If nothing else, the Dodgers have enough players to force the Rays to think long and hard about how their 2014 team would look without Price's 208 innings and 190 strikeouts, which is what he has averaged the last four seasons.
Is there a point at which the financial implications start to matter? Or do the Dodgers strive to win the World Series first and worry about money later?
They'll be tempted to do just that. To begin next season with a rotation that includes Clayton Kershaw, Zack Greinke and Price would make the Dodgers the National League's slam-dunk World Series favorites. That rotation is the equivalent of Koufax and Drysdale, plus Hershiser, to mix my Dodgers eras.
About the only downside is that sometime in the next two years, Kershaw and Price probably are going to sign the two largest contracts ever given to pitchers. Kershaw is a year from free agency, Price two.
These are the types of discussions that warm baseball fans through a long, cold offseason. That's especially true this year, at a time when four or five of the game's biggest stars could be on the move.
Some of it is related to contracts. Some of it is about filling needs. And in at least one case, a formerly happy marriage has become strained.
If you look at this offseason from a certain angle, you could see not only Price, but Max Scherzer, Brandon Phillips, Matt Kemp and Mark Trumbo all changing teams.
Let's run down the list:
Price: He made $10 million in 2013 and is about to get another significant raise through arbitration. And with the left-hander two years from free agency, this is the time for Tampa Bay to gauge his value.
The Rays did the same thing with James Shields a year ago and came away with a middle-of-the-order bat in Wil Myers. The Dodgers have enough high-end pitching to get Tampa Bay's attention.
The Rangers have enough Minor League depth to get a deal done, and a rotation that includes Yu Darvish, Price and Derek Holland would be as good as any.
Scherzer: If anyone is going to get more money than Kershaw and Price, it's this guy. The Tigers have $108 million committed to just six players in 2014, and Scherzer could double his $6.73 million 2013 salary after 21 victories, 214 1/3 innings and 240 strikeouts.
No general manager guards his intentions more than Detroit's Dave Dombrowski, but it seems likely he has already explored signing Scherzer to a long-term deal and is now going to gauge the trade market.
Phillips: One handy rule of thumb is to never, never rip your bosses in interviews. Phillips did just that, saying he found it strange the Reds found $225 million for Joey Votto after telling Phillips they didn't have that kind of money.
After another postseason disappointment, Cincinnati general manager Walt Jocketty was already looking to retool the club, and Phillips seems likely to go. Jocketty says he's not actively shopping Phillips, but he's clearly in a listening mode.
Kemp: The Dodgers have three veteran outfielders and youngster Yasiel Puig, and so one of the veterans -- Kemp, Andre Ethier or Carl Crawford -- seems likely to be moved. Kemp has by far the highest trade value. In fact, he may be the only one of the three who could get teams into a competitive bidding fight.
Kemp has missed 145 games the last two seasons and has six years and around $128 million remaining on his contract. If a potential trade cleared up payroll flexibility, cleared the logjam in the outfield and brought a combination of kids and big league-ready talent, the Dodgers probably would make the deal.
When he was last healthy -- in 2011 -- Kemp led the NL in home runs (39), RBIs (126) and total bases (353). For offensively-challenged teams, especially those with Minor League depth, Kemp could be the difference between missing and making the playoffs.
Trumbo: The Angels have zero interest in trading Trumbo, even though his 184 strikeouts and .234 batting average are troubling. But he may be dealt, anyway, because he's just 27 years old and has hit 66 home runs the last two years. The Halos are desperate to upgrade their pitching staff without increasing the payroll, so Trumbo could be the guy who helps the Angels acquire an arm or two.
Nothing is certain at this point in the offseason. But with so much parity in the game and with most teams hoping to avoid a luxury-tax bill, Price, Scherzer, etc., could end up being smart alternatives.
With the usual feeding frenzy expected over Jacoby Ellsbury, Shin-Soo Choo and other top free agents, the chance that so many stars would also be dealt has led to all kinds of chatter among general managers and their assistants.
How it plays out will be the fun part. Stay tuned.