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Exercise #4
Economics of education and review questions
I. Choosing educational levels
There are several costs that need to be incurred in deciding on whether to go to secondary
school or not. They include:
1.
The direct cost of maintenance of the child while not working. This cost will run
from 1 to 11 years old for those who only go to primary school and from 1 to 17 for those
who will go to secondary school.
2.
The school cost, which is higher for secondary than for primary school.
3.
The opportunity cost of going to school when in secondary school, i.e., the
forgone income on the labor market with primary education.
There are gains from going to secondary school in that future earnings will be higher than
for those who only attend primary school.
You can calculate the private net benefit from primary and secondary education as the net
of these earnings and costs (sum of the benefits minus the costs for each year of life).
If secondary education also creates a positive externality on others equal to 15% of the
income earned by those with secondary education, you can calculate the social net benefit
from secondary education.
You are given in the Excel file “Education” data on these profiles of costs and earnings
for ages 1 to 60.
You will use the concept of Internal Rate of Return to compare the present value of
choosing to attend primary or secondary school as seen in year 1.
The internal rate of return is the interest (or discount) rate that equates costs and benefits:
IRR = interest rate that equates PV(Earnings) to PV(Costs), or equivalently IRR =
interest rate for which PV(Net benefits) = 0.
In Excel, the IRR operator is = 100*IRR(From:To).
1. Calculate the private net benefits from primary and secondary education for each year,
and present them in a graph. Discuss how these profiles differ.
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Private Benefits of Promary and Secondary Education
3000
2500
2000
1500
1000
500
0
0
10
20
30
40
50
60
-500
-1000
Age
Private Net Benefit of Primary
Private Net Benefit of Secondary
As expected, the profiles are exactly the same for the pre-school and primary school
periods, since the costs are going to be the same for both groups. At 11 years old, the
difference between the two profiles starts to show. Children who drop out after primary
will stop paying the cost of schooling, and will start earning a salary, whereas those who
attend secondary are going to be paying school fees, plus they will not be earning any
wages (opportunity cost). After 17 years of age, children have already finished school,
and their earnings profile starts rising steeply, staying higher than the one for primary
educated children, which remains flat.
2. Define the IRR. You can use Wikipedia or your old Econ textbook, but give the
formula and the definition in your own words.
The internal rate of return (IRR) is a rate of return used in capital budgeting to measure
and compare the profitability of investments. It is also called the discounted cash flow
rate of return (DCFROR) or simply the rate of return (ROR). In the context of savings
and loans the IRR is also called the effective interest rate. The term internal refers to the
fact that its calculation does not incorporate environmental factors (e.g. the interest
rate or inflation). (Source: Wikipedia).
The IRR is the discount rate r that equates the present value of returns and the present
value of costs, i.e.,
T
Re turnt
å (1+ r )
t =0
t
T
=å
t =0
Costst
(1+ r )t
or if we have net returns, like in the school choice example:
2
T
Net Re turnt
å (1+ r )
t =0
t
=0
3. Calculate the IRR for primary and secondary education if life expectancy is:
30 years –
40 years –
60 years –
Primary
7.6%
8.93%
9.48%
Secondary
5.9%
9.24%
10.63%
3.1. If you decide on which educational plan to choose (primary or secondary) according
to the one with the highest IRR, which plan will you choose when life expectancy is 30,
40, and 60?
o 30 years – Primary
o 40 years – Secondary
o 60 years – Secondary
3.2. Reflect on how the HIV/AIDS crisis and the extension of life expectancy bear on
educational choices.
HIV/AIDS reduces the life expectancy, and therefore the IRR will be lower. It can be
rational to choose to get less education if you expect to live for a shorter period of time.
4. If there is a program that provides loans for secondary schooling, where the interest
rate to be paid is 10%, who can afford to take this loan? Remember that under this
program, the family will still be responsible for paying for primary schooling.
To compute the IRR in this case we have to add to the school fee cost the 10% interest
for each year of secondary education. Everything else will be the same as before. Asking
who is going to be able to afford secondary school education in this case is the same as
asking who is going to decide to go to secondary, instead of only primary. People who
have a life expectancy of about 40 years will have higher returns to secondary education,
than to only primary education, once we factor in the higher cost of education.
Primary
30 years –
40 years –
60 years –
7.6%
8.93%
9.48%
Secondary
(w/interest
Rate)
6.95%
10.06%
11.32%
5. With the 15% externality, what is the social IRR from secondary education for each
life expectancy group?
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Here, the externality will kick in only after the education cycle is finished.
The IRR for secondary schooling increases once we account for the social benefits of
secondary education. Particularly, for each life expectancy it will be:
Primary
30 years –
40 years –
60 years –
Secondary
(w/
Externality)
7.02%
10.11%
11.37%
7.6%
8.93%
9.48%
5.1. Provide a graph in which you compare the private and social benefits of secondary
education by year.
Private and Social Benefits of Secondary Education
3500
3000
2500
2000
1500
1000
500
0
0
10
20
30
40
50
60
-500
-1000
Age
Social Net Benefit of Secondary
Private Net Benefit of Secondary
5.2. Discuss why there would be logic to subsidizing secondary education.
If the social benefits of secondary schooling are 15% of the earnings of those who go to
secondary school, any subsidy to secondary schooling that amounts to less than the gains
(or the area between the two lines above), will represent a net welfare gain for the
society. Internalizing the externality through a subsidy makes investing in education more
appealing.
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