Please explain to me why the first sentence is correct, and the second, wrong:
「税金を無駄遣いしたあげく、消費税を引き上げるなんて許せない」（O)
「税金を無駄遣いしたものの、消費税を引き上げるなんて許せない」（X)
From my understanding, 「ものの」 is used to describe something as, "even though the fact is that ~", whilst 「あげく」describes how a bad result was observed even after having gone through a lot of effort for it. Thus, I do not understand why 「あげく」is used after 税金を無駄遣い, because wasting taxes does not seem like it implies "a lot of effort".
あげく is used to say something is continued up to some point of time only to end in an undesirable situation. What is continued doesn’t have to be effort. If it is, the final outcome that comes after あげく is most probably a failure. If it is already a bad thing, what happens at the end may be further deterioration or some other bad thing.
I found the following example in my dictionary.
彼は何度も事業に失敗したあげく、破産した。
After many failures in business, he went bankrupt.
Your example is structured this way.
［税金を無駄遣いしたあげく、消費税を引き上げる］なんて許せない。
Raising the rate of consumption tax is, as far as the speaker is concerned, a shocking development coming from the same people who have wasted tax payers’ money all this time.
ものの doesn’t work here. The sentence would be understood in the following way, with the clause ending with ものの adverbially working on 許せない in the main clause, not on 引き上げる. (I am not sure if "even though" works too well inside a content clause in English here, either.)
税金を無駄遣いしたものの、［消費税を引き上げる］なんて許せない。
Even though I (am the one who) wasted taxes, I (still) cannot accept they are going to raise consumption tax.
