A simple production model of my breakfast

This morning, I had a vegetarian quiche for breakfast. It was delicious, but also surprising. The filling of the quiche was mostly mushroom and spinach, with very little egg. I love mushrooms. However, the defining feature of a quiche is egg, and normally the egg to mushroom ratio in a quiche would be much more in favour of egg, rather than mushroom. What led to this delicious and unexpected treat? It turns out that a very simple model of production, as covered in the first week of my ECONS101 class, can help explain.

That model is shown in the diagram below. It shows different combinations of egg and mushroom that can be used to make a vegetarian quiche, with mushroom measured on the y-axis and egg measured on the x-axis. Let's say that there are only two recipe options for the bakery, A and B [*]. Recipe A uses a lot of egg (EA) and not much mushroom (MA), while Recipe B uses not much egg (EB) and a lot of mushroom (MB).

Which recipe should the bakery use? If the bakery is trying to maximise profits, then given that both recipes produce the same quantity (one quiche), the bakery should choose the recipe that has the lowest cost. [**] We can represent the bakery's costs with iso-cost lines, which are lines that represent all the combinations of mushroom and egg that have the same total cost. The iso-cost line that is closest to the origin is the iso-cost line that has the lowest total cost. The slope of the iso-cost line is the relative price between mushroom and egg - it is equal to -Pe/Pm (where Pe is the price of eggs, and Pm is the price of mushrooms).

Now think about that relative price. Eggs are currently priced very high (see here and here), so the relative price (-Pe/Pm) is a large number (in absolute terms). That makes the iso-cost lines relatively steep, as shown in the diagram below by ICA and ICB. In this case, the iso-cost line that passes through B (ICB) is the lowest iso-cost line. It is closer to the origin than the iso-cost line that passes through A (ICA). So, Recipe B is the lowest cost recipe, and the bakery should choose Recipe B.

However, eggs are not usually as expensive as they are right now. In 'normal' times, the relative price (-Pe/Pm) would be a smaller number (in absolute terms), because the price of eggs would be lower. That would mean that the iso-cost lines would be relatively flatter, as shown in the diagram above by ICA' and ICB'. In that case, the iso-cost line that passes through A (ICA') is the lowest iso-cost line. It is closer to the origin than the iso-cost line that passes through B (ICB'). So, Recipe A is normally the lowest cost recipe, and the bakery should normally choose Recipe A.

So, that explains my surprising and delicious breakfast. Normally, if I got a vegetarian quiche, it would be mostly egg with a bit of mushroom (Recipe A). But, now that eggs are relatively more expensive, I got a quiche that was mostly mushroom with a bit of egg (Recipe B). Delicious!

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[*] In the standard version of this model, A and B would be referred to as production technologies. In this case, it makes more sense to refer to them as recipes.

[**] We're assuming here that the bakery wouldn't change its price, depending on which recipe they used. It is costly to change prices (economists refer to these as menu costs), so the bakery would prefer to keep prices the same, even if the prices of eggs and mushrooms are fluctuating from week to week.