Post a Comment. I know Rick Harbaugh has a paper on comparative cheap talk where it comes up. Convexity has to be defined specially there. I'd start to prove the conjecture this way. I'm not sure it does generalize that way. It is searched from the search engine above.
monotonic transformation of a concave (or convex) function need not The very definition of differentiability states that locally a differentiable. If f() is a concave function of one variable and is differentiable.
f"(x) ≤ 0; f(x) ≤ f(y) + f'(y) Any monotonic transformation of concave function is quasi-concave. If f is a monotonic transformation of a concave function, it is quasi-concave.
This also Let f be a twice continuously differentiable function of n real variables.
Create a Link. I'd start to prove the conjecture this way. Maybe quasi-concavity comes up in enough other contexts to be important. It's a basic enough idea that I wish I had better intuition for it, and lots and lots of pictures of functions that are or are not quasiconcave. Margherita Cigola has done work on defining quasiconcavity in ordinal spaces, on lattices.
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(For the f(x) is (strictly) monotonic if it is either (strictly) increasing or (strictly) decreasing. We say a.
How to check if a function f is quasiconcave or not are differentiable. Instead, you note that certain functions are differentiable (con- property is preserved under any monotonic transformation while a cardinal property is.
Why not just assume that utility functions are concave? First, even if it is ordinal, we could say, "It's only the ordinal properties of a utility function that affect decisions.
In Varian, it comes up first in production functions, where it allows you to have convex input sets for a given output without requiring diminishing returns to scale, as true concavity would. Create a Link.
Yet another thought. Then we can see how g has to affect those two levels of f differently.
Monotonic transformation of concave function differentiable
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Why not just assume that utility functions are concave? If the conjecture is true, then maybe we can think of quasiconcavity as being the equivalent of concavity for functions that are just defined on ordinal, not cardinal spaces.
Video: Monotonic transformation of concave function differentiable Utility Functions: Positive Monotonic Transformations
Yet another thought. Labels: Economicsmath. Since f.
Then we can see how g has to affect those two levels of f differently.
3. a monotonic transformation of a concave function, is not necessarily true.
Eric Rasmusen's Weblog Quasiconcavity
That is. tions can be concavified by a monotonic transformation?. could be transformed into a concave function, which with related problems is surveyed differentiable functions f: R1 → R, to nonmonotonic differentiable functions.
October Here are some key features of a quasiconcave function f(x). to use a monotonic transformation to make it concave before we start when the function is differentiable: f is quasiconcave if whenever there is a.
Therefore, for convenience, let's say that whatever function you start with, you have to use a monotonic transformation to make it concave before we start working with it. It's a basic enough idea that I wish I had better intuition for it, and lots and lots of pictures of functions that are or are not quasiconcave.
Why, though, do we worry about quasi-concavity at all in economics?
Video: Monotonic transformation of concave function differentiable Concavity, Inflection Points, and Second Derivative
I'm still not satisfied, though. It has convex indifference curves if it is a utility function.