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Monotone Allocations without Single-Crossing: When to Bunch and When to Jump

  • Aloisio Araujo
  • Carolina Parra
  • Sergei Vieira
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Abstract

We study one-dimensional screening when the Spence-Mirrlees condition fails along a monotone dividing curve, on which all types value marginal output equally. A single ratio, marginal distortion over marginal rent, governs the problem. When the relaxed solution stays in the positive region, non-decreasing optima in the positive single-crossing region are continuous if the ratio increases in the decision. When it crosses a flat curve and marginal rents are separable, every continuous contract is improved by a jump. When it crosses a strictly monotone curve, a contract that pools and jumps continues along the mirror of the pool if the ratio does not increase along it. Optimality among all implementable allocations, deterministic or random, is proved by a measure on the binding constraints whose weights are the same ratio; with constant curvatures and no crossing, it is also necessary. As applications, we solve problems of procurement and nonlinear pricing.

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Cite

BibTeXRIS
BibTeX
@misc{araujo2026monotone,
  title = {{Monotone Allocations without Single-Crossing: When to Bunch and When to Jump}},
  author = {Aloisio Araujo and Carolina Parra and Sergei Vieira},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.19474},
  eprint = {2608.19474},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.19474},
}
RIS
TY  - UNPB
TI  - Monotone Allocations without Single-Crossing: When to Bunch and When to Jump
AU  - Aloisio Araujo
AU  - Carolina Parra
AU  - Sergei Vieira
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2608.19474
UR  - https://arxiv.org/abs/2608.19474
AB  - We study one-dimensional screening when the Spence-Mirrlees condition fails along a monotone dividing curve, on which all types value marginal output equally. A single ratio, marginal distortion over marginal rent, governs the problem. When the relaxed solution stays in the positive region, non-decreasing optima in the positive single-crossing region are continuous if the ratio increases in the decision. When it crosses a flat curve and marginal rents are separable, every continuous contract is improved by a jump. When it crosses a strictly monotone curve, a contract that pools and jumps continues along the mirror of the pool if the ratio does not increase along it. Optimality among all implementable allocations, deterministic or random, is proved by a measure on the binding constraints whose weights are the same ratio; with constant curvatures and no crossing, it is also necessary. As applications, we solve problems of procurement and nonlinear pricing.
ER  -