jnu 2003 doubts.plz help

[akanksha]

Q 4.  In an economy where capital and labour are the only factors of production
For a particular period
capital stock-1000,  output capital ratio-0.4,employment-200,wage rate-1..calculate the rate of profit
a. 5%
b.10%
c.20 %
d.not enough information to calculate the rate of profit


Q 29.A and B own equal no. of camels.Price of camel is same as the total no. of camels owned by A and B.Price of sheep is 10 and price of goat is greater than 2 and less than 10.Together A and B sell all the camels.The amt. of money they obtain by selling the camels is just sufficient to buy an odd no. of sheep and 1 goat.Determine the price of the goat.

[Homer Simpson]

4) i think its (d) - not sure about this!
29) price of goat = 6

[The Villain]

Please mail me the paper if anyone of you have it..

[akanksha]

@tsuki
can u plz explain hw did u do the 2nd q

[Homer Simpson]

Let X,Y,Z denote camel, sheep and goat

given, Px = Xa + Xb (Sum of quantities of both owners A and B)
             = 2Xa (Xa = Xb)

  Rx (Total revenue) = Px (Xa+Xb) = 4(Xa)^2

Now given that this revenue is just sufficient for an odd number of sheep and 1 goat, along with 2<Pz<10

      4(Xa)^2 = 10Y + Pz  (clearly, Xa has to be a positive integer for this to hold)

       10Y can take values like 10, 30, 50, 70, 90...
       i need to choose some 2<Pz<10 such that RHS is a perfect square divisible by 2
       The only possible choice is Pz = 6

[akanksha]

ok,,i got it !
tahnks tsuki

[bhavya jain]

@tsuki
In Q) 4, cn't we proceed in this way-
K=1000, Y/K=0.4. from this we get Y=400. so profit=Y-N.w= 400-200=200..

[akanksha]

ya..even i thought the same bhavya..but wont the rate of profit cm out to be 50 per cent which is not matching with any of the options??  

[bhavya jain]

yes..bu definitely it cn't be d)..someone plz help on this..
Sir, plz help.

[Anjali]

Great Tsuki ! :-)
For 1st I guess , it's c !

[Homer Simpson]

i am confused about 1. whats your reasoning?

[Anjali]

Profit rate = output-wage cost/ capital invested

[Homer Simpson]

thanks Anjali. got it now!

[akanksha]

guys can you please try out these ques. too.ill be highly greatful

Q.9    in a rectangular array (matrix) of distinct positive numbers, which has m rows and n columns, let x denote the largest of the smallest number in each column [i.e., x = maximum of I x j I, j belongs to {1,2...n} and x, is the smallest number in column j} and y the smallest of the largest number in each row [i.e., I yI,j belongs to {1,2...m} and y is the largest number in row i. then one can infer

(a) x > y
(b) y > x
(c) x >=y
(d) None of the above

Q.15.    Given a set of five distinct real numbers, the ZONK of the set is defined to be the average of the maximum and the minimum numbers in the set. Given a set of ten distinct real numbers, the GRAND ZONK of the set is defined to be the maximum of the ZONKs of all possible subsets of five real numbers included in this set. What is the GRAND ZONK of the set consisting of the first ten positive integers?

(a) 7.5
(b) 5
(c) 2.5
(d) None of the above

Q.25     A price taking firm makes machine tools (Y) using labour (L) and capital (K) according to production function : Y = L^0.25 K^0.25. Labour can be hired only at the beginning of every month. Wage rate = rental rate of capital = 10.
given the above information, the short run (week) TVC of producing Y machine tools = 10 Y^4/K * where the amount of capital is fixed at K*. In the long run (month) when both inputs can be varied, the
TC= 20 y^2

a) At the beginning of the month of January, the firm is making long - run decisions given that the price of machine tools = 400. What is the long- run profit max no. of machine tools? How many units of L and K should the firm hire at the beginning of January?

b) Suppose at the beginning of the third week of January, the price of machine tools increases to 691.20. What is the new short run profit max. level of Y. How many extra unit of L will the firm hire for the rest of January?

Q.27    A community of fishermen has access to a lake. the cost of sending a boat out to the lake = 1. Should "b" fishermen go out to catch fish (ie there are b boats on the lake), the total fish caught is
f(b)=10 b ^0.5.The price at which fish can be sold is 2. This price unaffected by the level of the catch from the lake.

a)  If a fisherman stays home,his net income =0. If he goes of to the lake his net income is (market Value of his catch - cost of 1) A fisherman takes the action (stay home or go to the lake) that maxijmises his net income. In equilibrium how many boats will be on the lake?

b)  The community decides to set a pre-boat fishing tax of t..what is the total tax collected by the community. ?
 

[Dreyfus]

For q9..I m getting x=y therefore none of the above ..I did this by two different arbitrary matrix!

[Dreyfus]

Q25 a) Y=10 L=K=100

[akanksha]

@vaibhav
 i m getting y as 10..but how did u get L and K..by differentiating profit function  with respect to labour and capital..?? what s the procedure.?

[Dreyfus]

Long run Tc=20y^2=10K+10L
And Y=(LK)^¼
And for q27..I m getting b=100

[akanksha]

k..thanx  a lot vaibhav...
do u know whats the tax rate cuming out 2 be.. m getting t as 10/b^0.5 -1..
what value of b should i put here..???

[Dreyfus]

For this I m getting total tax collected i.e. bt as 100t/(1+t)²
I just modified the total cost from b to b(1+t)