Marginal effects an elasticities in the log-log model

Problem

\[y=f\left( x_2,x_3 \right)=β_1x_2^{β_2}x_3^{β_3}\]

1. Find \(∂y/∂x_2\) and \(∂y/∂x_3\)
2. Find \(\left( ∂y/∂x_2 \right)(x_2/y)\) and \(\left( ∂y/∂x_3 \right)(x_3/y)\)
3. Find \(log y\)
4. Find \(∂log y/∂log x_2\) and \(∂log y/∂log x_3\)