Confusion with interpreting NHK title and subject scope when using て form


I read [this article on
NHK](https://www3.nhk.or.jp/news/easy/k10014270341000/k10014270341000.html)
about Christmas cakes and it has this title:

> クリスマスのケーキ 卵の値段が上がって高くなりそう

But I'm somewhat confused on how to properly interpret the title. I'm not sure
what 高くなりそう (seems to have become expensive) applies to. Does it apply to 卵の値段
(price of eggs) or クリスマスのケーキ (Christmas cakes)?

Currently I read it as

> Christmas cakes. The price of eggs have gone up and they (the price of eggs)
> seem to have become expensive.

But I'm not sure if this is correct since its seems like it could also easily
mean:

> Christmas cakes. The price of eggs have gone up and they (the Christmas
> cakes) seem to have become expensive.

How does the て form of 上がって effect the scope of the subject(s) here?

Should it be treated as a whole singular thing like 卵の値段が上がって高くなりそう? And the
subject used with 高くなりそう in this case is 卵の値段? This is how I currently
interpret it.

Or should 卵の値段が上がって高くなりそう be treated as 2 separate chunks like 卵の値段が上がって (the
price of eggs have gone up) and 高くなりそう (X seems to have become expensive). And
because 高くなりそう has no explicit subject, the X in this case defaults to
クリスマスのケーキ? This the other way it could be interpreted it seems.

If its interpreted this second way, why is that the case? As I would think
that 高くなりそう would be connected to 卵の値段 since its set as the subject in the
first part with が.

Would the meaning change if the title was just 卵の値段が上がって高くなりそう without any
mention of クリスマスのケーキ? Or would this be an incomplete sentence then since
高くなりそう would not be connected to anything?




I'm answering each question from your sentences.

Q. Does it apply to 卵の値段 (price of eggs) or クリスマスのケーキ (Christmas cakes)?  
A. クリスマスのケーキ(Christmas cakes).

Q. How does the て form of 上がって effect the scope of the subject(s) here?  
A. I feel no effect. If the sentence was "クリスマスのケーキ 卵の値段が上が **り、** 高くなりそう",
高くなりそう would apply to クリスマスのケーキ.

Q. Should it be treated as a who...  
A. You should treat it two seperate chunks.

Q. And because 高くなりそう has no explicit subject, the X in this case defaults to
クリスマスのケーキ?  
A. Partially yes. An explicit subject is just クリスマスのケーキ. **Subjects may stand
without が or は, especially in news headlines.**

Q. If its interpreted this second way, why is that the case?  
A. (I think the former answer is the one to it.)

Q. Would the meaning change if the title was just 卵の値段が上がって高くなりそう without any
mention of クリスマスのケーキ? Or would this be an incomplete sentence then since
高くなりそう would not be connected to anything?  
A. That would be felt an incomplete sentence. In my opinion, that's because
上がる&高くなる mean the same thing, but they are different words. Japanese language
don't hate repetition of the same words, so those who read it will think that
高くなりそう don't apply to 卵の価格, and will think that the subject of 高くなりそう is
missing.

