Solow Modal Question!!!! Amit Sir & Duck plz have a look....

[Sumit]

Consider an economy with production function
Y = K^α*T^β*(AL)^1−α−β
where K, A, L are, as usual, capital, technological progress and labour and T is the stock of land. α, β > 0. A grows at rate g and L grows at rate n. The stock of land is fixed though. Aggregate saving equals a fraction s of aggregate output. Assuming K depreciates at rate δ
Derive the steady state growth rate of capital
a)      K./K = (1-α-β)(g+n)/(1-β)
b)      K./K = (1-α-β)(n)/(1-β)
c)      K./K = (1-α-β)(g+n)/(1-α)
d)      None of these

Derive the condition when steady state growth rate of output per worker is positive.
a)      (1-α-β)g > βn
b)      (1-α-β)g < βn
c)      (1-α-β)g = βn
d)      None of these

PLz help...

[Devika]

Is it c? For the first part?

[Sumit]

Hi Devika,
I don't have the answers.
Could you share how you approach the question(Small hint will also work)....
Also are you Mathematical getting option c) or Is this just a best guess????

[Devika]

Both actually. I solved for the steady state capital, but the expression wasn't really reliable. Also, total capital will grow at the rate of n+g.
I should stop the guesswork x_x

[PBANSAL]

I THINK THE PRODUCTION FUNCTION SHOULD BE THIS
 K^α*T^1−α−β *(AL)^B
AND YOU WOULD GET THE SOLUTION FROM HERE,USING
GROWTH EQUATION .GROWTH OF OUTPUT WILL BE
B(N+G)/1-A
WHERE B=BETA AND A=ALPHA

[Xiang]

@pbansal- can u please show the steps?

should we just use the basic identities - 1) k/f(k)=s/del(k) or 2) s[f(k)]=(del+n+A)k?

Please tell how to solve these sums :'(

[PBANSAL]

Yes using basic equation will do.u can express it in terms of growth rates and then proceed

[Xiang]

@pbansal-can u please show it?

thank you

[shanks]

i) The question is correct. Answers are "C" and "A".

 Just take the log and differentiate wrt to time. Further manipulations are easy and will lead the result.

 Use A./A = g & L./L = n.

 to find K./K only relation between Y./Y and K./K is to be found. which is easy.


ii) For second part divide both sides by L to get Y/L on LHS. Again take log and use previous result to find the    answer.

[sakshi]

SHASHANK CAN U EXPLAIN A LITTLE MORE....
IN first question i m geeting till
Y./Y= A K./K+ (1-A-B)(g+n)
also in second part
y./y=A K./K+ (1-A-B)g + (-A-B)n
where A=ALPHA
B=BETA
y=Y/L
PLZ EXPLAIN WHAT 2 DO NEXT...??

[sakshi]

SHASHANK CAN U EXPLAIN A LITTLE MORE....
IN first question i m geeting till
Y./Y= A K./K+ (1-A-B)(g+n)
also in second part
y./y=A K./K+ (1-A-B)g + (-A-B)n
where A=ALPHA
B=BETA
y=Y/L
PLZ EXPLAIN WHAT 2 DO NEXT...??

[Xiang]

hey sakshi!

you are differentiating the equation with respect to what?

[sakshi]

hi xiang !
i m differentiating with respect to time "t"
m i wrong..??

[Xiang]

how to get the denominator :'(