{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:10:23Z","timestamp":1760058623152,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2025,4,14]],"date-time":"2025-04-14T00:00:00Z","timestamp":1744588800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>The aim of the first part of this paper is to show whether a set of Proper Efficient Points and a set of Pareto Efficient Points coincide in Euclidean spaces. In the second part of the paper, we show that supporting prices, which are actually strictly positive, do exist for a large class of exchange economies. A consequence of this result is a generalized form of the Second Welfare theorem. 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