Why paper money has greater value than its production cost?

Answer 1

At least in the U.S. that is not a true statement. It costs only a few cents to make a paper bill, so the production cost is always less than the bill's value.

Perhaps you are thinking of small-denomination coins such a the cent or nickel, which use enough metal to be worth more than their actual face value (depending of course on how much the metal costs change at any given time).

You also may be thinking of the problem with $1 bills due to the huge demand for them. Even though each bill only costs 6 or 7 cents to make, $1 bills wear out so quickly (18-20 months) that the government had to open a second printing plant in Texas just to keep up with demand. That's why some people are calling for the $1 bill to be abolished and replaced with the new $1 coins that will last 30-50 years instead.