In May, Jodi Beggs wrote an interesting article about rationing free goods. A local Baskin Robbins gave away free ice cream. Understandably, lots of people showed up, among them Jodi Beggs who snapped these pictures.
Beggs concluded, "that's a damn long line for a $4 item." Beggs then gave the standard opportunity cost story: If you value your time at $10 per hour -- as you would if you had a job that paid $10 per hour -- each hour in line would cost $10 because that's what you could otherwise earn while waiting in line.
In this post, I want to take this reasoning further:
If everyone values their time at $10 per hour, the equilibrium wait time for a "free" $4 cone would have to be 0.4 hours or 24 minutes. Then, how many people should we expect to see standing in line? That depends on the efficiency of the Baskin Robbins workers:
- What if each person adds two minutes to the wait time? Then, we'd expect the line to have 12 people in it.
- What if each person adds 30 seconds to the wait time? Then, we should see 48 people standing in line.
This idea came from an economist named Yoram Barzel in a 1974 academic paper entitled "A Theory of Rationing by Waiting," which was published in The Journal of Law and Economics. There's a whole lot more to the Barzel paper: namely, he covers the case where people have different costs of waiting in line, the case where people can buy as much as they want when they get to the front of the line, and other cases.
But, without going into the messy heterogeneous details, the point is: Depending on how long it took for the Baskin Robbins employees to dispense each ice cream cone, that horrendously long line actually might be the "right" length.