Efficiency in a search and matching model with right-to-manage bargaining

In a search and matching model with right-to-manage bargaining, matched workers and firms bargain over wages, given labor demand schedule of firms for hours worked per worker. Wages and hours worked per worker are determined as if they are determined in a competitive labor market with a distortion to wage markups. A positive inefficiency gap in the labor market diminishes workers' effective bargaining power relative to firms, because firms can adjust labor input and wage schedule via intensive margin. The Hosios condition does not necessarily hold even when workers' actual bargaining power is equal to unemployment elasticity of matches.