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### ECON 100 Tutorial: Week 21

www.lancaster.ac.uk/postgrad/murphys4/

NEW office hours: 2:00PM to 3:00PM tuesdays LUMS C85

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 = = 1.01923

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

Plugging in: P =

P =

P = 1.02

= 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:

=

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.

=

= 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?

- £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?

- £50 billion
- £100 billion
- £150 billion
- £200 billion

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

So, solving for M:

MV=PQ

M = QP/V

M = 1000*2/20

M = 100

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 identityMV ≡ 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: Ms ≡ Md≡ (PQ/V)

This is what Nigel is saying: 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 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

Question 5

Effect of tax:

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

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

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)

Explain the rationale for the hypothesis of the Liquidity Trap.

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

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 (a madlib)

Liquidity preference is alternatively described as the demand to hold_________asan alternative to interest-bearing 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________theLM schedule and the_______thechange 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 _____.

Question 8 (a madlib)

Liquidity preference is alternatively described as the demand to hold_________asan alternative to interest-bearing 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________theLM schedule and the_______thechange 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 _____.

Question 8 (a madlib)

Liquidity preference is alternatively described as the demand to hold_________asan alternative to interest-bearing 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________theLM schedule and the_______thechange 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 ____.

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 expectations-augmented Phillips curve holds that:

- employment contracts fully accommodate the rate of price inflation
- job-seekers never make systematic errors
- wage settlements are partially determined by the expected rate of price inflation
- reservation wages are determined by minimum wage legislation

2010 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, agents 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.

According to Friedman’s re-interpretation 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, agents 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.

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

If the causation is reversed, when actual inflation is below the expected rate of inflation, (DP/P) <(DP/P)ethen 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.’

- 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 …

Identify the missing word(s): Goodhart’s Law states ‘that any ____I____ will tend to collapse once pressure is placed upon it for control ____II____.’

- monetary target; lion
- observed statistical regularity; purposes
- fiscal budgetary stance; crow
- structured investment; pourposes

2010 Exam Q35

Have a Nice Break!

Don’t forget to study and work on your maths! There will be a worksheet on Moodle for week 22.

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