JNU-10

[a.m]

1.in a two good world a consumer's utility function is given by the following:
U{x,y}=max{x,y}, where x and y are the amounts consumed of the first and second good respectively . The price of both the goods are 2rs per unit. the consumers income is 100. His optimal bundle is ?

a. either i. zero units of x and 50 units of y or ii. 50 units of x and 0 unit of y
b. 50 units of x and 50 units of y
c. 25units of x and 25units of y
d. none of the above.


2.A function is selected at random from all the functions of the set A={1,2,3,4...,n} in to itself. The probability that the function is selected is one-to-one is :

a. 1/n^n
b. 2/(n-1)!
c. 1/n!
d. (n-1)!/n^n-1

3. inverse function of f(x)=x^2

[aastha]

q1 : a . since has concave preferences so there will a boundary optimum .

[a.m]

hi aastha.. please elaborate !

[a.m]

thank you. Got it :)

[duck]

Hi a.m ... :)

For Q2) Favourable number of cases = n!
and total number of functions = n^n
So, Probability = (n-1)!/n^n-1

For Q3) Whats the domain?

[Chinni18]

Question 51 from JNU 2010
If x < y + ε > 0, then
(a) x > y
(b) x ≤ y
(c) x > 0 > y
(d) x < 0 < y

Consider x=-2, y=1 and ε=2. Then (a) doesn't hold.
Consider x=4, y=2, ε=3. Then (b) doesn't hold.
Consider x=-2, y=1 and ε=3. Then (c) hold.
Consider x=2, y=3 and ε=1 then (d) doesn't hold.

Any suggestions anyone? How can all the options be wrong? And there are no restrictions on the values of x and y, so nothing seems wrong with the counter-examples...

[ritu]

u have taken wrong examples mostly....if option says x>0>y.....how can u take x= -2??????

[Chocolate Frog]

Chinni, this relationship holds for any value of ε > 0. Now think about it?

[aditi5000]

Okkkkkkkkkk.... So epsilon can be as large (or small) as required so long as it is > 0... so the inequality which will necessarily {always} hold is
x < = y ...
Ok... I think i got it... Thanks Chocolate frog!!

[Chinni18]

Oh so I was approaching the question from a wrong angle altogether..! Got it!! Thank you, Chocolate Frog!!

[Chocolate Frog]

Most welcome, Chinni and Aditi. :)

[Badmathsboy]

Option d also holds true. For every x<0 and y>0, the equation holds true. I cannot find what is wrong with option b right now, but I am sure option d is right (too?). Ritu is right, you've taken wrong examples.
PS: y=x^2 has no inverse. For a function to have a inverse, it has to be bijective. Simply, imagine the reflection of x^2 graph over x=y line and you get a relation, not a function.

[Chocolate Frog]

Of course. But (d) is contained in (b), don't you think? :)

[Badmathsboy]

hhhmmm... you are absolutely right, need to get my head over this. I'll probably ask someone. These JNU guys give confusing options.