The economic literature dealing with vertical contracts with two part-tariffs is extensive. However, very few works have considered these contracts in an uncertain environment (see Rey and Tirole, 1986). To our knowledge, there is neither a general theoretical framework nor experimental work that analyze risk sharing in this setting.
First, we elaborate a general theoretical framework incorporating a vertical contract offer with uncertainty about the realisation of the final demand. The contract offerer (Proposer) proposes a two part tariff contract (w, T) to be taken or left to the contract receiver (Responder), with w the variable part and T the fixed part of the contract. The utility functions of the Proposer and the Responder of the contract consider risk aversion and conform to the expected utility theory. For any utility function having the properties of a Von Neuman Morgenstern, the model predicts that w is used to share risk such as w is positive (whereas w is null in a certain environment).
Second, we run a lab experiment in a perfect strangers matching design to assess the model propositons. In the experiment, we control for the subjects' risk aversion by performing a risk test (Eckel and Grossman, 2002). We propose treatments that vary the level of demand uncertainty.