How does a difficulty increase affect a miner's income? At the time I write this, there are a lot of people getting into Bitcoin mining for the first time. Many buy ASIC hardware and are later surprised that their mining income suddenly drops due to a difficulty increase.

If I mine X bitcoins per day, then the difficulty goes up Y percent, how many coins do I get per day after this?

For instance, if my hashrate brings 1 BTC per day and the difficulty rises 30%, what is my average daily mining income with the same hashrate after this change in difficulty?
Your profit relates to the amount of hashing power you contribute to the network. Since your mining power is constant, your share of the total hashing power decreases relatively when the network's hashing power increases. I.e. we can deduce the following formula:

newProfit = currentProfit * currentDiff/newDiff.

At a currentProfit of 1BTC/d and a 30% increase in difficulty, you get: 

(1BTC/d)*100/(100+30)= (1BTC/d)/1.3 = 0.76923077 BTC/d

i.e. your profit decreases by ~23%.