The firm maximizes per-period profits
The union targets the same real wage Wt (i) for each of its members in order to maximize this objective function (since members’ preferences, the way their labor enters into the firm’s technology and the weight the union places on their welfare are all symmetric, it is optimal for the wage to be the same for all members). To try to achieve the desired real wage, the union sets the rate of increase of the nominal wages of its members at the start of every period, and cannot alter it later when the rate of increase of the price level becomes known. The real wage for worker i at time t is given by
One can think of ф as an indicator of the degree of competitiveness in thi labor market: the larger ф, the more elastic the demand for each union’s labor and the smaller its monopoly power. It is often asserted (Calmfors and Driffill 1988) that competition in the labor market is increasing in the number of unions In this context that may or may not be the case.