Try this solow model ques....

[Akshay Jain]

 
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  

[RajEco]

1. c

[Dreyfus]

I m also getting c for 1.....

[Dreyfus]

Nd a for 2..

[SoniaKapoor]

Raj,Vaibhav...how did you get c....plss help

[Dreyfus]

Just write steady state eq first interms of per labour output nd per labour capital.....den apply log nd differentiate it with respect to t nd solve for dk/dt*k..

[Akshay Jain]

The correct answers are 'c' for 1st nd 'a' for 2nd

[SoniaKapoor]

Vaibhav my answer is not matching .Please help me with solution.

[Dreyfus]

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[Anjali]

Thanks vaibhav . Please explain second part !

[SoniaKapoor]

Thanxx vaibhav..

[Dreyfus]

Steady state growth rate of k obtained in 1 is embedded with growth rate of labour.....thus the steady state growth rate of output per capita is the steady state growth rate of k  less growth rate of labour,n, and for this growth rate rate to b positive use inequality

[Anjali]

Yeah the 1st one is inclusive of technology also . But Iam not getting the question - why to reduce only growth labour parameter , why not technology parameter ?

[Anjali]

Akshay plz help me with the second part !

[Akshay Jain]

after getting the steady state level of capital/worker k*, compute steady state output per worker y* same as what u do in solow model.
Take logs both sides and dn differentiate it w.r.t. time t...you vl get (dy*/dt)/y*=growth rate of output per worker in steady state=some expression.....now this expresssion must be greater dn 0 for growth rate to be positive......u vl get condition "a" after solving...try this out else vl upload.....:)

[Anjali]

See first we will take the steady state equation :
Change in k = s * y-( dep+n+g ) *k
So at steady state change in k will be 0
Then we will take log and differentiate , that will give us growth rate
Now my equation is coming as
Growth rate of steady state capital = growth of output per worker
I guess Iam going wrong !

[Akshay Jain]

[SoniaKapoor]

Thanx Akshay :)