We consider a neoclassical growth model where labor collectively chooses labor share to maximize its steady-state wage rate. In the basic two-factor model, labor maximizes the steady-state wage rate by setting labor share equal to the elasticiTY of output with respect to labor. This is precisely the competitive outcome. Only when we consider the model with organized and unorganized labor types can organized labor raise its steady-state wage by choosing a higher than competitive labor share. Organized labor can benefit by choosing a higher labor share only at the expense of unorganized workers; not capital. We also analyze a version of the model that incorporates a tradeoff between collective bargaining opportunities and skill acquisition. All else equal, a higher skill premium leads organized labor to choose a higher labor share. Organized labor benefits again at the expense of skilled workers; not capital.
