Non-linear Sharing Rules

The e¤ect of a change in wealth on its allocation between two attributes is examined when they have both the same utility. We identify three classes of utility function that gen-erate non-linear sharing rules. The divergence between the two shares increases in absolute, average or marginal terms with the total amount of wealth, depending on whether DARA, DRRA and convex risk tolerance are considered. This result allows for a very wide range of applications, from the Arrow-Debreu contingent claims case to the risk-sharing prob-lem, including standard portfolio choice, intertemporal individual consumption, demand for insurance and tax evasion. ( Keywords: wealth-sharing problem; sharing rules; concavity; convex risk tolerance)