Right on, Stuka.
In fact, I would expect a US $4,000 a month Captain to seek more than a 100% increase, since in the open market, the job is worth $8,000 to $10,000.
The fact that the company claims it cannot afford to pay you more merely indicates that you are subsidising the company to the tune of $4,000 to $6,000 per month.
You may choose to accept their statement at face value, but without access to their books they may be fooling you.
If you accept that they genuinely can't pay more, then you have to discuss how they want to treat your input of $4,000 to $6,000 per month. You could do anything from a straight commercial loan to low cost benefits like travel, etc.
The fact is, there is a going rate for everything, fuel, aircraft, insurance, etc, etc, and labour is just another commodity. If the company is getting the going rate for it's product (tickets) you should look to see why it can only survive with the subsidy on labour from the employees.
It must be paying over the going rate for something, or is being managed inefficiently.
Neither of these two options is your fault, so you must receive some recognition for your generous input into keeping the company going.