\frac{A^{1-\beta_I}}{c_I(1-\beta_I)}\left[1-\left(\frac{1-\beta_I}{\beta_L-\beta_I}\right)c_L\beta_LA^{\beta_L-1}\right]\equiv f(A) = t | \frac{A^{1-\beta_I}}{c_I(1-\beta_I)}\left[1-\left(\frac{1-\beta_I}{\beta_L-\beta_I}\right)c_L\beta_LA^{\beta_L-1}\right]\equiv f(A) = t |