The word "as" plays no important role. It can be omitted without changing the meaning: "We hope that the measures taken by the government will succeed."

You could say - such as those taken by the government.

In the sentence "We hope that the measures to control prices, as taken by the government, will succeed," the word "as" introduces an example or specifies the measures being referred to. It can be understood as "in the manner of" or "such as." The phrase "as taken by the government" clarifies that the measures to control prices are those implemented by the government. Using "after" would change the meaning and indicate a sequence in time rather than specifying which measures are being discussed. Therefore, "as" is the correct choice in this context.