.06, Q =
1.04, V = 1, then solve for the % increase in P.
MV = PQ
(1.06)(1) = P(1.04)
P=
1.06
=
1.04
1.01923
So, P has changed by approximately 1.9%.
Question 1(b): MV ≡ PQ.
If V remains constant as Q grows by 2.5 per cent, and
as M grows by 10 percent, by what annual percentage
would prices rise?
This is just like Question 2(a).
First normalize everything to 1, then let’s use MV = PQ
to solve.
P = MV/Q
P = (1.10)(1)/(1.025)
P = 1.07317
So, P grows by approximately 7.3% annually.
Question 1(c): MV ≡ PQ.
If the V remains constant, as M grows at a constant annual compound
rate of 12.2 per cent, and Q grows at a constant annual compound rate
of 10 per cent, in how many years would the price level (P) double?
Again, for simplicity, let’s say M = V = P = Q = 1 initially.
We want to solve for the number of years in which P is doubled. So,
we solve for n:
We start with P = MV/Q
(1.122)n(1)n
Plugging in: P =
(1.10)n
1.122 𝑛
1.10
P=
P = 1.02𝑛
ln P = 𝑛 ln 1.02
ln P
𝑛=
ln 1.02
We’ve got n, so now we want to know what is n when P is doubled in
value. We’ll look at that on the next slide.
Question 1(c): MV ≡ PQ.
From the previous slide, we have:
ln P
𝑛=
ln 1.02
Because we want to know when P doubles, and
we’ve normalized all variables to 1 initially, we can
put 2 in for P and solve for n.
ln 2
𝑛=
ln 1.02
𝑛 = 35
So, it takes 35 years for P to double.
Question 1(d): MV ≡ PQ.
Use the structure MV ≡ PQ to explain demand pull inflation.
Initial equilibrium: MS0 ≡ MD0≡ (P0Q0/V0)
Final equilibrium: MSF ≡ MDF≡ (PFQF/VF)
The Monetarist view is that demand-pull inflation is caused by an increase in
money supply.
So that means: MSF > MS0
As a result:
MDF > MD0 and
PFQF/VF > P0Q0/V0
So at least one of the following are true:
Case 1: QF > Q0
Case 2: VF < V0
Case 3: PF > P0
The expectations-augmented Phillips Curve suggests that in the long run, increase
in inflation is unable to increase output, so QF = Q0
Our model doesn’t have any motivation for a change in money velocity, so VF = V0
Thus Case 3 must be true, PF > P0. This is Demand-pull inflation: an increase in
Money Supply leads to an increase in Prices.
Question 1(d): MV ≡ PQ.
Use the structure MV ≡ PQ to explain demand pull
inflation.
Gerry’s answer is:
In equilibrium: MS ≡ MD ≡ (PQ/V)
If there is a disequilibrium because of excess MS:
MS↑ ≡ (PQ/V) > MD
An excess supply of money (Ms) implies an increased
demand for goods and services which pulls up their
prices (P): MS↑ ≡ (P↑Q/V) > MD
which increases the transactions demand for money,
thereby restoring equilibrium at a higher general level of
prices:
MS↑ ≡ (P↑Q/V) ≡ MD↑
Here are a couple of Past Exam Multiple Choice
Questions that relate to Question 1.
Suppose that national income (measured in
1990 prices) is £1000 billion. Suppose further
that prices have doubled since 1990 and that
the typical unit of money circulates around
the economy 20 times per year.
What is the money supply?
a)
b)
c)
d)
£50 billion
£100 billion
£150 billion
£200 billion
2010 Exam Q36
Suppose that national income (measured in 1990 prices) is
£1000 billion. Suppose further that prices have doubled
since 1990 and that the typical unit of money circulates
around the economy 20 times per year.
What is the money supply?
This is an MV=PQ question; We are asked to solve for M
and we are given P, Q, and V:
Q = 1000
P=2
V = 20
a) £50 billion
So, solving for M:
MV=PQ
M = QP/V
M = 1000*2/20
M = 100
b) £100 billion
c) £150 billion
d) £200 billion
2010 Exam Q36
Fiscal monetarists argue that inflation is a
consequence of excessive growth in:
a) revenue from taxation
b) sovereign debt
c) the money supply
d) national output
2013 Exam Q36
Question 2
Using the identity MV ≡ PQ, given an explanation the following
statement:
‘.. it was clear that the liberalisation of the financial system ... the
increased competition between financial institutions would lead to a
steady increase in the ratio of broad money to GDP. This indeed has
been a consistent feature of the 1980s. There is every sign that the
people are holding the increased amounts of broad money quite
willingly. And so long as this is so its growth is not inflationary’
(Nigel Lawson - UK Chancellor of the Exchequer 1983-89)
Nigel is either saying while M↑, P will not ↑, completely ignoring
MV=PQ. Or he might be saying that if M↑ then he expects to see
V↓, therefore eliminating the need for P↑.
Gerry’s answer:
We know this is in equilibrium:
This is what Nigel is saying:
MS
≡ MD ≡ (PQ/V)
MS↑ ≡ (PQ/V) ≡ MD↑
Question 2
Lawson made that speech in 1986, when Inflation was falling and
GDP was increasing.
Lawson’s idea was that Money Supply can be increased without
worrying about inflation. We can see some of the results of his policy,
in the late 1980’s:
Monetary Policy
today places much
more emphasis on
controlling inflation.
Questions 3 & 4
These questions are about definitions. Gerry
wants to make the point that deflation of
economic activity or deflation of GDP is not the
same as deflation in the value of currency.
I’ll put his answers in the next slides.
Question 3 – Gerry’s answer
Explain the apparent paradox: that a rise in the world price of oil has a
deflationary impact upon economic activity, and causes a rise in price
indices.
Words can have a different meaning in lay conversation than as economics
jargon. For example, ‘inflation’ is generally taken to mean (in lay
conversation) an increase in some price index (say, the RPI). However, if the
RPI rises when commodities in widespread use have become (for whatever
reason) more scarce, this would not constitute (by the jargon of
economics) ‘inflation’. In economics, ‘inflation’ - or, rather, ‘price inflation’ is the persistent tendency of prices to rise in consequence of monetary
profligacy (currency debasement). The impact of monetary expansion is
first to increase and then to reduce (as prices rise) demand. A rise in the
world oil price is neither inflationary nor deflationary per se; though
adjustment would be different within an oil-rich economy (e.g., Saudi
Arabia) as compared to one with no fossil fuel reserves (e.g., Eire).
In general, there are difficulties in matching theoretical concepts (inflation,
unemployment, economic growth, money supply, etc.) and statistical time
series.
Question 4 – Gerry’s answer
If (the definition of) inflation is more complex than a rise
in price indices, how might it be defined?
A definition always requires a context. Even Keynes
accepts the context of the Quantity Theory of Money,
‘as soon as full employment is reached’ (TGT, p. 295)!
The Quantity Theory draws from the most general of
economic propositions: namely, that (unless demand
increases pro rata) the more there is of something, the
less valued it becomes. Thus, whenever the amount of
money held in circulation exceeds the demand to hold
money individuals are likely to increase their
expenditure thereby (with that increased the demand
for goods/services) causing prices to rise
Question 5
With the yield on savings at 3 percent, price inflation at
4 percent and unearned income taxed at 40 percent,
calculate the real rate of return on savings net of
taxation.
This question involves putting together 4 concepts:
Effect of interest rate:
savings + savings income = savings * (1 + % yield)
Effect of tax:
income after tax = income * (1 - tax)
Effect of inflation:
real value of income = value / (1 + inflation)
Rate of return:
(final value/initial value) - 1
Effect of tax:
Question 5
income after tax = income * (1 - tax)
Effect of inflation:
real value of income = value / (1 + inflation)
Effect of interest rate:
savings + savings income = savings * (1 + % yield)
Rate of return:
(final value/initial value) - 1
We combine the above 4 equations to make the following equation to find
total real rate of return, net of taxes:
1 + ( % yield ∗ ( 1 – tax ))
−1
( 1 + inflation )
1 + (0.03 ∗ ( 1 – 0.40 ))
−1
( 1 + 0.04 )
1.018
−1
1.04
0.9788 − 1 = − 0.0212
So in this case, we’re actually losing 2% on our investment!
Note: In Gerry’s solution,
he leaves out the -1
when calculating the rate
of return. So, he gets an
answer of 0.9788.
Obviously if the interest
rate is 3%, the real rate
of return net of taxes
should be lower than 3%.
Question 6
Explain the rationale for the hypothesis of the Liquidity Trap.
In a Recession, the IS Curve can shift back so that it intersects the
LM Curve in the flat portion.
When this happens, if we implement a monetary policy (that shifts
the LM Curve out) it would not be effective in increasing Y.
Question 6
Explain the rationale for the hypothesis of the Liquidity Trap.
Gerry’s answer essentially says the same thing:
If the interest rate is (relatively) low, bond prices are (relatively) high.
This implies two things:
The perceived risk of a capital loss to bond holders is also (relatively) high
The (relatively) low yield is insufficient recompense to run that risk
So money is preferred to bonds
‘a long-term rate of interest of (say) 2 per cent. Leaves more to fear than to hope, and
offers, at the same time, a running yield which is only sufficient to offset a very small
measure of fear’ (Keynes, 1936, p. 202)
With the Keynesian (liquidity preference)
theory, the interest rate is determined by:
a) the asset demand to hold money
b) the speculative demand to hold money
c) expectations relating to future bond prices
d) all of the above
2011 Exam Q37
According to Keynes people demand liquidity or
prefer liquidity because they have three different
motives for holding cash rather than bonds:
1. Transaction Motive
Transaction demand for money refers to the demand to
hold cash balances for day to day transactions.
2. Precautionary Motive
The precautionary motive relates the demand to hold
cash in order to meet certain unforeseen or unexpected
expenses like fire, theft etc.
3. Speculative Motive
The speculative motive relates to the demand for ready
cash in order to take advantage of changes in the
interest rates.
Question 7
With the speculative demand to hold money,
what is the speculation?
That bond prices will fall; that is, that interest
rates will rise.
Question 8
Liquidity preference is alternatively described as the
demand to hold_________as an alternative to interestbearing assets (bonds).
As the price of bonds rises, the interest rate _______. The
reason is that, (1) with a ______ coupon, the percentage
yield on bonds varies _______with their price, and (2)
financial markets are competitive.
Liquidity preference is therefore described as ‘interest
elastic’.
The less interest elastic the liquidity preference function,
the________the LM schedule and the_______the change
in the interest rate with any change in income.
This means that, as income _______ in response to a
fiscal policy boost, _______ private sector investment is
crowded out which implies that the multiplier effect on
income falls.
Liquidity preference is alternatively described as the demand to hold money as an
alternative to interest-bearing assets (bonds).
As the price of bonds rises, the interest rate falls. The reason is that, (1) with a fixed
coupon, the percentage yield on bonds varies inversely with their price, and (2)
financial markets are competitive.
Liquidity preference is therefore described as ‘interest elastic’.
The less interest elastic the liquidity preference function, the steeper the LM
schedule and the bigger the change in the interest rate with any change in income.
This means that, as income rises in response to a fiscal policy boost, more private
sector investment is crowded out which implies that the multiplier effect on income
falls.
Examples of Past Exam Multiple Choice
Questions that relate to last week’s tutorial
The original Phillips curve identified a
robust correlation between:
(a) unemployment and the rate of change of real
wage rates
(b) unemployment and the rate of change of
money wage rates
(c) wage levels and unemployment
(d) wage levels and inflation
2012 Exam Q35
Phillips Curve
• Inflation is
a change in
money
wages
The hypothesis of the expectationsaugmented Phillips curve holds that:
a) employment contracts fully accommodate the
rate of price inflation
b) job-seekers never make systematic errors
c) wage settlements are partially determined by
the expected rate of price inflation
d) reservation wages are determined by
minimum wage legislation
2010 Exam Q32
Expectations Augmented Phillips Curve
the expectations-augmented Phillips curve represented
conventionally as
ΔW/W = f(U) + φ(ΔP/P)e
Where:
ΔW/W = proportionate increase in wages (aka inflation)
P = prices
U = percentage unemployment rate
(ΔP/P)e = expected proportionate increase in prices
f is a coefficient with a negative value
φ is a coefficient with a positive value
According to Friedman’s reinterpretation of the Phillips Curve, if
inflationary expectations rise, the
Phillips curve:
a) shifts down
b) shifts up
c) becomes flatter
d) becomes steeper
2011 Exam Q32
Expectations Augmented Phillips Curve
Initially, unemployment and inflation are
at point A.
Expansionist monetary policy would
increase consumption, shifting to point B
along the Phillips curve
Unemployment is reduced but there is a
trade off; inflation.
After a short period, workers will
associate expansionist policies with
inflation and will push for higher wages.
This will stop the consumption stimulus
and also de-incentivize hiring. Agents will
shift their expectations curves to point C.
A second time around, D will be achieved,
leading more or less rapidly to point E.
This is why, in the long term, inflation has
little effect on unemployment and vice
versa. Expansionist monetary policy will
lead directly to inflation, with no
permanent effect on unemployment.
If job seekers under-estimate the rate of
inflation, the duration of the job-search:
(a) shortens, so that unemployment tends to rise
(b) lengthens, so that unemployment tends to fall
(c) shortens, so that unemployment tends to fall
(d) lengthens, so that unemployment tends to
rise
2012 Exam Q36
If job seekers under-estimate the rate
of inflation: (DP/P) > (DP/P)e
• Then they will over-estimate the value of an offered
wage contract
• And will accept a lower real wage more readily
• And thus will have a shorter period of
unemployment
• And unemployment will fall below the natural rate,
U < Un
If the causation is reversed, when actual inflation is
below the expected rate of inflation, (DP/P) < (DP/P)e
then unemployment will be above the natural
rate: U > Un
Identify the missing word(s): Goodhart’s
Law states ‘that any ____I____ will tend
to collapse once pressure is placed upon
it for control purposes.’
a)
b)
c)
d)
monetary target
observed statistical regularity
fiscal budgetary stance
structured investment
2010 Exam Q35
Goodhart’s Law
“Any observed statistical regularity will tend to
collapse once pressure is placed upon it for
control purposes.”
… an expansion of aggregate demand was expected to (increase
inflation and to) lower unemployment … but when the authorities
attempted to achieve this, the inflation -unemployment regularity
collapsed …
Have a Nice Break!
Don’t forget to study and work on your maths!
There will be a worksheet on Moodle for week 22.