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hi,
the cost function for long run is C=wL+rK, or C=10L+10K...now do constrained minimisation
Minimise C=10L+10K subject to Y=(KL)^0.5
you'l derive a relationship between L and K...substitute K in terms of L in production function, you shall get L=L(Y) this is the labor demand function and similarly find out K=K(Y) ....now just put these values in cost function C=10(L+K)..you shall get C=C(Y) the LR cost function ...
as far as i know the production function is Y=(LK)^0.25 from isi 2012 paper
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