Something like this is impossible to achieve outside of maybe one retargeting because there are several variables moving all at the same time.

Here's some quick-and-dirty to make some estimates:

http://blockexplorer.com/q/probabilityThat webservices link returns the probability of any given hash being successful based on the current difficulty.

Your hashrate expressed as hashes/s multiplied by 86400 seconds in a day tells you how many tries you get to solve a block every day.

If we call those P and H, based on the expected value theorem your average BTC income per day (not counting tx fees or pool fees, which could be estimated in if desired) --

P * H * 86400 * 25

P * H * 86400 itself basically tells you what fraction of a block on average per day you would win

Taking that original model, call the BTC/USD exchange rate E.

Your dollar revenue will on average equal:

E * P * H * 86400 * 25

Setting this equal to $50 and doing the algebra yields --

H = 1 / (E*P*43200)

For $50 right now that requires about 700 GH/s just ballparking 1 BTC = $600.

This relationship breaks down very quickly unless BTC price and difficulty increase perfectly in tandem.