Rising player salaries is a large part of the cause. When baseball players won the right to sell their labor to the highest bidder (free agency, see Flood v Kuhn,) salaries increased dramatically. For a good take on the case, baseball's 'reserve clause' (a contractual clause that effectively forced a player to stay with a club as long as the club wanted him,) and the effects of the Flood decision, see Snyder, A Well-Paid Slave. It's a little legalistic, but highly informative. Kind of required reading if you're into baseball history.

There are a bazillion sites out there that discuss the rise in salary. Google something along the lines of 'baseball player salaries 1900-2000' to see the quite dramatic rise after the Flood decision and the Congressional Act (The Curt Flood Act of 1998, Public Law 105–297 OCT. 27, 1998) that ensconced the decision in statute.

There are of course other factors at play, too. The most simple of these is that people are apparently quite willing to pay the prices clubs charge.

EDIT: date typo