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How to show that labor is essential in the Solow Growth Model Watch

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    I am currently stuck on a problem. To show that labor is essential i.e. F(K,0)=0 for all finite K>0 (A=0)

    Currently I have

    cY=F(cK,cAL)

    A = 0 c=1/(AK)=1/K

    Y/K=F(K,L)/K

    F(K,L)/K = 0

    For all L>0, L<Infinity, if F (K,L) doesn't tend to infinity, when K tends to infinity, it is bounded by some finite number

    Therefore,

    Lim K-> Infinity F(K,L)/K = 0

    If it does tend to infinity when K tends to infinity, due to L'Hopitals rule and the Inada conditions,

    Lim K-> Infinity F(K,L)/K = Lim K-> F(L) (K,L) = 0

    Due to Constand Returns to Scale, for finite L,

    Lim K-> infinity F(K,L)/K = Lim K-> Infinity F(1, L/K)

    = F(1,0) = 0

    Using CRS again,

    F(K,0) = KF(1,0) = 0

    for all finite K>0. Hence, proving that labor is essential.

    Can you check this for me please?
 
 
 
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