jnu question

[priyal]

1.Suppose we say that an allocation x is pareto optimal iff there does not exist an allocation,say y,such that :every individual in the economy considers y to be atleast as good as x,and atleast one individual considers y to be strictly better than x. now consider a society of 4 individuals. this society has five allocations to choose from a,b,c,d and e. individual preferences over these allocations are as follows:
1st individual: aP1  bP1  cP1  dP1  e
2nd individual: bP2  cP2  dP2  eP2  a
3rd individual:  cP3  dP3  eP3  aP3  b
4th individual:  dP4  eP4  aP4  bP4  c
aP1 bP1 cP1 dP1 e means that the 1st individual prefers allocation a over b,bover c....dover e.likewise for the preferences of other individuals.find out pareto optimal allocations for this society.expalin your answer step wise.

2. in year 0, industrial workers devote 50 percent of their total expenditure to food,25 percent to housing and 25 percent to clothing, between year 0 and 1, the prices of these 3 items increase by 15 percent,12 percent and 8 percent resp. how much does laspaeyres price index increase by between period 0 and period 1. explain answer step wise.

3.a foreign institutional investor who will settle only for returns in excess of 10 percent,is considering converting dollars into rupees to purchase a stock that is valued at rs.100 but is expected to appreciate in value to rs.110 at the end of one year.if the investing entity expects the rupee to depriciate in value from rs. 50 to dollar to rs.52.50 to the dollar in that year,it would purchase the stock only if the firm is expected to pay a dividend of:
a] rs.3 per share
b] rs.2.50 per share
c] rs.5 per share
d] more than rs. 5 per share

4.for an economy, the long run rate of growth of GDP is 5 percent per anum at full employment. the investment rate is 20 percent and the rate of groeth of labour force is 2 percent per anum.then the capital output ratio is:
a] 2
b] 5
c] 7
d] 10

5.if a,b are two distict real numbers both greater than unity, then it must be the case that
a] a/b<1
b] a/b>1
c] a+b>2a^b{square root of ab}
d] a+b<2a^b

6.if a,b are real numbers and a<b,then it is necessary that
a] a2[a square] <b2
b] a^<b^
c] a.c<b.c for any real number c
d] a-c< b-c for any ral number c

[for ques 5 and 6, how to parctice more questions like that..these are the question which generally comes in jnu exam]

[Khushboo]

Ans 1-  Pareto efficient allocation are only a,b,c,d but not e bcz d always does better than e. But 1st individual prefers a to any other allocation, any movement from here make him worse off.  Similarly 2nd individual prefers b to any other allocation, any movement from here make him worse off, as on.... Therefore, there is no way to make some one better off without making any one worse off.

2- P01 = E P1q0/ E P0Q0 x 100  [E means summation]
          = 1125/1000 x 100
          = 112.5

4- option a i.e 2

5- option c i.e a+b>2a^b{square root of ab}

6- option d i.e a-c< b-c for any ral number c

[Amit Goyal]

Thanks Khushboo for answering the questions.

Let me answer the remaining problem:
Investors invest $2 to buy one stock/share. Price of the stock in Indian currency(50X2) is Rs. 100.
The minimum value it expects to get after an year is $2.20. The minimum return in indian currency(52.5X2.20) is Rs. 115.50
Since the value of stock is going to be Rs. 110, the firm will invest only if it is paid a minimum dividend of Rs. 5.50 (115.50-110)
hence, the answer is (d)

[bhumika]

wldnt we apply rank voting method here?

[Amit Goyal]

No, just apply the definition of pareto efficiency.

[PRANAVjain]

SIR,PLZ TELL ME HOW WE'LL USE PARETO EFFICIENCY CRITERION HERE.a,b,c,d are pareto and not e.WHY?is it because that none has preferred e at all or any other reason

[Amit Goyal]

e is not pareto efficient because there is a way to make atleast one of the individuals better off without making someone worse off. If you move from e to d everyone would be better off hence atleast one is better off and others are not worse off.
a, b, c, d are pareto efficient because wherever you switch from any of these you will end up harming atleast one.

[Chandrani Sarma]

Khushboo, could you explain how you arrived at the answer to ques no. 4..