DMP: Two Labor Markets
Found my mistake. I guess I'm not allowed to move the thetas to the other side.

Define $q^{-1}$ be the inverse of $q$. Then,

$$ \theta = q^{-1} \left( \frac{c}{J} \right)$$

$$ \frac{W_1}{W_0} = \frac{f(\theta_0)}{f(\theta_1)} = \frac{f \left( q^{-1} \left(\frac{c}{J_1}\right)\right)}{f \left( q^{-1} \left(\frac{c}{J_0}\right)\right)}$$ 

$J_1 &gt; J_0$, hence $\theta_1 &gt; \theta_0$ and $W_1 &lt; W_0$.