It was early noted that the Phillips Curve explanation of wage dynamics lacks a solid microeconomic basis. As the explanatory unemployment variable in the Phillips relation is intuitively to be regarded as an indicator of labour scarcity, several authors have argued that the determination of factor shares (the wage/profit ratio) ought to be the logical intermediate step between unemployment and wage inflation. Contributions by Kuh, Solow and Stiglitz in the late sixties follow this line of thought. As soon as wage-setting by firms instead of the impersonal forces of excess demand has been considered, problems have arisen, however. Given the ubiquity of diminishing returns to labour in the short run in static economic models, it is hard to derive the desired result that the wage share increases when unemployment falls. Monopolistic price-setting among firms can only yield such a result, if arbitrary rules for mark-up pricing are enforced. Even more disappointing, the temporarily monopsonistic firm of labour market search models has been shown to increase its (real) wage, when it faces larger flows of unemployed job applicants. The aim of this paper is to show that search theory easily yields the result that factor shares turn in favour of wages, when unemployment falls. The only important prerequisite for this result is that money wages are treated as downward rigid. The analysis remains valid when firms experience constant returns to labour in the short run (up to a capacity limit or to a demand constraint). In fact, my analysis predicts that with such a simple, but presumably relevant, production technology, factor shares are determined by the stock of unfilled vacancies, which in turn is partly determined by the unemployment stock. As intuition says the share of wages in value added increases with the stock of vacancies and decreases with unemployment.