Experimental Tests of Solutions to the Double-Marginalization Problem A Reference-Dependent Approach

The \double-marginalization" problem associated with linear wholesale price contract has long been recognized as a threat to vertical channel coordination. Many solutions involving more complex contract formats have been proposed to address this problem. Extant economic theories predict these solutions to be revenue and division equivalent in that they all restore full channel e±ciency and give the same surplus to the upstream party assuming constant relative bargaining power. We conduct a laboratory experiment to test the empirical equivalence of two variants of a two-part tari® contract. The ̄rst variant charges the downstream party a ̄xed fee for participation and a uniform unit price. The second variant takes the form of a quantity discount contract with the total cost to the downstream party identical to that of the ̄rst variant for a given quantity. Surprisingly, the two-part tari® mechanism fails to solve the double-marginalization problem even in a well-controlled market environment. Both variants of the two-part tari® do not achieve full channel e±ciency; they are statistically no better than the linear wholesale price contract. Revenue equivalence fails because the second variant achieves a higher channel e±ciency than the ̄rst variant. Also, division equivalence does not hold because the second variant accords a higher surplus to the upstream party than the ̄rst variant. To account for the observed behavior, we allow the downstream party to have a referencedependent utility in which the upfront ̄xed fee is framed as loss and the subsequent contribution margin as gain. We derive a new set of theoretical predictions and estimate a structural model to infer the degree of loss aversion as well as the reservation utility of the downstream party. The estimated loss aversion coe±cient is 1.6 and the reservation utility ranges from 8% to 14% of the e±cient channel pro ̄t. We rule out other plausible explanations such as parties having fairness concerns and non-linear risk attitudes.