There are several theories of the distribution of national income between wages and profits. In the neo-classical model factor prices equal their marginal products, and the factorial distribution of income depends on the elasticity of substitution between labour and capital. The Kaldorian theory suggests that the wage share depends on the share of investment in output. In Discussion Paper No. 288, Research Fellow Michael Beenstock presents an alternative explanation, based on the Union Bargaining Model. In the UBM unions and management bargain over wages and employment; unions represent the interests of their median member. Beenstock assumes that each worker has an equal chance of being fired and that capital and labour are perfect substitutes.
The expected utility function of the median union member defines an indifference curve between real wages and employment. Profit maximization by the firm also defines a relationship between wages and employment. The intersection of these curves defines the `contract curve', along which efficient wage bargains might be struck. In this model the real wage must always exceed its marginal product, and so the wage share must always exceed the level implied by the neo-classical model. Risk aversion on the part of the median voter and diminishing marginal returns in the production function imply that the contract curve must have a positive slope. If unions are stronger they secure both more wages and more jobs, the wage gap increases and so does the wage share.
In practice, however, the factors that are responsible for changes in bargaining power are likely to induce shifts in, as well as movements along, the contract curve. Beenstock therefore considers the effects of exogenous shocks on the distribution of income in the UBM. His analysis suggests that while movements along the contract curve have unambiguous effects on the factorial distribution of income, shifts in the curve do not. Together they suggest that the overall effect of greater union power on wage and profit shares will be ambiguous.

To resolve this ambiguity Beenstock investigates the case of an increase in unemployment benefit, which tends to strengthen union power because it reduces the cost of unemployment to laid-off workers. He calculates the wage shares at the upper and lower limits of the `bargaining core' (i.e. the range of wage and employment combinations over which unions and employers are prepared to cooperate), and measures their sensitivity to changes in unemployment benefit. He uses a production function in which factorial shares are independent of factor proportions, so that any changes in the wage share must reflect shifts in the contract curve. Investment does not form part of the bargaining strategy. The calculations reveal that at the upper and lower limits of the bargaining core the wage share is insensitive to changes in unemployment benefit: the effects of movements along the contract curve are likely to dominate any potentially offsetting effects from shifts in the contract curve.
An important assumption of the analysis is that all workers have the same employment prospects and that seniority does not exist. In the seniority version of the UBM the wage is set equal to the marginal product of the worker with median seniority; this would undermine the central result of the paper. Nevertheless, Beenstock concludes that the UBM offers a competing paradigm to neo-classical and Kaldorian theories of factorial income distribution, and in a unionized economy where collective bargaining is cooperative may be of greater practical relevance

The Factorial Distribution of Income in the Union Bargaining Model
Michael Beenstock

Discussion Paper No. 288, March 1989 (AM)