Question

Given the out put Q= 2LogL + 4Logk, PL =$4, PK =$12.

Price of the goods is given Po.

A. Find the derive demand function for labour and capital.

B. Establish the supply function

C. Determine the expansion path expression for labour and capital

Answer 1

Product function Q= 2logL +4log K

Deriving the input demand law for both L and K:

$\frac{\delta Q}{\delta L}=\frac{2}{Lln10}+4logK$

$\frac{\delta Q}{\delta K}=lnL+\frac{4}{Kln10}$

 Supply function for the firm product:

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

Q=2log4+4log12=5.52

$\therefore$ 5.52=𝑄$_{s}$ (𝑃)

Q$_{s}$=$\frac{5.52}{P}$

expansion path expression for labour and capital

$\frac{\delta L}{\delta K}=-\frac{PK}{PL}$

$\frac{\delta L}{\delta K}=-\frac{12}{4}$

$\frac{\\{2}{Lln10}+4logK}{\ lnL+\frac{4}{Kln10}}=-3$