NEED SOLUTION!!

[xyz]

Hey friends, kindly help me out with this problem. It would be great if you post the solution too. Thankyou in advance.

[kk]

(1) production possibility frontier(PPF)  is the maximum amount of both the goods that can be produced using the factors of production.
if 200 units of labour used in bicycle then b=√200 =10√2
and if all the labour is used in w then w=0.5√200 = 5√2  
 and since production functions are homogeneous the PPF is a straight line with intercepts 10√2 and 5√2 (b taken along y axis and w in x axis )
so the equation is b+2w = 20√2

[xyz]

Thankyou so much kk. Kindly explain other parts also.

[kk]

the second question is about competetive equilibrium.. a competetive equilibrium is one where ppf is  tangent to indifference curves and also tangent to budget lines. given utility of both consumers u=bw slope of id curves is db/db = -b/w
slope of ppf is -2 so -b/w =-2 therefore b=2w

putting it in the ppf equation we get w=5√2 and b=10√2 which is also the pareto efficient allocation
and (3) can be solved as (1) and (2) were solved

[kk]

can u please check the answers of ISI 2014 ( economics part) i have posted the answers of first 5 questions..pls check if you are getting the same answers..here is the link to my post
http://discussion-forum.2150183.n2.nabble.com/ISI-PEB-Economics-2014-ANSWERS-1-TO-5-td7595987.html

(
ISI PEB (Economics), 2014 ANSWERS 1 TO 5..)

[xyz]

Thanx a tonn kk. Yea i'll check your answers for sure. Just one more help. Could you please help me solving the other question which i've posted in my next post?

[Rajat]

kk and xyz.
I got the following ppf

b = sqrt(Lb) and w = 0.5sqrt(Lw)
squaring both sides, b^2 = Lb  and 4w^2 = Lw
Also Lb + Lw = 200
therefore we get b^2 + 4w^2 = 200
So this happens to be the ppf in this case.

I agree with KK's intercepts but did not understand why ppf should be a straight line connecting the two intercepts. The same points could also be connected by an ellipse which is the equation I have obtained.

[kk]

sorry..you are right..the ppf is not a straight line but concave to the origin..because of increasing opportunity cost..w should take into account opportunity costs.i had made a mistake by considering that homogeneous production functions have straight ppf

[Rajat]

ok.. so we agree on the ppf equation.

How to go about questions 2 and 3 ? does it make a difference who owns the firm and labour ??

[kk]

the procedure for second answer remains the same..competitive equilibrium takes place where the ppf is tangent to the indifference curves.that is where slope of the id curve is equal to that of the ppf. by equalising the slopes of both we get a relationship between bicycles and w..and putting it in the equation of ppf we get the competitive equilibrium
 in the 3rd question it is like international trade.looking at comparative advantages.
if they produce separately both can produce either 10units of b of 5 units of w (intercepts of ppf for each)
but if they produce jointly then they can produce either 10√2 b or 5√2 w..
so they will produce jointly.and since production functions for both goods are same for both and total labour is 200 the equation of ppf remains same as earlier