Question

A firm has been the product function Q= InL +2Ink. Derive the input demand law for both L and K in term of the product price P when the facor prices are PL =2, Ok =8. Hence derive the supply function for the firm product given the out as a function of the product price .

Answer 1

Product function Q= InL +2Ink.

Deriving the input demand law for both L and K:

$\frac{\delta Q}{\delta L}=\frac{1}{L}+2lnK$

$\frac{\delta Q}{\delta K}=lnL+\frac{2}{K}$

 Supply function for the firm product:

Basic form of a supply function is 𝑄=𝑄𝑆(𝑃)

Q=ln2+2ln8=4.85

$\therefore$ 4.85=𝑄$_{s}$ (𝑃)

Q$_{s}$=$\frac{4.85}{P}$