Under the efficient contract model, the unions and firms bargain over employment and wages. It states that level of employment maximizes joint income of the firm and workers while, wages level represents pure transfer between them. This joint income of the firm and workers is maximized when marginal value product equals its outside opportunity wage. Considering that this is correct, and then it means that employment is not dependent on firm-specific wage rates but rather depends only on the alternative wage rate. Thus, in the contract efficient model, the labor is allocated between contract employment and outside opportunities based on shadow value which varies with both alternative wage rates and firm-specific.
Now, if we assume that a union’s utility only depend on the wage rate and not the level of employment, under the efficient contract model, wages in the industry increases leading to the increase of the union’s utility. This is because, objective have been place on the wages and not employment. That is, the union will gain higher utility than the firms.