Timeline for Micro: proving that cost minimizing input vector for producing y cannot produce more than y
Current License: CC BY-SA 4.0
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| Jul 14, 2021 at 16:18 | comment | added | Dayne | Fair point. We basically need an assumption that ensures that the lower boundary for V(y) is excluded in V(y') which is what you did very explicitly. In texts I think this assumption is introduced, indirectly, through production function. | |
| Jul 14, 2021 at 5:07 | comment | added | tdm | I'm not sure your argument is correct. Negating the statement in the question does not allow you to find an $x^\ast$ for all $y'$ and $y$ with $y' > y$ (but just for one of them). As a counterexample, let $V(0) = \mathbb{R}^n_+$ and let for all $y > 0$, $V(y) = \{x\in \mathbb{R}^n_+| x \ge 1\}$. Then your assumption is satisfied, but the condition in the question is not as for all $y' > y (>0)$ we have $V(y) = V(y')$. | |
| Jul 13, 2021 at 10:04 | history | answered | Dayne | CC BY-SA 4.0 |