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
A = 0 c=1/(AK)=1/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
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?
... and the ones that won't