Download ECON 102 Tutorial: Week 18

ECON 102 Tutorial: Week 18
Shane Murphy
www.lancaster.ac.uk/postgrad/murphys4/econ15
[email protected]
Today’s Outline
 Week 18 worksheet – Capital Markets:
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We’ll try to do some questions on the board today.
Please make sure you review all of problems on your own and
ask if you have any questions.
If you’re unsure of any solutions here, please see Chapter 22 in
your textbook – it provides detailed explanations and examples.
 Some notes about Friday’s Exam.
 If you didn’t get your exam last week, please collect it at
the end of class.
Question 1(a)
Data on before-tax income, taxes paid and consumption spending for the Simpson family in
various years is given below.
Y
T Taxes CConsumption
(Y-T)
Before-tax
Before-tax
Taxespaid
Consumption
Disposable
income (€)
(€) spending
(€)
income
(€)
paid
(€)
spending
(€)
Income
25,000
3,000
20,000
25,000
27,0003,0003,50020,00021,35022,000
27,000
28,0003,5003,70021,35022,07023,500
28,000
30,0003,7004,00022,07023,60024,300
30,000 4,000
23,600
26,000
Graph the Simpsons’ consumption function and find their household’s marginal propensity to
consume.
First, how do we graph a consumption function?
We put Disposable Income (Y-T) on the X-axis, Consumption Spending on the Y-axis.
So, the first thing we can do here is find Disposable Income.
The graph of the consumption function will be a straight line through these points.
We write the consumption function as: 𝐶 = 𝐶 + 𝑐(𝑌 − 𝑇)
where:
𝐶 is the y-intercept; it captures factors other than disposable income that affect C.
𝑐 is the MPC, or the slope of the consumption function.
It is the amount by which consumption rises when disposable income rises.
(𝑌 − 𝑇) is the disposable income.
Question 1(a)
Graph the Simpsons’ consumption function and find their household’s marginal propensity to
consume.
What is the marginal propensity to consume?
Before-tax Taxes Consumption Disposable
income (€) paid (€) spending (€) Income
We know that the MPC is the slope of our
25,000
27,000
28,000
30,000
3,000
3,500
3,700
4,000
20,000
21,350
22,070
23,600
22,000
23,500
24,300
26,000
consumption function, so we can find it by
taking the change in Consumption Spending
divided by the change in Disposable Income.
If disposable income increases from 22,000 to 23,500, a rise of 1500, consumption rises by
1350.
Since 1350/1500 = 0.9, it looks like the MPC is 0.9.
Can we write the Consumption Function out using the 𝐶 = 𝐶 + 𝑐(𝑌 − 𝑇) format?
To do this, we need to find the intercept of the consumption function, 𝐶.
To find 𝐶, we can plug into the equation any of the numerical combinations of consumption
and disposable income given above.
For example, if we set C = 20,000 and Y-T = 22,000,
We get 20,000 = 𝐶 + 0.9(22,000), solving for 𝐶, we get: 𝐶 = 200.
So the consumption function for the Simpson’s is C = 200 + 0.9(𝑌 − 𝑇).
Question 1(b)
How much would you expect the Simpsons to consume if their income was €32,000 and they
paid taxes of €5,000?
.
From the consumption function derived in part (a), we can plug in Y = 32,000 and T = 5,000:
C = 200 + 0.9(𝑌 − 𝑇)
C = 200 + 0.9(32,000 − 5,000)
C = 200 + 0.9 27,000
C = 24,500
Question 1(c)
Homer Simpson wins a lottery prize. As a result, the Simpson family increases its consumption
by €1,000 at each level of after-tax income. (‘Income’ does not include the prize money.) How
does this change affect the graph of their consumption function? How does it affect their
marginal propensity to consume?
.
The graph shifts upward by 1000 at each level of disposable income (the vertical intercept, 𝐶,
rises from 200 to 1200).
The MPC is unaffected, because the increase in consumption is the same at each level of
disposable income, so that the graph makes a parallel upward shift. So, the MPC, or the
slope of the consumption function, does not change.
Question 2
Suppose the economy can be described as follows:
consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600.
Find short-run equilibrium output in this economy.
In the Keynesian Cross, in equilibrium, output ,Y, equals planned aggregate expenditure PAE.
Y = PAE
or
Y = C + I + G + NX
Inserting values into this equation gives
Y = 1,000 + 0.75(Y – 600) + 1,000 + 500 + 0
Solving this equation for Y yields equilibrium output
Y = [1/(1-0.75)]*2,050
Y = 8,200
Question 3
For the economy described in Problem 2, where :
consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600.
And MPC = c = 0.75
Find the values of:
a. The income-expenditure multiplier.
The income expenditure multiplier = 1/(1-c), where c is the MPC.
Inserting the value for c (= 0.75) from Problem 2 gives us 1/(1-0.75) = 4.
b. The tax multiplier
The tax multiplier = –c/(1-c).
Inserting the value for c (=0.75) gives us -0.75/(1-0.75) = -3.
Question 4
For the economy described in Problem 3, where:
consumption function is C = 1,000 + 0.75(Y  T), IP = 1,000, G = 500, NX = 0 and T = 600.
The income-expenditure multiplier = 4 and the tax multiplier = -3.
Find the change in equilibrium output if the government cuts net taxes by 10.
We want to find the change in equilibrium output, ΔY, which result from a change in tax, ΔT.
To do this, we can multiply the tax multiplier times the change in taxes, ΔT.
So
ΔY = [-c/(1-c)]ΔT
In Q3, we calculated the tax multiplier = -c/(1-c) = -3, so we can plug that in here:
ΔY = (-3)*(-10)
ΔY = 30
So a cut in net taxes by 10 will raise equilibrium output by 30.
Question 5
Problems 5 to 8 assume that the economy is described by the following equations:
C = 1,800 + 0.6(Y  T),
IP = 900,
G = 1,500,
NX = 100,
T = 1,500, Y* = 9,000
Find the output gap in this economy.
The output gap is:
The difference between the economy’s potential output and its actual output at a
point in time. We can write this as: Y*-Y.
To find the output Y*-Y we need to calculate short-run equilibrium output Y.
In equilibrium, output Y equals planned aggregate expenditure PAE, so
Y = PAE
Y = C + I + G + NX
Inserting values into this equation gives
Y = 1,800 + 0.6(Y – 1,500) + 900 + 1,500 + 100
Solving this equation for Y yields equilibrium output
Y = [1/(1-0.6)]*3,400 = 8,500
So the output gap = Y*-Y = 9,000 - 8,500 = 500.
Question 6
Problems 5 to 8 assume that the economy is described by the following equations:
C = 1,800 + 0.6(Y  T),
900,
G = 1,500,
NX = 100,
T = 1,500, Y* = 9,000
IP = 800
Find the effect on short-run equilibrium output of a decrease in planned investment from 900
to 800.
So, we do the same thing steps as in Q5. Short-run equilibrium output is reduced to 8,250.
Question 7
Problems 5 to 8 assume that the economy is described by the following equations:
C = 1,800 + 0.6(Y  T),
IP = 900,
G = 1,500,
NX = 100,
T = 1,500, Y* = 9,000
Show the determination of short-run equilibrium output for this economy using the
Keynesian cross diagram.
Determination of Short-Run Equilibrium
Output (Keynesian Cross Diagram)
The line PAE = 3,400 + 0.6Y, referred to as the
‘expenditure line’, shows the relationship of
PAE to output.
The 45° line represents the short-run
equilibrium condition Y = PAE.
Short-run equilibrium output (8,500) is
determined at the intersection of the two
lines, point E.
This type of diagram is known as a ‘Keynesian
cross’.
Question 8
Problems 5 to 8 assume that the economy is described by the following equations:
C = 1,800 + 0.6(Y  T),
IP = 900,
G = 1,500,
= 100,
NXNX
= 950
 0.1Y T = 1,500, Y* = 9,000
If net exports are given by NX = 950  0.1Y find the value for short-run equilibrium output and
the multiplier.
This is just like Example 22.7 in the textbook (pgs. 588-590).
To find the short-run equilibrium output, we can do the same steps as in Q5, setting Y = PAE.
Y = C + I + G + NX
Y = 1,800 + 0.6(Y  1,500) + 900 + 1,500 + 950 - .01(Y)
Y = 0.5(Y) + 4,250
0.5(Y) = 4,250
Y = 4,250 (2)
Y = 8,500
So, actually we have the same short-run equilibrium output as we did in Q5.
To find the multiplier, in this case, we will get: 1/(1-c+m)
where m is the marginal propensity to import.
We get this because we know that Net Exports = Exports – Imports.
And, that Imports are dependent on Income, so IM = mY, where m is the marginal propensity
to import.
Since c is 0.6 from Problem 6 and m is 0.1, the multiplier = 1/(1-c+m) = 1/(1 - 0.6 + 0.1) = 2.
Question 8
Problems 5 to 8 assume that the economy is described by the following equations:
C = 1,800 + 0.6(Y  T),
IP = 900,
G = 1,500,
= 100,
NXNX
= 950
 0.1Y T = 1,500, Y* = 9,000
If net exports are given by NX = 950  0.1Y find the value for short-run equilibrium output and
the multiplier.
To find the short-run equilibrium output, we can do the same steps as in Q5, setting Y = PAE.
1
Y = C + I + G + NX
𝑡ℎ𝑒 𝑚𝑢𝑙𝑡𝑖𝑝𝑙𝑖𝑒𝑟 = 1 − 𝑡ℎ𝑖𝑠
Y = 1,800 + 0.6(Y  1,500) + 900 + 1,500 + 950 - .01(Y)
0.5(Y) ++ 4,250
4,250
YY == 0.5(Y)
0.5(Y) = 4,250
Y = 4,250 (2)
Y = 8,500
So, actually we have the same short-run equilibrium output as we did in Q5.
An alternative way to find the multiplier is to use the equation above.
Important Details about the Exam
What to know:
 Check your timetable for Exam time and location.
 You will need to write my name on your Exam booklet,
as well as your own. My name is Ayesha Ali.
What to bring:
 Bring a pen/pencil & eraser.
 Bring your library card number.
(You will not be allowed to turn in an exam without a library card number.)
 Bring a standard (non-programmable) calculator.
 Bring a paper English/Other Language dictionary if you
need one. Electronic dictionaries will not be allowed.
Next Class
 Week 19 Worksheet - Money Markets
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Chapter 23 in the Textbook
 Please email me by Saturday if you’d like me to go over
any Exam questions/solutions in class next week.
 Exam is on Friday this week –
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Tutors have 4 weeks to complete marking
The office will probably take a week or two for processing
So, if there are no problems at all, you should get your exam
results back in roughly 5 weeks.
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Please be patient and work hard in the meantime.
Good luck!