Dividing goods or bads under additive utilities

We compare the Egalitarian Equivalent and the Competitive Equilibrium with Equal Incomes rules to divide a bundle of goods (heirlooms) or a bundle of bads (chores). For goods the Competitive division fares better, as it is Resource Monotonic, and makes it harder to strategically misreport preferences. But for bads, the Competitive rule, unlike the Egalitarian one, is multivalued, harder to compute, and admits no continuous selection. We also provide an axiomatic characterization of the Competitive rule based on the simple formulation of Maskin Monotonicity under additive utilities.