Moulton Lava

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Location: New England, United States

Friday, October 31, 2014

The Parable of the Egg Man

Moulton's Boarding House has 12 residents. Every Sunday, Moulton serves brunch for the boarders (which includes a fresh egg). Moulton has a standing order with the Egg Man to deliver a dozen fresh eggs a week. The Egg Man employs a neighborhood urchin named Dennis to deliver fresh eggs from the Egg Man's cold storage warehouse.  Dennis gets paid a penny an egg for each one-way trip. So Dennis expects to earn 12¢ for each weekly delivery of a carton of eggs from the cold storage facility to Moulton's boarding house.

About once a month, one of Moulton's boarders misses the regular Sunday brunch to join his girl friend at another boarding house. But the peripatetic boarder also invites the girl friend to join him the following week for brunch at Moulton's table. Thus, most Sundays there are 12 people for brunch, but about once a month there are only 11, and about once a month there are 13 at the table.

Alas Moulton never knows which Sunday there will be an empty chair, and which subsequent Sunday there will be an extra person at the table. When Dennis comes with the standard carton of a dozen eggs, Moulton sometimes says, "I only need 11 eggs this week. Please take one of them back to cold storage.  And next week you can bring me 13 fresh eggs."

The accountant for the Egg Man notices that, at the end of the year, Moulton's Boarding House purchased 52 dozen eggs, as expected. But the delivery charges from Dennis come to $6.42 (for transporting 54 dozen eggs) rather than $6.24 (for delivering 52 dozen eggs). Dennis explains to the accountant that there were twenty-four occasions (twice a month) where he either carried one egg back to the cold storage facility or one extra egg to Moulton. As far as the Egg Man is concerned, Moulton purchased 52 dozen eggs over the course of a year. But as far as Dennis is concerned, he transported 54 dozen eggs — 53 dozen in the usual direction, and one dozen in the alternate direction. So he is owed $6.42 for his labors transporting eggs over the rough cobblestone streets. The Egg Man thus had an extra cost of 24¢, over and above his expected cost of $6.24 for paying Dennis to deliver eggs. The Egg Man ended up paying 3.85% more to Dennis than he would have expected if there had not been any perturbations in the number of boarders at Moulton's table.

Moral:  There's no such thing as a free brunch.

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