Thursday, July 11, 2013

The Colorado Car Dealership's Dilemma

Thanks to an excellent column in Sunday's Denver Post by Dave Maney, I now know why we did none of our recent car shopping on Sunday.  In Colorado, car dealerships are prohibited from being open on Sundays.  He also offers an interesting explanation for the law:
Car dealers can't open for business on Sundays in Colorado, even though Sunday shopping for everything else is now deeply ingrained in our culture. That's because of Title 12, Article 6, Part 3 of the Colorado Revised Statutes, unabashedly called the "Sunday Closing Law." It says, simply, that you can't have a car dealership open on "the first day of the week commonly called Sunday." Really? Those darn legislators! Is it to keep us all religiously observant and mindful of the Sabbath, or does it help car dealers keep costs down by being open only six days a week?
If you have taken a standard economics class, you'll recognize the basic structure of the game that the car dealers are playing with one another.  It is the prisoner's dilemma!  

To give some numerical context, suppose that two dealers are competing with one another, Mazda and Ford, and that the only margin of competition is whether they choose to be open on Sunday.  Suppose that weekly revenue is $70,000 if both Mazda and Ford are open on Sundays.  If both dealerships are closed on Sunday, they still each make $70,000 per week because car shoppers just adapt to the inconvenience.  However, if one dealership is open on Sunday and the other is closed, that dealership gets all of the business for the day: Open $80,000; Closed $60,000 (note: I'm assuming $10,000 per day in revenue).

Suppose also that each day of being open costs the dealership $5,000.  Then, both Ford and Mazda make $35,000 in weekly profit if they're open on Sundays, but they each make $40,000 in weekly profit if they're closed on Sundays.  On the other hand, if Ford is open on Sunday, but Mazda is closed,  Ford makes a profit of $45,000 ($80K-$35K) while Mazda makes a profit of $30K ($60K-$30K).  Here are the payoffs summarized in a normal form game:


As you can see from the game, Mazda has an incentive to be open if Ford is Open ($35K > $30K) and if Ford is Not Open ($45K > $40K).  The same applies to the Ford dealership.  In the language of game theory, both have a dominant strategy to be open on Sunday.  That is, the Nash equilibrium is (Open, Open) with payoffs of ($35K, $35K), even though both Ford and Mazda would make greater profit if neither dealership were open.  

From the standpoint of the dealerships, there is a strong incentive to steal business from the other dealership by opening on Sunday.  This is a dilemma because if the dealerships could coordinate on not opening on Sunday, both would be better off (at the expense of consumer convenience).  And, what better way to coordinate around closing on Sundays than to pass a law that prohibits being open.

I'd like to close with one observation on the realism of this explanation.  Maney's description acts as if car dealerships have a lot of costs to save by not being open on one day of the week, but as we all know, car salesmen work on commission.  Commission sales means a large fraction of the costs that dealerships are independent of when the dealership is open: it doesn't matter to the dealership's cost (or a salesman's earnings) how much was sold on Sunday versus other days of the week.  

Sure, car dealerships have other costs that depend on being open, but labor costs have to be important to their bottom line.  Given this observation, car dealerships strike me as an odd industry to be motivated enough by cost savings to insert this legal provision into the Colorado code.  On this basis, I would expect not-on-Sunday provisions to be more common among non-commission industries, but in Colorado, this provision is specific to car dealerships.  Perhaps it is the Sabbath that closed Colorado car dealerships after all.

2 comments:

  1. don't you think that by being closed on sunday it increases the scarcity of the good and therefore the price? I know, sunday is the only day i have to shop....

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    Replies
    1. I tried to abstract from price effects. For one, it makes the analysis of interesting strategic effects a little simpler, and I wanted to focus on the Prisoner's Dilemma setup.

      For another, it isn't clear that being closed on Sundays increases scarcity, and therefore, the price. As I mentioned in a previous post on the matter, it is useful to do some shopping while not in the presence of a car salesman. Given that car lots are usually in open air, you can do plenty of window shopping on car lots on Sunday, but salesmen aren't allowed to be there (and you can't technically work out a deal on Sunday afternoon). Moreover, car dealerships being closed on Sundays doesn't reduce the number of cars that are available to be sold, so even on this measure, I'm not sure that this makes cars more scarce.

      It's possible that being closed on Sundays improves the dealership's bargaining position, but I'm not clear on how this would increase bargaining power (especially given more shopping time while salesmen are not around).

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