Question: I applied Early Decision to a private university and got accepted. Unfortunately, it's an expensive school that my family doesn't want to pay for. If I get into another, cheaper university, such as the public university in my state which would be much cheaper, before I submit my deposit, is there a way I can avoid a penalty for backing out of the offer?
Did you apply for financial aid from your ED university? If you did--and if the aid you received doesn't make this college affordable--then you can withdraw for financial reasons without penalty, if you do so immediately (or you can appeal the aid award before you bail out entirely). You cannot, however, wait more than a month to find out if you were admitted to other potentially less expensive colleges and then say, "No thanks" to your ED school.
If you did NOT apply for financial aid from the ED college, then it is unethical for you to withdraw now since, presumably, you and your family knew what the cost would be before you applied and you signed the ED agreement anyway. However, if you are determined to withdraw, you can write to the admission office and tell them that your family's financial situation changed significantly since you applied and now you cannot afford to enroll. The admission officials will probably let you wheedle out of the commitment. (But if your family's situation has NOT changed, then you need to recognize that you are not being honest in saying that it has. The lie should get you out of the ED commitment but it might bring some bad karma with it!)
If you are going to do this, you must do it right away. And you should first warn your guidance counselor of your plan. At the time that you applied ED, your counselor was required to sign a statement confirming your commitment to your ED university. So this is something you should discuss with your counselor before taking further action. If your counselor is angry at you for not honoring your commitment, it could affect your future recommendations (if any are pending) or the counselor may even refuse to send transcripts to additional schools. So you and the counselor need to get on the same page before you say anything to the ED school.
Ultimately, if a student tells a college that he or she can't honor an ED obligation for financial reasons, the college probably won't pursue the matter. But you should not take your signed ED commitment statement lightly.