Friday, January 21, 2011

The economics of muffins or, why I love Ash

To eat all the muffins at once, or not: a discussion of rational decision-making

By A. Knittel

Objective: To determine whether to save all the muffins for later, eat all the muffins now, or to define a mixed strategy, saving some of the muffins and eating some now.

Analysis: When a fresh batch of muffins is prepared, the rational individual is faced with a series of decisions about the fate of said muffins. Saving the muffins for a later time would ensure that the individual had a ready supply of snacks, but the muffins lose value because they become something to be enjoyed in the future (and so are discounted). Eating all of the muffins in one sitting, however, invokes the possibility of diminishing returns. After eating 9 muffins, eating the 10th does not bring the same level of joy that the first did.

Given this dilemma, the rational muffin eater is left with the following options: a series of differential equations estimating the maximum utility for a given number of muffins, or a game theoretic model where one player aims to eat all the muffins immediately, the other aims to save all the muffins, and the optimal strategy for each is a mixed one.

Conclusion: The maximum muffin utility clearly occurs when there is a balance between the amount of time, though both analytic approaches require calibration using observed preferences for muffin eating.

Acknowledgements: I would like to thank Ash for providing critical comments during the development of this manuscript. She deserves most of the credit, though any remaining errors are my own.

Many of you know that I listen to a lot of podcasts each week. I listen while I walk the dog (2 x 15-45 minutes x 7 days), I listen while I ride the bus (2 x 10-20 minutes/day x 5 days), I listen while I cook dinner (20-50 minutes x 3-5 days), and sometimes I listen while I knit or while I work out (30-90 minutes x 1-2 days). Having done the quick math, you’ll realize that I listen anywhere between 6.5 and 21 hours each week. One of my favorites is the Planet Money Podcast that started at the peak of the financial crisis, but which has expanded to cover a variety of topics from an economic point of view. In recent months I’ve also added the Freakonomics Podcast to my repertoire. Though I am by no means an economist (and become frustrated when they try to take over disciplines I care about), I do enjoy a bit of the economics every now and then. Enter Ash.

As many of you know, I enjoy Ash all the time. She is on my short list of the most awesome people ever for a variety of reasons, none the least of which is her ability to highlight the econometric potential of every situation. By way of explanation for the above, the following is a (slightly modified) conversation:

Me: Um... I just paid $2.50 for a muffin. I think I might bake some stuff tonight to bring into school.

Ashleigh: Seems wise.

Me: Can you freeze things like muffins easily?

Ashleigh: Yes. They aren't quite as good, but they do freeze well.

Me: I think the freezing would not only be the best option for storage at school, but would eliminate the "I feel a tiny bit hungry so I’ll eat 10 muffins from my desk" option.

Ashleigh: But muffins taste so good at desks.

Me: But i think the literature is clear that the 10th muffin is less good than the 1st (when they are eaten all at once).

Ashleigh: Yes, that's true.

Me: So if i freeze them and bring them in then I can eat 1 at a time at my desk.

Ashleigh: Maximum utility from the set number of muffins... depending on the discount rate.

Me: How would the discount rate apply to muffins?

Ashleigh: Well, if you enjoy immediate gratification like the rest of the humans... there will be a muffin discount rate. I'm pretty sure there will be a positive one in this case.

Me: I see. So the pain and suffering of waiting for the next muffin will diminish the enjoyment compared to just eating them all.

Ashleigh: Basically the principle of a bird in the hand is worth 2 in the bush.

Me: A muffin in the hand is worth 10 in the freezer? But what if you have 1 in your hand AND 10 in the freezer? Then it is a question of whether the future discounting is more than the diminishing return, right?

Ashleigh: Yes, you've got it.

From there we may or may not have spent a total of several hours trying to work through the differential equations (which got ugly quickly) and also some game theoretic models, each time reaching the conclusion that we needed more concrete information about the preferences.

Basic Muffins

adapted from How to Cook Everything, by Mark Bittman

3 tablespoons melted butter, canola oil, or other neutral oil
2 cups all-purpose flour
1/4 cup sugar
3 teaspoons baking powder
1 egg
1 cup of milk (I used a mixture of rice milk and water... I really need groceries...)
1/2 cup hazelnuts
1/2 cup raisins
1/2 cup frozen strawberries

Preheat the oven to 400F and grease a muffin tin. Chop the hazelnuts, raisins, and strawberries in the food processor. I did them separately, but you could probably just throw everything in there. Mix the dry ingredients and set them aside. Beat together the egg, milk, and butter/oil. Dig a space in the dry ingredients, and pour the wet ingredients into it. Using a spatula, combine the ingredients by stirring and folding rather than beating, and stop as soon as all the dry ingredients are moistened. The better should be lumpy and thick, but quite moist. Stir in the nuts, raisins, and berries.

Spoon the batter into the greased tin, filling them about 2/3 full (avoiding further mixing of the batter). Bake 20 to 30 minutes, until they are browned and a toothpick comes out clean. Serve warm (even if you freeze them; Ash recommends toasting after they are thawed).

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