Omari has completed primary school and is considering whether he wants to go to

Question

Omari has completed primary school and is considering whether he wants to go
to secondary school. School fees are 5 per year for four years. If he completes
secondary school, he will get a job as a mechanic; if he does not, he will work
as a manual laborer. The income profiles of each occupation are:

If Omari has a discount rate of 0.05:
A. Is it worthwhile for Omari to invest in secondary education?
Now suppose Omari lives in a malarial area. Suppose his probability of getting
malaria is based on two things: whether or not he uses a bednet, and howmany
other people in his 100-person village use bednets.
The probability that he gets infected with malaria if he doesn’t use a bednet
is: 0.3 – 0.3*(fraction of bednet users)
If he does use a bednet: 0.5 – 0.3*(fraction of bednet uses)
Suppose getting malaria reduces earnings in one year by $200.

B. Calculate the private and social benefits of purchasing and using
a bednet.
C. Depending on the cost of producing a bednet, the government
might be able to improve social welfare by subsidizing the sale of bednets.
What are the highest and lowest production costs that justify the use of
subsidies?

AGE 13 14 15 16 17 18 19 20 21 22 23 24 25 MANUAL LABORER 15 15 20 30 40 40 40 50 50 50 60 60 60 MECANIC 0 0 0 0 50 50 50 65 65 65 80 80 80

Explanation / Answer

A) Here we will consider the NPV(net present value) of both cases i.e. working as a manual labour or MECHANIC

NPV (manual labour) = 15/(1-0.05) + 15/(1-0.05)^2 + 20/(1-0.05)^3 + 30/(1-0.05)^4 + 40/(1-0.05)^5 + 40/(1-0.05)^6 + 40/(1-0.05)^7 + 50/(1-0.5)^8 + 50/(1-0.05)^9 + 50/(1-0.05)^10 + 60/(1-0.05)^11 + 60/(1-0.05)^12 + 60/(1-0.05)^13 = 13552.203 $
NPV (MECHANIC) = -(5*4) + 50/(1-0.05) + 50/(1-0.05) + 50/(1-0.05) + 65/(1-0.05) + 65/(1-0.05) + 65/(1-0.05) + 80/(1-0.05) + 80/(1-0.05) + 80/(1-0.05) = 938.4457 $
Since, NPV (manual lanour) > NPV (mechanic) , he should invest and go for manual labour.
It is not worthwhile to invest in secondary data.  
Total number of people living in village is 100
Let number of people using bednet be x.
The probability that Omari gets infected with malaria if he doesn’t use a bednet
is: 0.3 – 0.3*(fraction of bednet users) = 0.3 -0.3 * (x/100) = 0.3 - 0.003x
If Omari does use a bednet: 0.5 – 0.3*(fraction of bednet uses) = 0.5 - 0.3*(x/100) = 0.5 - 0.003x
Malaria reduces his earning by 200$
Then, NPV (manual labour) = 13552.203- 200 = 13352.203 $
and NPV (mechanic) = 938.4457- 200 = 738.4457$
Since, NPV(manual labour) > NPV(mechanic) it is better not to opt for secondary education.

B) Private benefit of purchasing a bednet ;
Probabilty If Omari does use a bednet: 0.5 – 0.3*(fraction of bednet uses) = 0.5 - 0.3*(x/100) = 0.5 - 0.003x
The probability that Omari gets infected with malaria if he doesn’t use a bednet
is: 0.3 – 0.3*(fraction of bednet users) = 0.3 -0.3 * (x/100) = 0.3 - 0.003x
Here, we see that 0.5-0.003x > 0.3 - 0.003x , ,means the probability of getting malaria without using bednet is low as compared to the probability of using bednet.
The social benfit comes as there is a gain of 200$ if you are not sick due to malaria.
C) The government will improve social welfare by producing bednet as this will result in less number of people falling sick due to malaria.

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