Demand Signalling Under Unobservable Effort in Franchising: Linear and Nonlinear Price Contracts

We study the signalling strategy of a principal who is privately informed about its high demand potential to an uninformed risk-neutral agent. We analyze the model in the context of a contract between a franchisor and a franchisee. We examine the distortions of a two-part pricing scheme necessary to credibly inform the franchisee (agent). We also study whether the inability of the franchisor (principal) to observe the agent's effort moderates or exaggerates the distortions from the first-best two-part pricing scheme. A surprising outcome is that even though the principal incurs greater signalling cost, the magnitude of distortion in the two-part scheme is smaller when service is unobservable than when it is not. Thus, a signalling strategy employing the fixed and variable fees is harder to detect under moral hazard. Empirical studies failing to control for moral hazard may incorrectly conclude that signalling strategy does not occur. We later consider a three-part scheme to verify whether or not the scheme reduces signalling cost. Interestingly, we find that there exists a unique three-part scheme that results in the first-best profit even in the presence of two-sided information asymmetries. While the two-part scheme can never achieve the first-best profit, the three-part scheme always achieves the first-best profit. The costless three-part separating scheme relies on variable income to induce the agent to undertake first-best service. The reliance on variable income to alleviate moral hazard contrasts with the two-part scheme's focus on reducing the variable income to overcome the inability to monitor. The finding provides additional empirical implications.