Transcript ECON 102 Tutorial: Week 20

ECON 102 Tutorial: Week 21
Shane Murphy
www.lancaster.ac.uk/postgrad/murphys4/econ15
[email protected]
Today’s Outline
 Week 21 worksheet – Fiscal Policy & Monetary Policy:
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This weeks material is very math-heavy. Make sure you also revise
definitions, diagrams, and explanations from the book/lecture slides.
Some things the worksheet doesn’t cover that I think are of interest:
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Definitions of Fiscal & Monetary Policy
Goals of Fiscal & Monetary Policy
How do Fiscal & Monetary Policy work to meet these goals
Are there particular strenghts & weaknesses of Fiscal & Monetary
Policy?
What affects the effectiveness of Fiscal & Monetary Policy?
If you’re unsure of any solutions here, please read Chapters 25 and
26 in your textbook – they provides detailed explanations and
examples.
 Exam 3 will be available at the end of class today.
Question 1
Problems 1 to 4 use the following equation for the IS curve:
1
𝑌=
𝐴 − (𝑎 + 𝑏)𝑖
1−𝑐
Assume 𝐴 = 1,040, (𝑎 + 𝑏) = 1,000 and 𝑐 = 0.75, and rate of interest is constant at 𝑖 = 0.04.
Find the equilibrium level of Y.
Plug in and solve:
𝑌=
1
1,040 −
1−0.75
1
1,040 − 40
0.25
𝑌=
𝑌 = 4 1,000
𝑌 = 4,000
So, the Equilibrium level of Y is 4,000.
1,000 0.04
Question 2
Problems 1 to 4 use the following equation for the IS curve:
1
𝑌=
𝐴 − (𝑎 + 𝑏)𝑖
1−𝑐
Assume 𝐴 = 1,040, (𝑎 + 𝑏) = 1,000 and 𝑐 = 0.75, and rate of interest is constant at 𝑖 = 0.04.
Find the change in equilibrium output if net exports fall by 40.
First we need to find out what happens if NX decreases by 40? NX isn’t showing up directly in
our IS equation. Does it affect any of the variables in the IS curve equation?
A fall in net exports of 40 reduces 𝐴 by 40. (Remember that 𝐴 = C + I + G − cT + NX.) So
that means that 𝐴 is now 1,000.
Now we can plug in and solve, as we did in Q1:
1
𝑌=
1,000 − 1,000 0.04
1−0.75
𝑌 = 4 960 = 3,840
So, the Equilibrium level of output now is: 3,840. This is lower than Y* = 4,000 from Q1.
So, if Y*>Y what kind of output gap are we looking at? Recessionary or Expansionary?
We have a Recessionary gap of 160, because 𝑌 ∗ − 𝑌 = 4000 − 3840 = 160.
How can we deal with a recessionary gap through fiscal policy in a Keynesian Model?
How Governments Use Discretionary Fiscal Policy
to Stabilize the Economy
In a recessionary gap (Y* > Y),
The gov’t wants to increase PAE, or decrease the
gov’t deficit. To do so, they have two options:
 Increase Gov’t Spending or
 Decrease Net Taxes
In an expansionary gap (Y* < Y),
The gov’t wants to do the opposite:
 Decrease Gov’t Spending or
 Increase Net Taxes
Questions 3 - 6 look at how we do this mathematically.
Question 3
Problems 1 to 4 use the following equation for the IS curve:
1
𝑌=
𝐴 − (𝑎 + 𝑏)𝑖
1−𝑐
Assume 𝐴 = 1,040, (𝑎 + 𝑏) = 1,000 and 𝑐 = 0.75, and rate of interest is constant at 𝑖 = 0.04.
By how much would government have to increase its expenditures to stabilise output if net
exports fall by 40?
We know that autonomous expenditure, 𝐴, is defined as (C + I + G - cT + NX), so in order to
balance a fall of 40 in net exports NX, government spending G would have to increase 𝐴 by
the same amount, 40, to stabilize output.
Question 4
Problems 1 to 4 use the following equation for the IS curve:
1
𝑌=
𝐴 − (𝑎 + 𝑏)𝑖
1−𝑐
Assume 𝐴 = 1,040, (𝑎 + 𝑏) = 1,000 and 𝑐 = 0.75, and rate of interest is constant at 𝑖 = 0.04.
By how much would gov’t have to cut net taxes to stabilise output if net exports fall by 40?
The equation for the IS curve in this example indicates that net taxes are autonomous (and
not automatic). So, changes in net taxes have the same qualitative effect as changes in
government expenditures.
However, a 40-unit cut in net taxes increases PAE by c(40) at each level of Y.
So, to compensate for a loss of 40 in net exports, net taxes will have to be cut by 53.33. (i.e.
40/c, which is 40/0.75.
Question 5
Background info:
Suppose that in a particular economy the consumption function, planned investment and the
demand for money can be described as follows:
Consumption function
𝐶 = 𝐶 + 𝑐 𝑌 − 𝑇 − 𝑎𝑖
Planned investment
IP = 𝐼 − 𝑏𝑖
Demand for money
MD = 𝑘𝑌 − ℎ𝑖
c = 0.8, a = 400, b = 600, k = 0.2, h = 1,000
Total autonomous expenditures are 𝐴 = 1,010
Government expenditure 𝐺 = 500
The money supply 𝑀= 910
The economy is currently in short-run equilibrium with i = 0.05 and Y = 4,800.
Suppose the full employment or natural level of output is Y* = 5,000, implying a recessionary
gap Y* – Y = 200.
----------------------------------------------------------------------------------------------------------------------------Question:
By how much would the government have to increase its expenditure to close the
recessionary gap?
Question 5
By how much would the government have to increase its expenditure to close the
recessionary gap?
As in Q3 and Q4, we know that G affects Y indirectly, through 𝐴.
So, what we want to find is How will Y change (in the IS-LM model) for a change in 𝐴.
If we know what is ∆𝑌 given ∆𝐴, then we can find what ∆𝐴 is if ∆𝑌 = 200.
To find that out, we’ll start with the equation for the Equilibrium Y in the IS-LM model (this
comes from Week 20’s tutorial, from equation (3) in Maths Box 24.3 in Chapter 24):
𝑌=
1
𝑓𝑘+ℎ(1−𝑐)
ℎ𝐴 + 𝑓 𝑀
where f=a+b
Keeping money supply constant, a change in equilibrium income ΔY is related to a change in
autonomous expenditure ΔA as follows:
1
∆𝑌 = 𝑓𝑘+ℎ(1−𝑐) ℎ∆𝐴
We can rearrange to solve for ΔA:
∆𝐴 =
1
ℎ
𝑓𝑘 + ℎ(1 − 𝑐) ∆𝑌
Next, we can use the information given to plug in and solve for ∆𝐴.
where f=a+b
Question 5
We know:
Consumption function
Planned investment
Demand for money
𝐶 = 𝐶 + 𝑐 𝑌 − 𝑇 − 𝑎𝑖
IP = 𝐼 − 𝑏𝑖
MD = 𝑘𝑌 − ℎ𝑖
c = 0.8
a = 400
b = 600
k = 0.2
h = 1,000
f = a+b = 400 + 600 = 1,000
Total autonomous expenditures are 𝐴 = 1,010
Government expenditure 𝐺 = 500
The money supply 𝑀= 910
The economy is currently in short-run equilibrium with i = 0.05 and Y = 4,800.
Y* = 5,000, so the recessionary gap is Y* – Y = 200.
----------------------------------------------------------------------------------------------------------------------------Now, we can plug in the values above into our equation for ∆𝐴:
1
∆𝐴 = ℎ 𝑓𝑘 + ℎ(1 − 𝑐) ∆𝑌
1
∆𝐴 = 1,000 1,000 ∗ 0.2 + 1,000(1 − 0.8) 200
∆𝐴 = 80
So government expenditure would have to be increased by 80 in order to raise 𝐴 by 80,
which will then raise equilibrium income Y by 200 and close the recessionary gap.
Question 6
Using the data in problem 5 how much would government have to cut net taxes to close the
recessionary gap?
We already know that Autonomous expenditure is 𝐴 = C + I + G − cT + NX.
And a decrease in autonomous net taxes T is an increase in autonomous expenditure, which
will increase Y.
How do changes in equilibrium income Y in the IS-LM model depend on changes in A?
That is what we found in Problem 5, but in the case of a change in net taxes, we have to take
into account an additional factor, the coefficient on T, – c.
That means ΔY is related to a change in net taxes ΔT as follows:
1
∆𝑌 = 𝑓𝑘+ℎ(1−𝑐) ℎ(−𝑐)∆𝑇
Now, we want to rearrange to isolate ΔT:
1 1
ℎ
∆𝑇 = − 𝑐
𝑓𝑘 + ℎ(1 − 𝑐) ∆𝑌
The expression in front of ΔY is the same as in Question 5 apart from the factor (-1/c). So the
result in Q5 just needs to be multiplied by (-1/c) i.e. by (-1/0.8).
1
So:
∆𝑇 = − 0.8 80 = −100
The net taxes would have to be cut by 100 in order to raise equilibrium income Y by 200 and
close the recessionary gap.
How Central Banks Use Monetary Policy
to Stabilize the Economy
To get rid of a recessionary gap (Y* > Y),
A central bank will increase the money supply. Doing so will have two
effects:
 Reduce Interest Rates
 Stimulate consumption and investment spending
Conversely, to close an expansionary gap (Y* < Y ), the central bank will
do the opposite – reduce the money supply.
Questions 7-11 look at how this works.
Question 7
The demand for money is MD = 0.2Y  1,000i and the money supply is 𝑀 = 910.
If Y = 5,000 what is the equilibrium rate of interest?
In equilibrium
so
M = MD
M = 0.2Y – 1,000i
We can re-arrange to solve for i:
𝑖=
1
(0.2𝑌
1,000
𝑖=
1
(0.2(5,000)
1,000
− 𝑀)
And insert 5,000 for Y and 910 for M:
𝑖 = 0.09
So the equilibrium interest rate is 0.09 or 9%.
− 910)
Question 8
From Question 7, we know: the demand for money is MD = 0.2Y  1,000i
the money supply is 𝑀 = 910
When Y = 5,000 the equilibrium rate of interest, i = 0.09
Find the change in the rate of interest if Y increased by 100.
From the interest rate equation derived for Q7, we can calculate the interest rate change Δi
associated with a change in income ΔY, assuming money M is constant:
1
∆𝑖 = 1,000 (0.2∆𝑌)
Now, we can plug in 100 for ΔY:
∆𝑖 =
∆𝑖 =
1
(0.2 ∗
1,000
1
(20)
1,000
100)
∆𝑖 = 0.02
So the interest rate would rise by 2 percentage points from 9% to 11%.
Question 9
Draw an IS-LM diagram to show how the equilibrium values of the level of output and the rate
of interest change when the central bank increases the money supply.
When the money supply is increased, the LM curve shifts to the right.
The new equilibrium is given by the intersection of the existing IS curve and the new LM curve
and is characterised by a lower interest rate and a higher output level.
Question 10
Draw a diagram which illustrates money market equilibrium when the economy is in a
liquidity trap situation.
First, let’s define what is a liquidity trap:
An economy is in a liquidity trap if money demand is perfectly elastic with respect to interest
rate changes, i.e. the money demand curve is horizontal.
• Even if the whole money demand is not horizontal it might be for a certain range of
interest rates. For example, the money demand curve could be downward-sloping curve
at higher interest rates, but horizontal at lower interest rates that are close to zero.
• If the money supply curve intersects the money demand curve in the horizontal section
of the money demand curve, the economy is in a liquidity trap.
In this case an increase in the money supply has no effect on the interest rate (the interest
rate does not fall), because the public is willing to hold the additional money supply at the
existing interest rate.
So Monetary policy becomes powerless to lower the interest rate further – and hence
powerless to shift the LM curve (see Figure 26.3) and to increase output. Only an
expansionary fiscal policy can increase the equilibrium output level.
Question 11
Suppose we have the same economy as in Q5:
Consumption
𝐶 = 𝐶 + 0.8 𝑌 − 𝑇 − 400𝑖
Investment
IP = 𝐼 − 600𝑖
Money Demand MD = 0.2𝑌 − 1,000𝑖
𝐴 = 1,010
𝑀 = 910
If potential output is 5,000 by how much would the central bank have to change the money
supply to close the output gap?
The output gap is Y* − Y = 200, so the Central Bank will have to increase the money supply.
1
The IS curve is given by
𝑌 = 1−𝑐 𝐴 − 𝑓𝑖 ,
𝑓 = 𝑎 + 𝑏, 𝑎 = 400 from the consumption fn, 𝑏 = 600 from the investment fn, and c = 400
i.e. the marginal propensity to consume in the consumption function.
We plug in and calculate the equilibrium interest rate i corresponding to this potential output.
1
5000 =
1,010 − 1,000𝑖
1 − 0.8
𝑖 = 0.01
Now we can plug this value for i into the MD function with potential output = 5,000
MS = MD = 0.2*5,000 – 1,000*0.01
MS = 990
So, the Central Bank will have to increase the money supply by 990 – 910 = 80.
Next Class
 Week 22 Worksheet: IS-LM and Aggregate Demand
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Gerry Steele posts materials & slides on Moodle – use these to
help get through the tutorial worksheet.
The worksheet has a link to a spreadsheet you’ll need to use to
answer the last question. I think that all you have to do in the
spreadsheet is change the value of G and write down what
happens as G changes.