CPC goes up after raising the budget

I wanna run a campaign for likes and intend to get it for 2 cents/like. The problem is, after spending much on testing and finally getting it for 2 cents, whenever I try to increase the budget the CPC goes up as well. What can I do to avoid this and maintain the CPC after raising the budget? Should I just let the ad run anyways? I usually start at $4/day and then change it to $12/day. Hope anyone can help. Thank you

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