1. office hours: 8:00AM – 8:50AM tuesdays LUMS C85
ECON 102 Tutorial: Week 16
Ayesha Ali
office hours: 8:00AM – 8:50AM tuesdays LUMS C85

2. 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.

3. Some definitions before looking at Question 1
The following is from your textbook (Pgs ), 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:
Which means that Real Output per Person depends on:
How much each worker can produce (that’s 𝑌 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.

4. 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 for each country in 1979 and in 2003.
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.
Table 20.1
Country
1979
2003
Canada
0.44
0.50
Germany
0.33
0.43
Japan
0.47
0.52
Using this equation, we can calculate:
labour productivity for Canada in 1979 is
𝑌 𝑁 = $19,
𝑌 𝑁 = $45,209
Calculating average labour productivity for the three countries, we get:
1979
2000
Canada
$45,209
$58,402
Germany
$52,188
$58,770
Japan
$34,743
$51,223

5. 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= 𝑦 2003 − 𝑦 𝑦 = 29,201 −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%.

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 ).

7. 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.
To find this, we can multiply the saving rate (s) by the average labour productivity (y = 𝑌 𝑁 ).
So we have:
i = sy
Plugging in, we get: i = 10% * 50,000
i = 5,000

8. 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

9. 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

10. 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.

11. 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.
Gross
Required
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).
From the solutions: The diagram should include a production function, investment function and a long-run equilibrium investment (aka required investment) line (a straight line with slope d+n = 1.5% + 0.5% = 2% or 0.02).
The economy is originally at point E on the production function, with a capital-labour ratio k of €20,000 per worker and labour productivity y of €50,000 per worker.
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). Since 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.
Diagram – given state: empty diagram, only with axes and labels “Output per worker y = Y/N” and “Capital per worker k = K/N”.
Diagram – required state:
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.

12. 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

13. Question 5
More investment was made in education – how does this effect
(a) average labour productivity
(b) the growth rate of total output
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

14. 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.

15. 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 planes (from Table 20.3)
Total output (from Table 20.3),
no. of passengers
Capital stock value K
Capital- labour ratio (=K/N),
€ per worker
Labour productivity (=Output/N),
passengers per worker 5
1,000
€5 million
50,000 10 6
1,080
€6 million
60,000
10.8 7
1,120
€7 million
70,000
11.2

16. 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
(b) A crash educational programme which dramatically increases the skills of the Bangladeshi labour force.
In other words: k increases
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.

17. 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).

18. 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.

19. 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% * 5% - ( ) * 1%
ΔA/A = 1.8%
So 1.8% is the contribution to output growth made by factors other than capital and labour.

20. 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 will be covered on the test.
No specimen test – questions will be very similar to Tutorial questions & book questions.