1. ## Monotone

Is the function z=max(x,2y) monotone? I suppose it is monotone but not strictly montone, isn't it? Sry for posting this rather trivial question, but in our book the max function is described as not monotone, which seems rather weird to me.

Thanks

2. ## Re: Monotone

Originally Posted by Schdero
Is the function z=max(x,2y) monotone?
What definition of monotone (or monotic) are you using for a function $f:\mathbb{R}^2\to \mathbb{R}$ ?

3. ## Re: Monotone

Originally Posted by FernandoRevilla
What definition of monotone (or monotic) are you using for a function $f:\mathbb{R}^2\to \mathbb{R}$ ?
Are there various definitions? I thought if f(x)''>0 f(x) is strictly monotone, if f(x)''>=0 it is monotone (in both cases monotonely increasing to be exact). What alternative definition is widely accepted? My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences.

4. ## Re: Monotone

Originally Posted by Schdero
Are there various definitions?
Look here:

Monotonic function - Wikipedia, the free encyclopedia

My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences
I'm sorry, in that case I'm afraid I can't help you. Perhaps another member, let's wait.

5. ## Re: Monotone

Originally Posted by Schdero
Are there various definitions? I thought if f(x)''>0 f(x) is strictly monotone, if f(x)''>=0 it is monotone (in both cases monotonely increasing to be exact). What alternative definition is widely accepted? My example is in a book on econometrics. The question is, whether or not the indifference curves of the utility u=max(x,2y) represent monotone preferences.
What you give, f''> 0, is not a definition but as property. A function is strictly monotone increasing if and only if whenever x< y, f(x)< f(y). But that requires an order on the argument of the function. And there is no standard order in two dimensions.