workers reach a balance point, it is stable and developing for both parties. That reciprocal behavior generates efficiency gains has been confirmed by several other papers e.g. Berg, Dickhaut and McCabe (1995) - even under conditions of double anonymity and where actors know even the experimenter cannot observe individual behaviour, reciprocal interactions and efficiency gains are frequent. Fehr, Gächter and Kirchsteiger (1996, 1997) show that reciprocal interactions generate substantial efficiency gains. However the efficiency-enhancing role of reciprocity is, in general, associated with serious behavioural deviations from competitive equilibrium predictions. To counter a possible criticism of such theories, Fehr and Tougareva (1995) showed these reciprocal exchanges (efficiency-enhancing) are independent of the stakes involved (they compared outcomes with stakes worth a week's income with stakes worth 3 months’ income, and found no difference). As one counter to over-enthusiasm for efficiency wage models, Leonard (1987) finds little support for either shirking or turnover efficiency wage models, by testing their predictions for large and persistent wage differentials. The shirking version assumes a trade-off between self-supervision and external supervision, while the turnover version assumes turnover is costly to the firm. Variation across firms in the cost of monitoring/shirking or turnover then is hypothesized to account for wage variations across firms for homogeneous workers. But Leonard finds that wages for narrowly defined occupations within one sector of one state are widely dispersed, suggesting other factors may be at work. Efficiency wage models do not explain everything about wages. For example, involuntary unemployment and persistent wage rigidity are often problematic in many economies. But the efficiency wage model fails to account for these issues. Mathematical explanation Paul Krugman explains how the efficiency wage theory comes into play in a real society. The productivity of individual workers is a function of their wage , and the total productivity is the sum of the individual productivity. Accordingly, the sales of the firm to which the workers belong become a function of both employment and the individual productivity. The firm's profit is Then we assume that the higher the wage of the workers become, the higher the individual productivity: . If the employment is chosen so that the profit is maximised, it is constant. Under this optimised condition, we have that is, Obviously, the gradient of the slope is positive, because the higher individual productivity the higher sales. The never goes to negative because of the optimised condition, and therefore