JNU 2002

[Ankit Agrawal]

Q 2. an individual ranks any two bundles (x,y) and (x',y') in the following manner: if either x>x' or if x=x' and y>y', the individual prefers (x,y) to (x',y'). An individual's income is Rs. 100/week. Price of good x=Rs. 2/unit. Price of good y=Re. 1/unit. The individual will consume:

(a) 25 units of x and 50 units of y
(b) 100 units of y
(c) 50 units of x
(d) 45 units of x and 10 units of y

[duck]

Hi Ankit.. :)

Such preference is called "Lexicographic preference".
eg: if you give a consumer to state his preference over these bundles:
A=(1, 10) and B= (0,100)
His preferences would be : A preferred to B.

Now, if he has some income. He'll definitely go and buy all of good"x".
So, answer would be 50 units of x and 0 units of y.
 

[Ankit Agrawal]

Got it! Thanks:)

[Ankit Agrawal]

Some more from the same paper:

Q4. In a closed economy, the marginal propensity to consume halves but the level of investment remains the same. Assuming all other things do not change, at the new equilibrium, in comparison to the earlier one:

(a) Savings doubles
(b) Income halves
(c) Savings in unchanged
(d) We cannot necessarily claim any of the above

Q 9. If a and b are real numbers such that for any c>0, a<b+c, then
(a) a<b necessarily
(b) a>b necessarily
(c) a=b necessarily
(d) a<=b necessarily

[Sumit]

@duck: could you plz explain the shape of "Lexicographic preference" indifference curve????
@ankitaggarwal079:  Q4. C)savings is unchanged=there will be increase in private savings and equal amount of decrease in public saving..so,total savings remain unchanged.
Q9: I think options are wrong...a could be greater, smaller & equal to b..

[maahi]

a>b can be ruled out :
a=98 b=47 c = 3
98<50 not satisfied
 i think it should be a<=b .

[kavya]

@ ankit the ans. is (d) a<=b necessarily...since it says for any c>0 which => if a is even slightly > b there would be some  value of 0<c< a-b for which a> b+C which according to the given info. is not possible. Hence, a<=b .

[Ankit Agrawal]

It cannot be a<=b.

Take a=80
b= -10
c=100

b+c=90
a<90

But, a>b

On 3 May 2013 16:57, "kavya [via Discussion forum]" <[hidden email]> wrote:

@ ankita the ans. is (d) a<=b necessarily...since it says for any c>0 which => if a is even slightly > b there would be some  value of 0<c< a-b for which a> b+C which according to the given info. is not possible. Hence, a<=b .

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[tkt]

 Given  a<b+c which means  a-b<c --1.
Also, c>0 --2.
Now, for 1. and 2. to hold true,
0<a-b<c

which means
0<a-b or
 a-b>0 or
 a>b necessarily

[duck]

Hi.. :)

@Sumit: Lexicographic preference cannot be represented by Indifference Curve.

[Sumit]

@duck: thanks..

[Ankit Agrawal]

Take a= -10; b=20; c=30.

Your conclusion that 0<a-b<c if wrong.

I guess the options are wrong

[kavya]

@ ankit but it is clearly mentioned that a<b+c is true  for all c this will be true let me explain ...in ur eg if we are to take c=20 then b+c=10 < a=80 ..thus a cannot be = 80. u have to take a value of a given value of b such that for every single c>0 .. a<b+c . you will realize that for this to be true a<=b.

[RHIDIMA]

we not only have lexicographic preferences over x, but we have on y as well as y>y'. So why will the individual go & buy only x given px>py???

[duck]

Hi.. :)

Read the statement properly:
It says if either x>x' or if x=x' and y>y', the individual prefers (x,y) to (x',y'). So, in both the cases, he is first looking at x and not y. And hence, he would always like to consume "x" first irrespective of its price relative to price of "y".

[RHIDIMA]

Ohkk Than wat do we infer from y>y'?

[duck]

Consider an agent who lexicographically prefers x to y.
Now, he would always prefer a bundle (1,0) over (0,100) no matter what the price is.
And if he is given an option between choosing from (1,0) and (1,100) then, he'll go for (1,100).
Note: The amount of "x" in (1,0) and (1,100) is the same. So, he'll check the amount for "y" and whichever bundle will have more "y" , he'll choose that.

Crux of the statement is:
Agent will always prefer bundle with more of "x". And if the amount of "x" is same then, he'll prefer that bundle which has more of  "y".

[RHIDIMA]

Thnks for the explanation. I understood. But sorry to bother u with my doubts..
I understood that when x is lexicographically preferred over y, the consumer will always prefer more of x to y and if he has same qty for x, he'll see for y. But my question is that in the Q both things are mentioned x>x' & y>y', than how do we say that x is only lexicographically preferred? I hope u r getting my question...

[duck]

you haven't read the statement carefully:
Its if either x>x' or if x=x' and y>y'

[RHIDIMA]

ohkk i understood...