| Maybe it cancels out somehow? Let's put in some concrete numbers to see if it does. Specifically, let's say that people value the ability to buy raspberries at $1.00, which means that they value their time at $0.01 per place-in-line (so waiting in a line of 100 people costs $1.00 of their time, and as such joining a line of 100 people would involve a $1.00 benefit (buying raspberries) for a $1.00 cost (waiting in line) and so 100 people long is the point where anyone is indifferent to joining the line. Before the coffee is introduced, the first person in line receives $1.00 in value, the second receives $0.99, and the hundredth receives $0.01, and the 101st does not join at all, for a total of $50.50. Now add in the coffee which costs $1.00 and is valued at $0.75. This causes the line to get longer by 75 people. The first person in line receives $1.75 in value, the second receives $1.74, the 175th receives $0.01, and the 176th does not join at all. This is a total of $154.00, which is $103.50 more than the total value of the line before the coffee was added (at the cost of the government spending $175.00 on coffee). Which yields a social cost of $71.50. Which is not $100. Hm. If I replace $1.00 as the value of buying raspberries with $5.00 (and so the cost of waiting one place in line is $0.05), the numbers work out as line length 100 -> 115, total value $252.50 -> $333.50, cost of coffee $0.00 -> $115.00, which yields a social cost of $34.00. Which is not only "not $100" but also isn't even the same as the last value. Maybe the assumption is that, say, at 6:00 every morning, every person has a choice of "wait in line until 9:00 am for raspberries" or "don't". But then if everyone who waits gets raspberries, then you'd expect either everybody or nobody to join the line. Or maybe the coffee is only given to the first 100 people in line? Or only given to the people who join the line after the first 100? Yeah I got nothin. Maybe I'm missing something though. Edit: maybe if you include the cost of providing the raspberry subsidy, the numbers line up? In the first case, that would be $1.00 x 75 more people, so the cost would go up to $146.50, while in the second case that would be $5.00 x 15 more people, bringing the social cost to $109.00. So yeah, still not sure what's going on. There's probably some configuration of assumptions which yields a social cost of exactly $100 without needing magic numbers, but I'm sure not finding it. |