DSE 2014 doubt

[cheesecake]

How to go about this question?

[cheesecake]

this too!

[onionknight]

[onionknight]

Let price per unit be x
Maximise t-cx
subject to theta*sqrt(x)-t >=0

which boils down to maximizing theta*sqrt(x)-cx. Differentiate and set derivative=0, you'll get x=theta^2/4c^2

profit=theta^2/4c

[cheesecake]

ohh! got it! thanks.. i couldn't figure out how to remove the c :P

[kk]

Question 42.   Ms. A selects a number X randomly from the uniform distribution
on [0; 1]. Then Mr. B repeatedly, and independently, draws numbers
Y1; Y2; :::: from the uniform distribution on [0; 1], until he gets a number
larger than X=2, then stops. The expected number of draws that Mr. B
makes equals
(a) 2 ln 2
(b) ln 2
(c) 2=e
(d) 6=e

[kk]

am getting 1/2ln 2 not 2ln 2

[cheesecake]

How have you solved it?

[shar311]

can you please give the solution?

[suchi]

Hi!

has anyone solved this?

[Amit Goyal]

Here is the complete solution:

[Rob]

i dint understand the 4th step in this ques. plzz explain if anyone can do.thnks

[Amit Goyal]

Given the information, the first (N-1) of Y_1, Y_2, Y_3, ... , Y_N are less than x/2 and the Nth is greater than x/2. Therefore, Given the info, the conditional distribution of all random variables from Y_1 to Y_(N-1) is the same and equal to uniform U(0, x/2) and of Y_N is U(x/2, 1) and the forth line follows from this.

[Rob]

Thanks a lot sir ,..sir one thing i want to noe from where i can practice these type of questions

[shar311]

Hey guys, Please help me with this one..

Series 01, Q3 (Fixed point question). In the solution given by Amit Sir, function g(x) has been assumed as f(x)-x. Now later to prove that g(x) has a fixed point, it has been stated that g(a)>=0 and g(b)<=0 (x belongs to [a,b]). How do we come to this conclusion?

Series 01 Q6-10, I have a doubt, maybe a very trivial one which isn't clicking but would like members to help me clear it out. "Agent 1 strictly prefers bundle (a,b) to bundle (c,d) if, either a > c, or a = c and b > d." does this mean it is a case of perfect substitutes? Because while solving demand for 'x' by agent 1 is m1/px while that of 'y' is zero.

Any help would be much appreciated.
Thanks.

[Sris]

it means the person lexographically prefers x to y....

between two bundles he will demand  the bundle that has more of x...and if two bundle has same amount of x ...he will prefer the bundle that has more y..

so dd for x= total income/price

and dd for y= zero..

google for further details

[throwaway]

@shar311 : Q3  - g(a) = f(a) - a.
Now it is given that the function's range is also [a,b]. This means that f(a) belongs to [a,b]. Thus it can be either equal to a, or bigger than a (but less than b). Which means f(a) >= a, and hence g(a) <= 0.

Similarly for g(b).

[shar311]

Thanks a lot guys..:)

[himanshu890]

please elaborate it properly
i can not  figure out the the information given in the question
please help


DSE 2014
Q39

[Amit Goyal]

Detailed Solutions to DSE 2014 exams are posted here:
http://economicsentrance.weebly.com/lessons.html