axioman comments on How Low Should Fruit Hang Before We Pick It?

[axioman]

I do not understand your proof for proposition 2.

[TurnTrout]

Is there any particular part of it that seems locally invalid? Can you be a little more specific about what’s confusing?

[axioman]

Where does

$$u\left(\overline{a}\text{'}\right)-\frac{I\left(\overline{a}\text{'}\right)}{R_1}=u\left(\overline{a}\right)-\frac{I\left(\overline{a}\right)}{R_2}$$

come from?

Also, the equation seems to imply

$$R_1=R_2$$

Edit: I focused too much on what I suppose is a typo. Clearly you can just rewrite the the first and last equality as equality of an affine linear function

$$R\to R$$

at two points, which gives you equality everywhere.

[TurnTrout]

Oops, you’re right. I fixed the proof.

[OBajgar]

I would also suggest changing the last sentence of the proof to “since otherwise one of the plans wouldn’t be optimal”. (the next natural step my internal autocomplete expected in the proof was substituting back to the first equation, and I kept wondering for quite a while what the unspecific “one of them wouldn’t appear” means in that context)

[OBajgar]

And if you’ll be editing: there’s probably also a typo in the second paragraph of the Technical Appendix: a confusing “N” instead of an “R” .

[TurnTrout]

fixed, thank you.