isi 2009 me2

[SHIKHA]

Suppose there are 10 individuals in a society, 5 of whom are of high ability,
and 5 of low ability. Individuals know their own abilities. Suppose that each
individual lives for two periods and is deciding whether or not to go to college in
period 1. When individuals make decisions in period 1, they choose that option
which gives the highest lifetime payoff, i.e., the sum of earnings and expenses
in both periods.
Education can only be acquired in period 1. In the absence of schooling,
high and low ability individuals can earn yH and yL respectively in each period.
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With education, period 2 earning increases to (1 + a)yH for high ability types
and (1 + a)yL for low ability types. Earnings would equal 0 in period 1 if an
individual decided to go to college in that period. Tuition fee for any individual
is equal to T. Assume yH and yL are both positive, as is T.
• (i) Find the condition that determines whether each type of person will
go to college in period 1. What is the minimum that a can be if it is to
be feasible for any type of individual to acquire education?
• (ii) Suppose yH = 50, yL = 40, a = 3. For what values of T will a high
ability person go to college? And a low ability person? Which type is
more likely to acquire education?
• (iii) Now assume the government chooses to subsidise education by setting
tuition equal to 60. What happens to educational attainment?
• (iv) Suppose now to pay for the education subsidy, the government decides
to impose a x% tax on earnings in any period greater than 50. So if an
individual earns 80 in a period, he would pay a tax in that period equal
to x% of 30.The government wants all individuals to acquire education,
and also wants to cover the cost of the education subsidy in period 1
through tax revenues collected in both periods. What value of x should
the government set?




DONE WITH FIRST THREE PARTS...NOT ABLE TO SOLVE (iv) PART ....PLZ HELP HOW TO PROCEED...EVEN ANSWER IS GIVEN BY SIR(REFER BELOW LINK) ..BUT I DIDNT GET IT..HELPPP!!

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/isisolutions2009.pdf

[Ram]

Hi, Here the total subsidy given to the people is 300 i.e. because high ability people can give max 100 and low ability people can give 80 but government is giving subsidy so the total subsidy for 10 people is 5(100-60)+5(80-60)=300 now government has to tax people so that tax revenue will be equal to the subsidy.
Here Govt can tax people those have gone for school in period 1 and they cant people who didnt go to school because their income is less than or equal to 50 and the tax is on income which is in excess of 50.
so the income of people is 5(((1+a)yH-50)+((1+a)yL-50)) this is from (1+a)yH-50=200-50, (1+a)yL-50=160-50. The total tax revenue is
(x/100)5(150+110)=300 from this we will get the value of X as 23.08%

here we are considering income of everyone because everyone will go to school in period 1 because of Govt subsidy....

[SHIKHA]

thanks ram..got it....