1. society
2. work
3. unemployment

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UNIVERSITY OF ESSEX
SPING TERM 2014
DEPARTMENT OF ECONOMICS
EC111 – INRODUCTION TO ECONOMICS
ASSIGNMENT 2
This assignment is to be handed in to Room 5B.209 before 12 noon on Monday 3rd March
2014. You will be receive and electronic receipt. You should not hand in assignments to your
class teacher. Please note that the University has a zero tolerance policy on late submission of
coursework. Any assignment submitted after the deadline will receive a mark of zero (see
Undergraduate Economics Handbook).
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clearly on the front page of your assignment.
This assignment is divided into two sections. Each is worth 50 percent of the marks. Write
your answer in the spaces provided. You should answer all the questions. Use diagrams or
mathematical expressions where appropriate.
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CLASS NUMBER:…………………………………………………………………
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SECTION A (10 questions, 5 marks each)
State whether each statement is true or false giving a brief explanation in the space provided.
Use diagrams where appropriate. Your mark will depend on your explanation e.g. even if the
statement is correct, putting “TRUE” will get no marks unless you justify your answer.
1. Direct tax is a tax paid on consumption goods.
FALSE
Direct tax is a tax levied on incomes, not expenditures. Taxes levied at the point of sale of
good are indirect taxes, such a VAT.
2. An increase in the marginal propensity to save increases the value of the Keynesian
multiplier.
FALSE:
The consumption function is:
(
Saving is:
< 1.
)
; the marginal propensity to save is 1 – b, where 0 < b
The multiplier is derived (in familiar notation, in a closed economy and with a lump sum
direct tax for simplicity) from
. So equilibrium
national income is:
(
)
The multiplier is smaller the larger is (1 – b).
[This is enough but, just to note that it also true in the full IS/LM model where
̅
( )
( )
There are extra terms in the multiplier (and further terms would be included if we take taxes
to depend on national income). But it remains true that and increase in (1 – b) reduces the
value of the multiplier.]
3. If the government increases its expenditure and its (lump sum) direct tax by the same
amount, there will be no increase in national income.
FALSE
In the basic Keynesian model we have:
national income is:
. So
(
)
If direct tax and government spending increased by the same amount:
(
, we have:
)
In this setting the balanced budget multiplier is 1 because the first round effect of the tax
change is smaller than the first round effect of government expenditure. [In an IS/LM setting
the balanced budget multiplier is less than one but still positive].
4. An increase in the interest rate reduces the present value of an investment project by
more the further in the future are the revenues from the investment.
TRUE
The present value of a stream of future income is:
(
)
(
)
(
)
The further in the future the larger is the discount factor. In the example from the lecture the
PV of project A falls by more than that of project B when the interest rate increases because
A is spread over a longer time horizon.
Year 1
Year 2
Project A
(
Project B
PV; r = 0.1
200
PV; r = 0.2
175
200
183
)
5. In an IS/LM economy an increase in the indirect tax rate will reduce investment.
FALSE:
A increase in the indirect tax rate reduces national income for a given interest rate, i.e. it
reduces the multiplier, which means that the IS curve shifts to the left. Where we have (in the
usual notation):
. The IS curve is:
r
LM
IS1
IS2
Y
The leftward shift of the IS curve reduces national income and also the interest rate. As
investment is given by:
, the fall in the interest rate increases investment.
6. If the central bank raises the reserve requirements of the banking system the money
supply will fall.
TRUE:
The money multiplier is (in familiar notation):
(
(
)
)
The derivation of the money multiplier is in the lecture notes—I have skipped it here.
The banking system’s (cash) reserve to deposit ratio is θ. Increasing θ will reduce the money
multiplier. But note that if the banks, for prudential reasons, choose a value of θ that is above
the new reserve requirements than it might not have any effect.
7. An increase in national income, with a constant money supply, will reduce the price
of bonds.
TRUE
An increase in national income shifts the demand for money to the right. If the money supply
is fixed, then people will try to sell bonds in order to hold more money for transactions. The
price of bonds falls and the therefore the interest rate increases (because c/Pb = r) by just en
to induce the public to hold the original amount of bonds.
MS
r
MD2 (Y2)
MD1 (Y1)
M
8. If labour supply and labour demand are equal, there will be job vacancies but no
unemployment. .
FALSE
W/P
E
LS
V= U
(W/P)1
E
LD
L
In a realistic labour market there will always be some unemployment. Turnover means that
there will be both vacancies and unemployment. Vacancies are the distance between labour
demand and the EE curve; unemployment is the distance between labour supply and the EE
curve. At the equilibrium of labour supply and demand vacancies are equal to
unemployment.
9. In the long run there is no trade-off between inflation and unemployment.
TRUE
LRPC
̇
̇ ( )
̇ ( )
̇ ( )
U1
U*
U
The short run Phillips curve is downward sloping. But there is a different SRPC for each
level of expected price inflation. If the unemployment rate was held below U* (e.g. at U1)
wages would rise faster than expected inflation (e.g. at ̇ ( )). Wage inflation feeds through
to prices so that net period expected price inflation will be ̇ ( ). Wage inflation will be
again be higher than expected inflation so the inflation rate will continue to accelerate.
The only unemployment rate that keeps inflation stable is U* which is the Non-Accelerating
Inflation Rate of Unemployment. The long run Philips curve is vertical.
10. If the unemployment rate is higher than the Non Accelerating Inflation Rate of
Unemployment (NAIRU) the price level must be falling.
FALSE
In the familiar notation we have:
Phillips curve: ̇
̇
Markup equation: ̇
̇
(1)
(2)
Expectations formation: ̇
̇
(3)
Substituting (2) and (3) into (1) we have:
̇
̇
The unemployment rate for a constant rate of inflation, ̇
So: ̇
̇
(
̇
, is the NAIRU
)
If unemployment is higher than the NAIRU then the inflation rate will be falling( ̇
̇
), but the price level will not necessarily be falling, e.g. ̇
.
SECTION B (2 questions, 25 marks each)
1. A closed economy with a fixed price level has the following relationships:
Consumption: Y = 50 + 0.8Yd,
Investment: I = 150 – 10r
Government expenditure: G = 250
Direct tax: Td = 0.25Y
Real money demand: MD/P = 0.5Y – 20r
Money Supply MS = 400
Y is national income; Yd is disposable income and r is the interest rate. The price level, P,
is fixed at P = 1.
a) [7 marks] Find equilibrium national income.
The IS curve: Y = C + I + G
Y = 50 + 0.8 (1 – 0.25)Y + 150 – 10 r + 250
Y = 1125 – 25r
The LM curve: MS = MD/P
400/1 = 0.5 Y – 20r
Y = 800 + 40r
Solving for r
1125 – 25r = 800 + 40r; r = 5
Using the IS curve, Y = 1125 – 125 = 1000. (Using the LM curve gives the same result).
b) [6 marks] Now the consumption function shifts down to become: C = 0.8Yd. Suppose
that in order to maintain the original income level government could either increase
government expenditure or cut the tax rate. Find the necessary level of government
spending or tax rate. Which of these policies would be preferred and why?
If income is to be maintained at Y = 1000 then, from the LM curve, the interest rate must stay
at r = 5 as in (a) above
For an expansion of G we have the IS curve:
Y = 0.8(1 – 0.25)Y + 150 – 10 (5) + G
For Y = 1000 we have:
1000 (1 – 0.6) = 100 + G; G = 300
The budget deficit is G – Td = 300 – 0.25(1000) = 50
Alternatively, to calculate the tax rate necessary to keep Y = 1000:
Y = 0.8(1 – td)Y + 150 – 10 (5) + 250
1000(1 – 0.8(1 – td)) = 350;
800td = 150; td = 0.1875
The government might prefer to use tax policy as this can be introduced quickly whereas
large public works take time to plan.
On the other hand the government may be concerned about the deficit:
When government expenditure is used the deficit is: G – Td = 300 – 0.25(1000) = 50
When the tax rate is used the deficit is: G – Td = 250 – 0.1875(1000) = 62.5
Changes in direct tax are less powerful because the first round effect is on income and not
expenditure. Tax must be reduced by more to obtain the same effect on income and thus the
deficit is higher.
c) [6 marks] With the consumption function as in (b) above, in the absence of fiscal
policy, would monetary policy be an effective alternative? By how much should the
money supply be increased?
The IS curve:
Y = 0.8 (1 – 0.25)Y + 150 – 10 r + 250
For Y = 1000 the interest rate must be reduced to zero, which is just possible. This increases
investment from 100 to 150, compensating for the downward shift in consumption.
The LM curve:
MS/P = 0.5 Y – 20r
For r = 0 and Y = 1000 (with P = 1) the money supply must be raised from 400 to 500.
d) [6 marks] Now suppose that wages and prices were perfectly flexible and full
employment national income is Y = 1000. With the money supply at the original
level, MS = 400, what is the effect of the downward shift in the consumption function
on investment and the interest rate? Compare this outcome with (c ) above and
explain.
We now have a classical model in which the economy is always at full employment.
The IS curve: as in (c ) above, for Y = 1000 the interest rate must be r = 0; I = 150 – 10(0) =
150. This is the same as in (c ) above.
The LM curve: for r = 0 and MS = 400 gives P = 0.8. In the classical economy the fall in the
price level raised the real money supply to MS/P = 400/0.8 = 500, the same as in (c ) above.
In the classical model prices adjust and no policy intervention is necessary. The fall in the
price level is equivalent to the same proportionate increase in the money supply.
2. Use economic analysis to answer the following questions with reference to the British
economy in the global financial crisis (GFC) and its aftermath.
a. [5 marks] What caused the GFC and how would you expect it to have affected the
money multiplier during and immediately after the crisis?
The GFC was financial crisis that started in 2007 and became a full crisis with the failure of
the US investment bank Lehman Brothers, in September 2008. The deeper cause was that
banks in the US and elsewhere had bought securities that were repackaged sub-prime
mortgages, on which there were widespread defaults. Banks that held these securities looked
at risk of becoming illiquid and vulnerable to failure. Interbank lending began to dry up and
banks sought to raise their reserve ratios to protect themselves,
One implication follows from the derivation of the money multiplier, given in the lecture
notes as:
(
(
)
)
If the banks raised their reserve to deposit ratio, θ, then the multiplier will fall. (Also if the
public’s ratio of cash to deposits, σ, fell this would also decrease the multiplier.) This means
that for a given amount of high-powered money, H, the money supply, M, would fall.
b. [5 marks] Comment on the Bank of England’s response in the first two years after the
crisis. What is meant by the ‘zero bound’ for interest rates? Does it mean that there is
no further scope for monetary policy to stimulate the economy?
In order to stabilize the financial system the Bank (together with the Treasury) assisted in
rescuing Northern Rock and guaranteed deposits, and then took shares in two major banks,
Lloyds and Royal Bank of Scotland.
The Bank dramatically reduced its base rate from 5.5 percent at the end of 2007 to 0.5
percent by the middle of 2009.
The lower bound for interest rates is zero. If it was negative then the lender would be paying
interest to the borrower. No lender would do this, as it would be more profitable not to lend.
One the base rate had been reduced to zero there was little scope to reduce it further. But the
Bank embarked on Quantitative Easing, a version of what was formerly known as Open
Market Operations. This involved purchasing large amounts of long-term assets principally
government bonds (gilts)--₤200B up to 2010, and £375B up to now.
So there was some further scope and the aim was to increase bond prices and bring down
long term interest rates (or yields) more generally. (The evidence suggests that the effect of
the first round of QE was to reduce the interest rate on bonds by about 1 percentage point
(100 basis points).
c. [5 marks] Using IS/LM analysis show in a diagram what reaching the zero lower
bound for the interest rate implies about the effectiveness of fiscal policy.
r
LM1
IS1
LM2
IS2
Y
Being close to the lower bound means that the LM curve is very flat over that range. A shift
in the LM curve from LM1 to LM2 would reduce the interest rate by very little (e.g. along IS1)
and have little effect on national income. On the other hand fiscal policy would be more
effective. Shifting from IS1 to IS2 has a larger effect on national income. It does not drive up
the interest rate by very much (as the LM curve is flat) and so and increase in government
expenditure does not ‘crowd out’ investment.
d. [5marks] The government’s budget deficit rose substantially during the recession.
How would you identify how much of that increase was due to fiscal stimulus and
how much was due to the recession itself.
The way to do this is to calculate the ‘structural’ or ‘adjusted’ budget deficit. This shows how
much the deficit would have changed if national income was unchanged (or more precisely
for a constant income gap).
G2
G, T
t1 Y
G1
t2 Y
Y2
Y1
Y
In the diagram the budget initially has a deficit of G1 – t1Y1 at income Y1. In the recession the
government increases its expenditure and lowers the tax rate, but the recession still reduces
income to Y2. The deficit increases to G2 – t2Y2. The structural deficit increases by much less:
G2 – t2Y1.This is the part that can be attributed to the change in policy.
e. [5 marks] Most observers believe that the fiscal multiplier is low--less than 2, and
possibly around 1. Examine possible reasons for the low multiplier.
There are a number of reasons why the multiplier is fairly low:
Consider a multiplier in which taxes are related to income and we have an open economy
where imports are also related to income. The expression for the expenditure multiplier
would be:
The multiplier will be lower: (i) the lower is b (the MPC), (ii) the higher are the tax rates (td
and te), and (iii) the higher is the marginal propensity to import. [E.g. for b = 0.6; td = 0.25; te
= 0.2; f = 0.25, the multiplier would be 1.]
Another reason the multiplier may be low is that it is measured for times when fiscal policy
crowds out other components of spending. This could be because (in the IS/LM setting) it
raises interest rates which reduces investment. Or if there is close to full employment there
could be supply constraints that lead to reduced consumption or investment.
Government spending and tax policy may have other, more indirect, effects e,g, on consumer
confidence or business expectations. But it is likely to depend on the exact circumstances
whether such effects would enhance or diminish the impact of a fiscal stimulus.