This paper analyzes a model with many homogeneous agents, whose effort can be allocated to two tasks. One task produces a public good that is an important input for the production of the final output. The other task only affects the agent's own output. We show that, when the public input and the private input are complementary, the principal should offer a fixed-wage contract to some agents and a revenue-sharing contract to the remaining agents. Furthermore, we show that, when the ex ante contracts are subject to ex post renegotiation, agents with the fixed-wage contract should not own any asset, whereas agents with the revenue-sharing contract should own the physical asset in which the private input is embedded. Meanwhile, the principal should retain residual rights of control over the public good. This paper offers an explanation of the co-existence of company-owned units and franchised units in a franchise company. It adopts and extends important features from both the multi-task theory of the firm and the incomplete-contract theory of the firm.
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