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Free-disposal and CR of scale can not imply convex production set. But it is true for single-input and single-output model. Therefore, I am wondering how to prove if production set Y satisfies free-disposal and constant returns of scale, then Y is convex when there are only 2 commodities.

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  • $\begingroup$ free disposal means that you can have any output that is equal or less than the maximum possible output for any given input. CRS functions are linear. The set is convex in a trivial sense. Think carefully about how to use the mathematical definitions of these three ideas (CR, free disposal, convex set) so that you can use the first two to show that you satisfy the third. $\endgroup$ – 123 Oct 9 '18 at 18:26

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