What effect does the hiring cost have on the wage bargaining outcome (wage curve)?
In Cahuc, Carcillo, and Zylberberg: Labor Economics, they derive the following wage curve: $$w = z + (y-z) \frac{\gamma[r+q+\theta m(\theta)]}{r+q+\gamma \theta m(\theta)}$$
where $z$ = unemployment benefit, $y$ = marginal product of labor, $\gamma$ = bargaining power of the worker, $r$ = interest rate, $q$ = rate of exogenous job destruction, $\theta$ = labor market tightness, $m(\theta)$ rate of job filling.
On the other hand, following Pissarides (2000) we get the following wage curve: $$w = (1-\gamma)z + \theta \gamma c + \gamma y$$ where $c$ = hiring cost.
The first wage curve (from Cahuc et al.) would suggest that $c$ does not affect the wage curve while the second one (from Pissarides) would suggest that it does.
My thoughts so far are: 1. The wage curve tells us the outcome of bargaining but $c$ does not affect bargaining because $c$ is only directly relevant for $\Pi_V$ (the employer's outside option) but $\Pi_V$ is always zero in equilibrium. Therefore, the employer's outside option is not any worse if $c$ is higher. 2. In deriving the wage curve, Pissarides substitutes labor demand into the wage curve. So, $c$ enters the Pissarides' wage curve only through labor demand and not in any other way, suggesting, again, that bargaining itself is unaffected by $c$.
So, what is the effect of a change in $c$ on the wage curve? Does an increase in $c$ shift the wage curve?