You should use ‘increasingly’. Adverbs are used to modify adjectives, and that is what the sentence needs. We could reword the first part of the sentence this way:
- The role the economy plays in our daily lives is increasingly important.
That means that the role is becoming more and more important.
The only way you could use the adjective 'increasing' would be if you added the word 'and' (or at the very least a comma):
[i]an increasing [b]and[/b] important role[/i]
That would change the meaning to this:
[i]- The role the economy plays in our daily lives is increasing and (it is also) important.[/i]
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[i][size=75]"I find it very difficult to relax. I find it increasingly difficult to find outlets for my frustration." ~ Judd Nelson[/size][/i]