What is the significance of Relative Risk Aversion

I know that the relative risk aversion is defined as

$$R(c) = cA(c)=\frac{-cu''(c)}{u'(c)}$$ where $u(c)$ denotes the utility curve as a function of wealth $c$.

But I do not understand the intuition for it. Can you explain the intuition for relative risk aversion?

Answer

In utility theory the basic assumption is that $u(c)$ is strictly monotonically increasing in wealth: people prefer more over less. Hence, $\forall c, u'(c) > 0$. The second assumption is that the amount of utility added, as $c$ increases, diminishes, so $\forall c, u''(c) < 0$. Combining these two observations we have that

$$\forall c, A(c) = \frac{-u''(c)}{u'(c)} > 0.$$

This can be interpreted as follows, if for a particular $c$ $u'(c)$ is large $A(c)$ will be small. Thus if utility curve is sensitive to increases in wealth the risk aversion is low. For $u''(c)$ the reverse holds: if $u''(c)$ for a particular value of $c$ risk aversion will be low. $A(c)$ captures both sensitivities and also produces some kind of a trade-off between them.

The quantity $R(c)$ is just $A(c)$ scaled by the wealth. This scaling has the advantage that this quantity is not sensitive to a change in numéraire of $c$.

By the way, the Wikipedia page is excellent.