I don't quite understand what you're trying to do, but I think you need to input a number into your system. Here's why: Consider two households, Alice and Bob. Alice reports a surplus of P=2 based on income of $11,023 and expenses of $11,021. Your research finds that her expenses are only $11,019, so her actual surplus is R=4. I think we can agree that Alice is truthful.
Bob reports a surplus of P=20,000 based on income of $30,000 and expenses of $10,000. Your research finds that his income is actually $50,000, so his actual surplus is R=40,000. I think we can agree that Bob is falsifying his income.
Both of your examples of criterion depend only on the ratio of P and R, so that Bob and Alice have the same output.