Log-log model with one explanatory variable

Problem

Our model is given by

\[y_i=β_1x_i^{β_2}ε_i\]

  1. Is this model linear in data? Is it linear in parameters?
  2. Take log of both sides and define \(β'_1=log β_1\) . Is the model linear in parameters? Is it linear in data?
  3. Show that \(β_2\) is the elasticity of \(E\left( y \mid x \right)\) with respect to \(x\) .

Solution