Download ECON 102 Tutorial: Week 16

ECON 102 Tutorial: Week 16
Shane Murphy
www.lancaster.ac.uk/postgrad/murphys4/econ15
[email protected]
Today’s Outline
 Week 16 worksheet:

In class today, we’ll only go through the problems that you have
questions on; otherwise please make sure you review all of
problems on your own and ask if you have any questions.

If you had any difficulty with the material on this tutorial,
please review Chapter 20 – it’s actually quite helpful.
Some definitions before looking at Question 1
The following is from your textbook (Pgs. 503-505), and is helpful in understanding the
relationship between output (GDP) per person, labour productivity, and the share of the
population employed.
The notations that your book uses are:
Y = real GDP
N = number of employed workers
POP = total population
So, using this notation, we can write Real Output per Person as:
Y
Y
N

x
POP
N
POP
Which means that Real Output per Person depends on:
𝑌
 How much each worker can produce (that’s 𝑁)
 The percentage of the population that is working (that’s
𝑁
)
𝑃𝑂𝑃
So, in Q1, we want to find the Average Labour Productivity. We can use the above relationship
to define the average labour productivity as:
𝑌
𝑁
=
𝑌
𝑃𝑂𝑃
𝑁
𝑃𝑂𝑃
In other words, average labour productivity equals real GDP per person divided by the share
of the population employed.
Question 1
Data for Canada, Germany and Japan on the ratio of employment to population in 1979 and
2003 are as in the table below. Using data from Table 20.1, find average labour productivity
Table 20.1
for each country in 1979 and in 2003.
Country
Canada
Germany
Japan
1979
0.44
0.33
0.47
2003
0.50
0.43
0.52
In the previous slide, we established that the equation for Average Labour Productivity is:
𝑌
𝑁
=
𝑌
𝑃𝑂𝑃
𝑁
𝑃𝑂𝑃
Average labour productivity equals real GDP per person divided by the share of the
population employed.
Using this equation, we can calculate:
labour productivity for Canada in 1979 is
𝑌
$19,892
=
𝑁
0.44
𝑌
= $45,209
𝑁
Calculating average labour productivity
for the three countries, we get:
Canada
Germany
Japan
1979
$45,209
$52,188
$34,743
2000
$58,402
$58,770
$51,223
Question 2
Using the data from problem 1, how much of the increase in output per person in each
country over 1979–2003 is due to increased labour productivity and how much is due to
increased employment relative to population?
What we want to do here is find the % change in output per person, in labour productivity,
and in the employment to population ratio, for each of the three countries.
For example in Canada,
𝑝𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑒𝑟 𝑝𝑒𝑟𝑠𝑜𝑛 =
𝑦2003 −𝑦1979
𝑦1979
=
29,201 −19,892
19,892
= 46.8%
GDP per person increased 46.8% in Canada and 63.1% in Japan.
At the same time labour productivity rose 29.2% and 47.4%, while the ratio of employment to
population only rose by 13.6% and 10.6% in the two countries.
So, most of the increase in output per person in Canada and Japan resulted from higher
labour productivity rather than a higher employment-population ratio.
In contrast, in Germany, the increase in output per person resulted more from higher
employment than from higher labour productivity:
Over this period GDP per person increased 46.7% (similar to Canada)
At the same time, the ratio of employment to population rose 30.3% while labour productivity
only increased 12.6%.
Question 3
In a given economy average labour productivity is €50,000, the capital-labour ratio is €20,000
and the saving rate is 10 percent. If the population grows at 0.5 percent per year and 1.5
percent of the capital stock depreciates each year what are the values of:
(a) gross investment
(c) required investment
(b) net investment?
And what would you predict about the future behavior of the capital-labour ratio and average
labour productivity in this economy?
According to the Solow model the values to be calculated depend on
the savings rate
s = 10%
labour productivity
y = €50,000
depreciation
d = 1.5%
population growth
n = 0.5%
the capital-labour ratio
k = €20,000
First thing to identify here, before we can answer this problem, is that this question is asking
about the Solow Growth Model (textbook pgs. 506-518).
Question 3(a)
In a given economy average labour productivity is €50,000, the capital-labour ratio is €20,000
and the saving rate is 10 percent. If the population grows at 0.5 percent per year and 1.5
percent of the capital stock depreciates each year what are the values of: (a) gross investment?
Gross investment (i) is equal to investment per worker.
𝑌
To find this, we can multiply the saving rate (s) by the average labour productivity (y = 𝑁).
So we have:
i = sy
Plugging in, we get:
i = 10% * 50,000
i = 5,000
Question 3(c)
In a given economy average labour productivity is €50,000, the capital-labour ratio is €20,000
and the saving rate is 10 percent. If the population grows at 0.5 percent per year and 1.5
percent of the capital stock depreciates each year what are the values of: required investment
Required investment is the amount of investment required to keep the capital-labour ratio
constant. So, required investment depends on two factors – the rate of depreciation and
population growth.
The required investment per worker is equal to the depreciation rate X the amount of capital
plus the labour-force growth rate times X the amount of capital.
We can write required investment as (d +n)k.
So, from here, we can plug in values for d, n, and k from the information given.
required investment per worker = (d + n) k
(d + n) k = (1.5% + 0.5%) * 20,000
(d + n) k = 400
Question 3(b)
In a given economy average labour productivity is €50,000, the capital-labour ratio is €20,000
and the saving rate is 10 percent. If the population grows at 0.5 percent per year and 1.5
percent of the capital stock depreciates each year what are the values of:(b) net investment?
And what would you predict about the future behavior of the capital-labour ratio and average
labour productivity in this economy?
Net investment is defined as the change in the capital ratio (Δk) and it is equal to the
difference between investment per worker and the required investment.
We can write it as:
net investment = gross investment – required investment
Δk = i – (d + n)k
Δk = 5,000 – (1.5% + 0.5%) * 20,000
Δk = 4,600
Question 3
In a given economy average labour productivity is €50,000, the capital-labour ratio is €20,000
and the saving rate is 10 percent. The population grows at 0.5 percent per year and 1.5
percent of the capital stock depreciates each year.
What would you predict about the future behavior of the capital-labour ratio and average
labour productivity in this economy?
From parts (a) – (c), we know that:
a. gross investment, i = 5,000
b. net investment, Δk = 4,600
c. required investment per worker, (d + n) k = 400
In this problem, we have a scenario where gross investment initially exceeds required
investment; so the capital-labour ratio and labour productivity in this economy will increase.
In long-run equilibrium, gross investment equals required investment, and net investment per
worker is zero. Once the economy reaches this equilibrium, both output per worker (labour
productivity) and capital per worker will be constant, and total output will grow at the same
rate as the population.
Hence, long-run increases in labour productivity and living standards require technical
progress.
Question 4
Using the data in problem 3 draw a diagram to illustrate what you would predict about the
future behaviour of the capital–labour ratio and average labour productivity in this economy.
So, basically, what we want to draw here, is a scenario where the net investment is positive
(i.e. gross investment > required investment). So, we’ll use the framework of the Solow
Growth Model to show this.
From prob. 3, the economy is
originally at point E on the
production function.
The economy is also at point A
on the investment function,
with gross investment i of
€5,000 per worker (due to a
high savings rate s of 10%).
Required investment at this
capital-labour ratio is,
however, only 400 (point B).
Gross
Required
Because gross investment is much higher than required investment, the capital-labour ratio
will be rising and the economy will move to the right, along the production function and
along the investment function, until it reaches the long-run equilibrium points E* and A*
where gross investment = required investment = (d+n)k.
Question 5
Suppose that due to a programme of
government investment in education the
average years to schooling increased from
10 to 12 years.
Using Figure 20.8 explain how this might
effect (a) average labour productivity and
(b) the growth rate of total output Y.
Figure 20.8
More investment was made in
education – how does this effect
(a) average labour productivity
(b) the growth rate of total output
Question 5
If the investment in education
increases average labour
productivity (so y = Y/N rises),
then both the production function
and the investment curve shift up.
This implies that the growth rate
of total output (Y) will exceed the
rate of population growth (n).
However, once the new
equilibrium is established, labour
productivity stabilises and the
growth rate of total output (Y) will
again equal the rate of population
growth (n).
(Or we could say, that gross
investment = required investment
at the equilibrium.)
Figure 20.8
Question 6
Refer to Table 20.3 (from your textbook).
Assume that the airline has 100 employees and that each plane is valued at €1 million.
Find the capital–labour ratio and average labour productivity at each valuation of the capital
stock.
Question 6
Table 20.3 (from your textbook)
Assume that the airline has 100 employees and that each plane is valued at €1 million.
Find the capital–labour ratio and average labour productivity at each valuation of the capital
stock.
Solution 6:
First calculate the capital stock value from the number of planes times the value of a single
plane. Divide this by the number of employees to obtain the capital-labour ratio.
Calculate labour productivity from total output divided by the number of employees.
No. of
Total output
Capital
CapitalLabour
planes
(from Table
stock
labour ratio productivity
(from Table 20.3),
value K
(=K/N),
(=Output/N),
20.3)
no. of
€ per worker passengers per
5
6
7
passengers
1,000
1,080
1,120
€5 million 50,000
€6 million 60,000
€7 million 70,000
worker
10
10.8
11.2
Question 7(a)
Bangladesh is one of the poorest countries in the world with a low capital to labour ratio and
a low stock of human capital.
Figure 20.5
Using a production function
diagram such as Figure 20.5
illustrate the likely impact of:
(a) A large inflow of foreign
direct investment which
increases the Bangladeshi
capital stock
(a) In other words: k increases
(b) A crash educational
programme which dramatically
increases the skills of the
Bangladeshi labour force.
(b) In other words: human
capital increases, which
means that y increases.
Figure 20.5 The Production Function
The y = f(k) curve is known as the production function and shows how
average labour productivity y = Y/N increases with the capital per
worker or the capital–labour ratio k = K/N.
For a constant labour force N the slope of this line measures the
marginal product of capital MPK. Given the assumption of diminishing
marginal product the slope will become smaller and the curve flatter
as the capital–labour ratio increases.
Question 7(a)
Using a production function diagram illustrate the likely impact of (a) A large inflow of foreign
direct investment which increases the Bangladeshi capital stock.
(a) A large increase in the capital stock k moves the economy to the right along the existing
production function (assuming the human capital stock h is unchanged), from one point A on
the curve (with a low capital-labour ratio and low output per worker level) to a new point B
on the curve (with a higher capital-labour ratio and higher output per worker level).
Question 7(b)
Using a production function diagram illustrate the likely impact of (b) A crash educational
programme which dramatically increases the skills of the Bangladeshi labour force.
A crash educational programme increases the human capital stock per worker (h) as opposed
to the physical capital stock per worker (k) and shifts the production function upwards. So for
a given capital-labour ratio the economy moves to a higher output per worker level.
Question 8
Suppose that 30% (or 0.3) of total income accrues to the owners of capital and the remainder
to labour and in a given year the capital stock increases by 5% and the labour force by 1%. If in
that year the economy records a growth rate of 4%, which is your estimate for the
contribution of total factor productivity to economy growth?
First of all, what is the equation for total factor productivity? You can find it on pg. 518.
ΔA/A = (ΔY/Y) – α(ΔK/K) – (1 - α)(ΔN/N)
ΔA/A is the contribution to the growth in total output that is made by factors other
than capital and labour (i.e. technical progress)
ΔY/Y is the output growth rate
α
is the share of income accruing to capital owners
1 - α is labour’s share of total income
ΔK/K is the rate of change in the capital stock
ΔN/N is the rate of change in the labour force.
If we plug in values from the question, we get:
ΔA/A = 4% - 0.3 * 5% - (1 - 0.3) * 1%
ΔA/A = 1.8%
So 1.8% is the contribution to output growth made by factors other than capital and labour.
Next Class
 Week 17 Worksheet – Capital Markets

Chapter 21 in your textbook
 Planet Money Podcast: #602

This podcast illustrates some of the functions that banks
provide in the economy.
 You should be getting your exams back next week,
during tutorial.
 Test 3 (Short Answer) on Friday of Week 18 (2 weeks)



50 minutes; 4 questions, you must answer each one.
Material from Weeks 13-17 will be covered on the test.
No specimen test – questions will be very similar to Tutorial
questions & book questions.