A Theory of Wages and Labor Demand With Intra‐firm Bargaining and Matching Frictions*

Abstract

This article provides a model of labor market equilibrium with search and within-firm strategic bargaining. We yield explicit closed form solutions with heterogeneous labor inputs and capital. The solution exhibits overemployment. We show that higher relative bargaining power for some groups of workers may lead to overemployment relative to other groups, with such other groups being underemployed instead if they have a lower relative bargaining power. Similarly, the hold-up problem between capitalists and employees does not necessarily lead to underinvestment in physical capital.Beyond the neo-classical analysis, firms are the field of several strategic interactions between capital owners and labor, between marginal employees and incumbents, and more generally between different groups with various bargaining positions within the firm. It is usually considered that the bargaining power of workers entails an employment level that is lower than in a competitive labor market, and any increase in the bargaining power of workers raises unemployment. These results are true for a wide class of models, and notably in the now standard framework to analyze unemployment, namely search and matching models of Pissarides (2000). However, Stole and Zwiebel (1996a, 1996b) show that the above results are totally changed in the intra-firm bargaining model, where employees engage in individual wage negotiation with the firm. In fact, under the assumption that contract incompleteness does not enable either party to commit to future wages and employment decisions, they show that intra-firm bargaining yields no rent for employees and gives rise to overemployment compared to a competitive labor market. The basic idea of Stole and Zwiebel is that a firm with a diminishing marginal productivity of labor can decrease the bargained wage, which increases in the marginal productivity of labor, by raising employment. In Stole and Zwiebel's setting, firms overemploy strategically, up to the point where workers get their reservation wage. * Manuscript

Population Aging, Migration Spillovers, and the Decline in Interstate Migration

“…14 An alternative to this setup is to have large firms and study the intra-firm bargaining as in Cahuc et al (2008). The advantage of this framework is to allow for a nontrivial complementarity between workers of different types, which is shown to have some empirical support in Wasmer (2003).…”

Do Matching Frictions Explain Unemployment? Not in Bad Times

“…By the same logic, there is full employment in the absence of recruiting costs in models using different bargaining procedures (Cahuc et al 2008;Elsby and Michaels 2008;Hall and Milgrom 2008;Rotemberg 2008). Shimer (2004) and Hall (2005a) introduce wage rigidity into search-andmatching models, in the form of a constant real wage.…”

“…The SZ model, characterized by Assumptions 3 and 4, retains the key elements of the large-firm search-and-matching models with diminishing marginal returns to labor and the Stole and Zwiebel (1996) intra-firm bargaining procedure studied in Cahuc et al (2008) and Elsby and Michaels (2008).…”

Employment and Hours of Work

“…In principle, the bargaining problem selects the appropriate function from a set of admissible functions to maximize the Nash product, and the first-order condition is exactly (10).…”

“…This mechanism also operates in our framework. 2 Bertola and Caballero (1994), Bertola and Garibaldi (2001), Cahuc and Wasmer (2001), and Cahuc et al (2008) also developed search models incorporating large firms. See also Kudoh and Sasaki (forthcoming).…”