isi 2012

[seema]

A price taking firm makes machine tools Y using labour and capital according to the following production function Y = (LK)^0.5
Labour can be hired at the beginning of every week while capital can be hired only at the beginning of evry month. Its given that wage rate=rental rate of capital=10. Show that the long run (month) cost function is 20Y^2.

[s]

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

[seema]

ya i got it nw. thnx :)
& yes it is (LK)^0.25