Look at this electricity bill, Andy.

- Wow! That's a lot.
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In this short dialogue, what is the part of speech of 'a lot'?

1. The electricity bill is a lot.
(Is this sentence grammatical? What other expressions can we use instead of 'a lot'?)

In the dialogue, "a lot" is a noun phrase.

http://dictionary.reference.com/browse/a%20lot?s=t

Sentence 1 is OK, but it'd read better if you write this:
The electricity bill is really high.

The part of speech of 'a lot' in this dialogue is a noun phrase, specifically functioning as a subject complement.

Regarding the grammaticality of the sentence "The electricity bill is a lot," it is not technically incorrect, but it might not convey the intended meaning. More commonly, we say "The electricity bill is a lot of money" or "The electricity bill is very high." These expressions highlight the idea that the bill amounts to a large sum of money or that it is significantly higher than expected.