ECON 100 Tutorial: Week 16
www.lancaster.ac.uk/postgrad/alia10/
a.ali11@lancaster.ac.uk
office hours: 3:45PM to 4:45PM tuesdays LUMS C85
Permanent Income Hypothesis
People will spend money at a level consistent with
their expected long-term or lifetime income. When
young, people generally borrow, when middle aged
people pay off their loans and save for retirement,
and when old, people spend what they saved.
Question 1(a)
A woman thinks that her life-time
earning will be as follows:
Assuming that the interest rate is zero,
calculate her annual permanent income.
Age
Earnings per
# years
year ($)
19-23
5
35,000
24-28
5
50,000
29-34
6
60,000
35-44
10
30,000
45-64
20
50,000
Because the interest rate is zero,
65-79
15
15,000
PI = sum of income each year
= 35,000 + 35,000 + … + 15,000 + 15,000
= 5*35,000 + 5* 50,000 + … + 20*50,000 + 15*15,000
= 175,000 + 250,000 + 360,000 + 300,000 + 1,000,000 +
225,000
= 2,310,000
So the annual permanent income = 2,310,000/61 = $37,869
Question 1(b)
Age
Suppose at the age of 29 she wins $250,000 in
29-34
the state lottery.
29
What effect will this have on
35-44
her annual permanent income?
Earnings per
# years
year ($)
6
60,000
1
250,000
10
30,000
45-64
20
50,000
65-79
15
15,000
Over the last 50 years of her life, her income is:
PI = 60,000*6 + 30,000*10 + 50,000*20 + 15,000 * 15 + 250,000
PI = 360,000 + 300,000 + 1,000,000 + 225,000 + 250,000
PI = 2,135,000
Note: In Coskeran’s solutions he takes the permanent income in part (a) and subtracts from it the income
she already earned up to age 29 and then adds on the lottery winnings.
Annual permanent income after age 29 is now 2,135,000/51 = $41,863
Permanent Income Hypothesis
In practice people don’t know exactly when they will
die, so they will not consume 100% of their lifetime
income. Instead they will consume a percentage of
it, so they will have some left over if they outlive
their life expectancy.
Question 1(b)
Suppose at the age of 29 she wins $250,000 in the state lottery. In the
previous slide, we calculated her Annual permanent income after age 29 as
$41,863.
Assuming she consumes 85% of her permanent income, what will be her
marginal propensity to consume when she is 29?
Her consumption prior to age 29 was (37,869*0.85) = $32,188
And at age 29, after re-assessing her annual PI, is (41,863*0.85) = $35,583
We want to find her Marginal Propensity to Consume (MPC)
MPC = change in consumption/change in income.
Increase in income = 250,000
MPC = (35,583 – 32,188)/250,000 = 0.01358
Note: My answers here differ slightly from the solutions posted to Moodle. There was an
error in the Moodle solutions that I have corrected. (the error was that the period where the
individual’s age was 29-34 was counted as a 5-year period, but actually it is a 6-year period).
Question 1(c)
Earnings per
# years
year ($)
As her career progresses, the woman realises that Age
Her earning opportunities are greater than she had 35-64
30
65,000
thought. From the age of 35 to 64 she now earns 65-79
15
15,000
$65,000 a year. What is her new annual permanent
income from the age of 35? In both cases, assume
Earnings per
Age # years
year ($)
she still has her lottery winnings from (b).
Her new annual permanent income is
Annual PI = (30*65,000 + 15*15,000)/45
Annual PI = (1,950,000 + 225,000)/45
Annual PI = $48,333
29-34
6
60,000
29
1
250,000
35-44
10
30,000
45-64
20
50,000
65-79
15
15,000
So her annual consumption is $48,333 * .85 = $41,083
Prior to this re-assessment of her earnings, her consumption was $35,583, in
part 1(b).
Question 1(c)
As her career progresses, the woman realises that her earning opportunities
are greater than she had thought. From the age of 35 to 64 she now earns
$65,000 a year.
We calculated that her new annual permanent income from the age of 35 is
$48,333.
What is her marginal propensity to consume at the age of 35?
MPC = Δ consumption ÷ Δ income
So, first, let’s calculate her annual consumption:
Annual consumption is $48,333 * 0.85 = $41,083
Prior to this re-assessment of her earnings, her consumption was $35,583, in
part 1(b). So the change in consumption is $41,083 - $35,583 = $5,500
Next, let’s calculate her change in income.
In the year that the woman was 35, her change in income was 35,000.
So, when she was 35, her MPC = 5,500/35,000 = 0.157
The effect on MPC is greater with long run change in permanent income than
it is with the short-run change in permanent income.
Question 2
In an attempt to boost consumer spending, a government decides to cut VAT
for a year from 20% to 15%.
The Opposition argue that it would be better to cut the standard rate of
income tax permanently by one percentage point.
According to the permanent income hypothesis and the life-cycle hypothesis,
which of these policies is more likely to raise consumer spending?
Effect of cutting VAT for a year from 20% to 15%:
According to the PIH, the limited tax cut should have little impact on
consumption. Households save a high proportion of the tax cut to allow for
the return to higher VAT in the future.
The life cycle hypothesis suggests a similar outcome as households fail to
consume faced with the prospect of higher future tax.
There might be a substitution effect, however, if households decide to bring
forward consumption, particularly of consumer durables such as washing
machines and TVs. Future consumption would fall to compensate for this
rise, a possibility the government would need to bear in mind in its future
fiscal policy.
Question 2
In an attempt to boost consumer spending, a government decides to cut VAT for a
year from 20% to 15%. The Opposition argue that it would be better to cut the
standard rate of income tax permanently by one percentage point.
According to the permanent income hypothesis and the life-cycle hypothesis, which
of these policies is more likely to raise consumer spending?
Effect of cutting standard rate of income tax permanently by 1%:
A cut in income tax would have a permanent, albeit small, effect that could cause
households to raise spending based on their higher future expected disposable
income.
As shown in the answer to question 1, the MPC is likely to be higher from a
permanent change in income than from a one-off, transitory, change in income.
The reason is the distinction between temporary and permanent income. If people
anticipate a rise in tax rebates or any other form of stimuli (this is true for companies
as well, not just consumers) to be temporary, they will save this money instead of
spend or invest it. But when they anticipate a permanent rise in income (like getting
a new or better paid job) they are much more likely to spend or invest now as they
anticipate a certain future stream of income. With a temporary cut or rebate, they
know that next year this won't happen so they better put the money away for now.
Question 3(a)
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1 I = 350
What is the equilibrium income in the economy?
In this question, we are focusing on the long-run equilibrium.
In the long run, we set Y to be equal in all years (that’s the PIH).
So that allows us to say: Y = Y-1
Then YP = 0.75Y + 0.25Y-1 can be rewritten as:
YP = 0.75Y + 0.25Y
YP = Y
So then we can re-write C as C = 0.8Y
And we can plug C an I into our equilibrium equation: Y = C + I
Y = 0.8Y + 350
0.2Y = 350
Y = 1,750
Question 3(b(I))
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1
I = 400
If investment rises to 400, what is the new equilibrium
income?
We’ll use the same steps as in part (a):
In the long run, Y = Y-1 (because of the PIH)
So, YP = 0.75Y + 0.25Y-1 = 0.75Y + 0.25Y = Y
If YP = Y, we can re-write C as C = 0.8Y
Plugging into our equilibrium equation:
Y = 0.8Y + 400
0.2Y = 400
Y = 2,000
Question 3(b(II))
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1
I = 400
If investment rises to 400, what is the long run value of the
multiplier?
First we need to know the equation for the multiplier:
Multiplier = Change in income / Change in investment
Income changed from 1,750 to 2,000 and Investment changed from 350 to 400.
Multiplier = 250/50
Multiplier = 5
Question 3(b(III))
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1
I = 400
If investment rises to 400, what is the long run marginal
propensity to consume?
How can we find the MPC?
MPC is the slope, i.e. the coefficient on Y, of our Aggregate
Demand (AD) line. Sometimes, we call it the Aggregate Expenditure (AE) line.
In the long run, our AD line is Y= 400 + 0.8Y
So, our Long-run MPC = 0.8
We found this in part (a)
Question 3(b(IV))
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1
I = 400
If investment rises to 400, what is the short run marginal propensity to
consume?
We know that MPC = slope of the AD line.
To find short-run MPC, we need to find the short-run AD equation.
In the short run, we are only concerned with the current period Y. So,
we’re going to treat Y-1 as a constant.
Y = 0.8YP + 400
Y = 0.8(0.75Y + 0.25Y-1) + 400
This is our short run AD line. Note, Because we are
treating Y-1as a constant, Y-1 does affect the intercept
Y = 0.6Y + 0.2Y-1 + 400
but it does not affect the slope.
So our short-run MPC = 0.6 (that’s the coefficient on Y, or the slope of the short-run AD line).
Question 3(b(V))
The economy can be described as follows:
Y=C+I
C = 0.8YP YP = 0.75Y + 0.25Y-1
I = 400
If investment rises to 400, what is the short run value of the
multiplier?
We know how to find the value of the multiplier.
Multiplier = 1 /(1 – MPC)
So, the short-run multiplier = 1 / (1 – short-run MPC)
In part (b(IV)) we found the short-run MPC = 0.6.
So,
Short-run multiplier = 1/(1 – (0.6)
Short-run multiplier = 2.5
The answers to ii) and v) show a general point that, according to this particular model, the
multiplier is lower in the short-run than in the long-run.
Question 3(c)
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1
I = 400
If full-employment income in the economy were 2,500, what problems
would a government face in trying to use fiscal policy to achieve fullemployment?
As a review, lets think about how much short-term government
spending would be necessary to overcome this deflationary gap.
In this case, equilibrium Y = 2000. So, the deflationary gap = 500.
We already found the short-run multiplier is 2.5.
We know ΔY/ ΔG = multiplier, so then ΔY/multiplier = ΔG.
So our increase in G should be 500/2.5 = 200 in the short run
So to close the deflationary gap in the short run, we need an increase
in government spending from 0 to 200.
Question 3(c)
The economy can be described as follows:
Y=C+I
C = 0.8YP
YP = 0.75Y + 0.25Y-1 I = 400
If full-employment income in the economy were 2,500, what problems
would a government face in trying to use fiscal policy to achieve fullemployment?
In this simple model, it is possible to figure out what level of G
would result in Y=2500 in the long run. Can you do it? Do you
get G = 100? So in the first year, G=200, but in subsequent
years G falls to 100.
However, we could imagine the calculation getting even more
difficult, if PI depended on more past years than just Y-1. Also,
it may be politically difficult to reduce G and avoid an
inflationary gap (a bubble in the economy).
That is essentially what Coskeran’s answer is talking about in
the next slide.
Next Week
• Work through the Tutorial Worksheet
• Go through any problems from David Peel’s lecture