\[
x_{1}=m^{b_{1}} p_{1}^{-a_{11}} p_{2}^{a_{12}}\left(m>0, p_{1}>0, p_{2}>0\right)
\]
The demand for good \( x_{2} \) is given by :
\[
x_{2}=m^{b_{2}} p_{1}^{a_{21}} p_{2}^{-a_{22}}\left(m>0, p_{1}>0, p_{2}>0\right)
\]
(Where \( b_{11}, b_{2}, a_{11}, a_{12}, a_{21}, a_{22} \) are positive constants, \( m \) is money income \( p_{1} \) and \( p_{2} \) are per unit prices of goods \( X_{1} \) and \( X_{2} \) respectively). Find the direct as well as the cross partial price elasticities of demand for both goods.
- Determine whether the goods are substitutes or complements.
