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@joshua posted:

May I know what is the difference between (1) and (4)?

Is the "(as)" indicating we can omit it or add it in the sentence?

"As" is optional. There is not much difference between using and omitting it. I think "as" sounds more idiomatic, while it will be omitted immediately after a noun if the participle refers to the noun:

- The original budget constraint is (as) shown in the diagram shown below. (I do not recommend repeating "shown" — I'm only using it twice for pedagogical reasons.)

Last edited by Gustavo, Co-Moderator

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