quasi linear utility function if you have a quasi linear utility function, for example $U(l,c)=c-l^{1+γ}/(1+ γ)$ the supply function of l is inelastic right? But can we extend this argument and say that any quasi linear function is going to give you an inelastic function of the non lineal good?
Forgot to mention the production function. But this is the function $y(l)=A(l)^{1-a}$. A is the productivity 
So if you take the efficiency condition  you get that $l=(A(1-a))^{1/(a+γ)}$
Thank you.

Thank you.
We solve the utility maximization problem of the individual whose utility function is $u(c, l) = c - \frac{l^{1+\gamma}}{1+\gamma}$ to get the supply function. The problem can be written as:
\begin{eqnarray*} \max_{c,l} &amp; &amp; c - \frac{l^{1+\gamma}}{1+\gamma} \\ \text{s.t.} &amp;&amp; c \leq wl\end{eqnarray*}
In this problem, we are assuming that the only source of income of the consumer is his wage income. When we solve the problem we get the labor supply function as:
\begin{eqnarray*} l(w) = w^{1/\gamma}\end{eqnarray*}
The elasticity of labor supply curve is this case is constant and equal to $\frac{1}{\gamma}$. Supply will be elastic if $0 &lt; \gamma &lt; 1$ and inelastic if $\gamma &gt; 1$.