The Excelsior Acquisition - S3-E16
Plot hole: In Series 1, Episode 7, "The Dumpling Paradox, " Sheldon makes an oblique reference to his financial status: "Frankly, if I could afford the rent, I'd ask you [Leonard] to leave, " meaning he cannot pay the rent on his two bedroom apartment by himself - not that he doesn't want to, he can't. However, in "The Execlsior Acquisition, " we find that he does not even cash his pay cheques. He doesn't even deposit them into a bank account - he leaves them in a drawer in his desk. In Series 2 Episode 14 "The Financial Permeability", he lends Penny a large amount of money from a huge bankroll he just happens to have lying about - again, without cashing his pay cheques! He is obviously independently wealthy. Either he doesn't have enough money to afford the rent or he has enough to work without being paid while practically giving large amounts of cash away. Can't be both.
Suggested correction: Not being able to afford doesn't necessarily mean he doesn't have the money, especially a man like Sheldon. He works with a budget and he sticks to it. In his budget he has a certain amount set aside for rent, anything more than that and he can't afford it alone.
Nonsense. If he was sticking to a "rigid budget" he wouldn't have even thought of lending a hopeless credit risk like Penny a single cent. Instead he throws a huge bankroll at her without even discussing a repayment plan.
Rubbish, I stick to a strict budget but still have the money to lend to close friends. Like Penny is to him.
He might have different budgets for different things. People could get a higher margin because they could be of more use to the scientific mind of Sheldon.