When is there more employment, with individual or collective wage bargaining?

In a standard Diamond-Mortensen-Pissarides labour market with frictions, the authors seek to determine when there is more employment with individual wage bargaining than with collective wage bargaining, using a wage equation generated by the standard total surplus sharing rule. Using a Cobb-Douglas production function (AL, < 1), they find that if the bargaining power of the individual is high compared to the bargaining power of the union, there is more unemployment with individual wage setting and vice versa. When the individual worker and the union have the same bargaining power, if the cost of opening a vacancy is sufficiently high, there is more unemployment with individual wage setting. Finally, for a constant marginal product of labour production function AL, when the individual worker and the union have the same bargaining power, individual bargaining produces more unemployment.