Academic journal article Economic Inquiry

Some Comments on Free-Riding in Leontief Partnerships

Academic journal article Economic Inquiry

Some Comments on Free-Riding in Leontief Partnerships

Article excerpt


Holmstrom (Bell Journal of Economics, 13, 1982 324-40) showed that freeriding is inevitable in partnerships where inputs are substitutes. Legros and Matthews (Review of Economic Studies, 68, 1993, 599-611) and Vislie (Journal of Economics Behavior and Organization, 23, 1994, 83-91) showed that when inputs are strict complements (Leontief technology), free-riding can be avoided with a linear sharing rule. This paper considers the robustness and some extensions of the positive result of these articles. First, I show that Legros and Matthews's and Vislie's results are not robust to the introduction of participation constraints and limited liability. However; I construct a novel rule that mitigates that problem. Second, I perturb the (deterministic) model of the other authors. It turns out that free-riding is avoidable with noise added to joint output and is inevitable when noise is added to individual productivity. (JEL C72, D20, D29, D82)


A long tradition in economics compares the performance of different ownership arrangements of firms. Capitalist firms are defined through separating ownership and production by having an outside owner, and partnership firms split the value of production in full between the partners. Building on Alchian and Demsetz (1972), the seminal paper by Holmstrom (1982) argues that partnership firms may suffer from free-riding problems. Holmstrom (1982) shows that efficient provision of effort is not consistent with Nash behavior in static partnership games where inputs are substitutes and actions are noncontractible. Capitalist firms, on the other hand, can mitigate the free-rider problems by a principal breaking the budget (i.e., keep some of the surplus for oneself) whenever one observes a low joint output.

Motivated by the many examples of partnerships in the real world, considerable literature has questioned the generality of Holmstrom's result. [1] The present article considers a particular branch of that literature; works that explore effort taking in Leontief partnerships, partnerships where joint output is determined by the partner with the least effort. [2] Legros and Matthews (1993, section 3.1) and Vislie (1994), hereafter abbreviated LMV, find that if production is determined in such a manner, there exists a linear sharing rule, denoted [[beta].sup.*], that implements the efficient provision of effort and hence eliminates free-riding. The intuition for this result is that, given that the other agents stick to the efficient action, no agent can gain by providing more effort (because output does not change) and can be made to support the full decrease in output since his deviation is proportional to the change in output.

The present article discusses the robustness of the implementation result of LMV in two different directions: by introducing participation constraints (and limited liability) on one hand, and by introducing noise in the production on the other hand.

Let me articulate why it is important to test for robustness along these two directions. First, the partnership literature has largely ignored whether a partnership can be expected to agree ex ante on efficient sharing rules (when such rules exist). The interesting problem is that a partner with a strong bargaining power may wish to settle on a non-efficient rule, if that gives him- or herself a greater return. Hence, it is of importance to have sharing rules that make provision of effort incentive compatible under any distribution of participation constraints, to distribute a large share of surplus to agents with strong bargaining power.

Proposition 1 (see below) constructs a simple sharing rule that solves the participation problem. This sharing rule, which is inspired by the Groves's mechanism, has the attractive property of implementing the efficient provision of effort under any conceivable distribution of participation constraints. …

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