quasi linear utility function
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 $\gamma &gt; 1$.