Rubinstein2005-page98

Rubinstein2005-page98 - 5 Z is a convex set(This assumption...

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October 21, 2005 12:18 master Sheet number 96 Page number 80 80 Lecture Seven Figure 7.1 The following restrictions are usually placed on the technology space (fig. 7.1): 1. 0 Z (this is interpreted to mean that the producer can remain “idle”). 2. There is no z Z K + besides the vector 0 (no production with no resources). 3. Free disposal : if z Z and z z , then z Z (nothing prevents the producer from being inefficient in the sense that it uses more resources than necessary to produce the same amount of commodities). 4. Z is a closed set.
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Unformatted text preview: 5. Z is a convex set. (This assumption embodies decreasing margi-nal productivity. Together with the assumption that 0 ∈ Z , it implies nonincreasing returns to scale : if z ∈ Z , then for every λ < 1, λ z ∈ Z .) The Production Function Consider the case in which commodity K is produced from com-modities 1, . . . , K − 1, that is, for all z ∈ Z , z K ≥ 0 and for all k 6= K , z k ≤ 0. In this case, another intuitive way of specifying the techno-...
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