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.