What is the economic interpretation of this utility function? I have a utility function $U(c,l)={{C^\alpha-1}\over {\alpha}}+{{l^\alpha-1}\over {\alpha}}$ where C denotes consumption, l denotes leisure. What is the economic interpretation of the term $\alpha$ ($\alpha&lt;1)$? Does changes in $\alpha$ affect the economic interpretation of the utility function as a whole?

The full problem is to derive the optimal labour supply. I get the answer $L={{1}\over {1+[w(1-t)^{{\alpha}\over {\alpha-1}}]}}$ where t represents  the tax rate. I am trying to understand the effect of $\alpha$ on the labour supply as I increase the tax rate $t$. How can I intuitively explain the role of $\alpha$ in this case?
This looks like constant relative risk aversion (CRRA) utility . Usually CRRA is written like $U = \frac{C^{1-\rho}-1}{1-\rho}  $ (I omitted second part for brevity) in your case $a=1-\rho$. $\rho$ is the relative risk aversion. By extension $a$ is the function of $\rho$ so as $a$ increases (due to smaller $\rho$) the person should become less risk averse.