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

1. 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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