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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...
M.A Economics
Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com |
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Is it c? For the first part?
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In reply to this post by 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????
M.A Economics
Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com |
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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 |
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In reply to this post by Sumit
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 |
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@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 :'( |
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Yes using basic equation will do.u can express it in terms of growth rates and then proceed
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@pbansal-can u please show it?
thank you |
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In reply to this post by Sumit
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. |
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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...?? |
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In reply to this post by shanks
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...?? |
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hey sakshi!
you are differentiating the equation with respect to what? |
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hi xiang !
i m differentiating with respect to time "t" m i wrong..?? |
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how to get the denominator :'(
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