ISI 2011 ME 2

[tim]

hi,
cn someone pls help me solve Q8 part b ?

[lovekesh]

Mine is coming 15%. write down the equations of MPL and MPK in terms of Y, L, K. then write another growth accounting equation of the production function. Solve the equations and i got 15%.

[ritu]

hi lovekesh can u post ur answers for all parts. of 8th...and ur approach again..pls:)

[tim]

i tried the way u told..and still nt gettng d answer...cn u pls write the equation. ?
and one more thing..where to put the value of price of the good (5%)

[ritu]

pls reply lovekesh....

[lovekesh]

y=AK^0.5L^0.5
MPL = y/2L
MPL=real wage
y-L = w ( read these as rates instead of absolute values)
y-k = r
w-r = k-L----(a)
from production function
y= a+1/2K+1/2L-----(b)
these are growth rates
put y=w+L in eqn b
and put k from eqn a in equation b
w+L = a+1/2(w-r+L) + 1/2L
L gets cancelled
a= (w+r)/2
w=25 real wage growth
r= 5 real rental growth rates
a= 15

[seema]

answer of ques 9 ?

[tim]

thnk u lovekesh.

just wanted to confirm one thing - u subtracted price of the good from wages (30-5).
ans is that wat uve put in the eqn ?

[ritu]

lovekesh why have u taken wage to be equal to average product of labor?????in a perfectly competitive economy
p.MPl=w
p.mpk=r
??m i wrong????

[Tania123]

Can someone also explain Q2(b) what's the reasoning for the difference in consumption?

[Dr. Strange]

case 1: when they pay their own bill,
utility function is cobb douglas
so x1=M/2px=x2,    y1=M/2py=y2

CASE 2: when they divide the bill,

budget equation for 1,
py * y1 + px(x1+x2)/2 =M
U=x1*y1
substitute y1 in U
differentiate wrt x1 and equate to 0
same thing do for x2
we will find x1=x2=2M/3px
y1=y2=M/3py

Since both consumers think that only half of the load of anything that they order (that they wouldn't order when they were eating alone) would fall on them, they wastefully end up spending too much on food and end up with a lower utility.
Hence consumption of x for both decreases.