Reference Dependence and the Structure of the WTA/WTP Gap

Abstract

This paper studies the willingness-to-accept/willingness-to-pay (WTA-WTP) gap under objective probabilities. Preferences over finite lotteries satisfy completeness, transitivity, continuity, weak independence, reference partition, and range dependence. Weak independence requires von Neumann-Morgenstern independence only for mixtures that preserve the reference point and do not move outcomes across the induced gain-loss partition. The representation, weak rank-dependent utility (WRDU), evaluates gains and losses by separate subutilities anchored at the reference point and recombines them through a range-dependent Lagrangian penalty coefficient \r{ho} on the loss-side component. The reciprocal index ${\lambda = 1/\rho}$ reports the WTA-WTP loss-aversion convention. The main result characterizes a normalized admissible transaction class in which the WTA-WTP gap follows from the asymmetric buying and selling indifference equations. In this class, ${\lambda} > 1$ suppresses WTP and elevates WTA, while $\rho > 1$ corresponds to gain seeking or loss attenuation. A fixed reciprocal loss-aversion index has no internal mechanism that makes the wedge converge to zero as transaction scale changes; attenuation requires a transaction path on which $\rho > 1$ and $\lambda$ converge to their common neutral value one. The analysis gives a decision-theoretic account of the endowment-effect wedge based on weakened independence, reference anchoring, semi-affine subutility normalization, and range-dependent penalization. The result is distinct from the Rabin calibration implication and does not rely on constant-relative-risk-aversion utility or probability weighting.