Table 1.

Utility functions and derivatives.

	Quadratic	CRRA
Level	${\alpha }_{1}c-\frac{{\alpha }_2}{2}{c}^2$, α1,α2 > 0	$\frac{c^{1-\sigma }-1}{1-\sigma }$, σ > 0
u′	α1 − α2c	c−σ
u″	−α2	−σc−σ−1
u‴	0	$(\sigma +1)\sigma c^{-\sigma -2}$