Thinking on the Margin & Birthday Cake

Marginal thinking is a key concept in economics, but it is often one that is misunderstood. Most of our thinking is in fact on the margin, so it is a concept already baked into our understanding. (Sorry for the cheesy pun).

I’ll use icing a birthday cake for as the example for today. Imagine that you are making your friend a typical birthday cake: yellow cake with chocolate icing. You’ve made the cake and are going to add the icing. Your decision isn’t WHETHER to ice the cake, it is HOW MUCH to ice the cake.

First you make your two layers of cake. When it is cool, you put a thin layer of icing on top (called a crumb coat). After the crumb coat, you stick it in the fridge for 20 to 30 minutes. This allows the base layer to harden a bit and the final layer of icing to go on smoothly. After a bit of time, you take your cake out of the fridge. While you could serve the cake as is, with just a thin level of icing you don’t feel that it will be enough.

How much icing should you add? Well it’s obvious: you add just enough icing so that the icing amount balances with the cake. In other words, you add just enough so that the additional benefit from the tastiness of the icing doesn’t take away from the cake. Too much icing and you are left only tasting icing. Too little icing, and you taste buds are left wanting a little more sweetness.

In economic terms, you could think of this as your marginal benefit and marginal cost. Each amount of icing you add to the cake brings a bit more sweetness (the marginal benefit), but each amount also takes away from tasting the cake (the marginal cost). If the benefit from adding a little more icing (the marginal benefit) outweighs the additional cost of not tasting the cake as much, then … you should add more icing! As soon as you get to the point where the benefit of the next bit of icing would be less than the additional cost of taking away from the cake, then you should stop. Thus, you should continue to add icing until the marginal benefit is just equal to the marginal cost. That will be your optimal amount.

This analysis is used in your economics class when discussing profit maximization. As a firm produces and sells more, its revenue continues to increase. Each additional revenue is its marginal revenue. Each additional unit produced also has a cost. If the additional revenue is greater than the additional cost (MR > MC), the firm should continue producing. As soon as the next unit has a greater additional cost than additional revenue, the firm should not produce any more. (Aka: profit max occurs where marginal revenue is just equal to marginal cost).

It's almost like a seesaw. Your optimal cake occurs where the seesaw is horizontal. If the left side (the marginal benefit) is greater, then you could do better by adding a little more icing, lowering the marginal benefit of the icing.

Add a touch more icing... the marginal benefit of a little more icing falls and the marginal cost rises. We are getting closer to equilibrium! Here is an important time to point out that just because marginal benefit is falling, doesn’t mean that total benefit is falling. In fact, as your seesaw is getting closer to horizontal, you are getting closer to that max point.

You continue adding more icing (increasing production) as the marginal benefit falls and marginal cost rises. You stop when you get to that sweet spot:

There are a couple common mistakes when thinking about profit maximization. First, you are not trying to maximize revenue: that would mean you have all icing and no cake (the marginal benefit definitely is less than the marginal cost at that point). Another is that you are trying to minimize costs. In this scenario, that would mean you don’t use any icing. That doesn’t sound optimal… who wants birthday cake without icing?

So... remember... just keep adding icing until the marginal benefit of icing is just equal to the marginal cost of adding the icing.

*Special thanks to Spencer Clouatre for this post idea!

Classic Birthday Cake

Today I'm not going to write out a recipe. Rather, I'll refer you to a recipe I've tried now a couple of times, and it always gets excellent reviews. In fact it is King Arthur Flour's 2019 Recipe of the Year!

My big tip is to use parchment paper when making cakes! I used some old cake pans when I made this last weekend, and the cake really had a hard time coming out of the pan. I've never had issues when I've used parchment paper.

Enjoy! Happy birthday! And remember, marginal benefit = marginal cost!