Given $$U(c,1-h)=log\left (c-\frac{Bh^{1+\gamma}}{1+\gamma} \right ),$$
where $B>0$,$\gamma \geq0$, $h$ denotes the household's optimal labour supply and $c$ denotes consumption. The budget constraint of the household is $c=wh + W$, where $w$ is the real wage and $W$ is wealth.
I have to find out why the labour supply curve will not be negatively sloped.
My attempts: I have solved for optimal choice of labour supply, $$h^{*} = \left (\frac{w}{B} \right )^{\frac{1}{\gamma}}$$.
To find the slope, I have taken the derivative of the labour supply with respect to $w$.
$$\frac{\mathrm{d} h^{*}}{\mathrm{d} w} = w^{\frac{1 - \gamma}{\gamma}} \frac{1}{\gamma B^{\frac{1}{\gamma}}}.$$
So I need to show that $\frac{\mathrm{d} h^{*}}{\mathrm{d} w} \geq 0$ to show that the labour supply curve will not be negatively sloped. Any hints on how to proceed would be greatly appreciated.