All of us have been to buffets.
Imagine that you’ve paid for one of your favourites, and now you are in.
How do you decide how much to eat?
To simplify the problem, let’s assume there’s only one type of food. Your benefits curve is probably going to look something like the following.
Initially as you first start eating, you feel really good and thus the total benefit increases rapidly. As you eat more and more, you start getting a little full and that succulent slice of sashimi just doesn’t taste as nice as it did at the start. You are still benefiting from eating more, but just less than before.
Eventually, you get to the point where you are so full that the food starts to make you feel a little bit queasy. The benefits from eating at this point actually starts to fall. Yikes!
Well fortunately, this is not rocket science, and we all know that we should stop eating right when we start feeling bloated (or whenever you think your benefit curve is going to start coming down).
But is there a more systematic way to think about the problem?
Introducing the Concept of Marginal
The curve we have drawn above is the total benefits curve. It shows how much benefits you receive for all the combined units of food consumed.
But we could have drawn a different curve and thought about the problem in a slightly different way. Say, what is the change in total benefits from consuming an additional unit of food? Economists have gave this measure a special name — marginal benefit.
Marginal benefit is defined as the additional satisfaction that a person receives from consuming an additional unit of a good or service.
To help you understand this more clearly, here’s a possible (and approximate) set of total and marginal benefits from the above example.
|Quantity of food||Total Benefits||Marginal Benefits|
As you can see from the above, the marginal benefit falls as we consume more and eventually turns negative. Suppose we were to plot this on a graph:
So the point where which we intuitively know to stop eating in a buffet, is at the point where marginal benefits equals to 0. This is when the total benefits curve starts to decrease and come down.
Marginal and Derivatives
So yesterday in the additional questions I asked you to maximise
5x - 2x^2 + 5. Well, turns out that this curve does not look all that different from our toy example, if we just replace x by units of food and think of
5x - 2x^2 + 5 as an expression for the total benefits.
Am I losing you here?
Well take a look at the above two diagrams again. Do you notice something? The marginal benefits diagram is the derivative of the total benefits with respect to quantity!
Here’s a quick refresher of what a derivative is:
Derivative of x^2 with respect to x = 2x
Derivative of 5x – 2x^2 + 5 with respect to x = 5 – 4x
When we differentiate total benefits with respect to quantity, we get the marginal benefits!
And, if you recall, how do you find the turning point of the curve in Math? You set its derivative equals to 0.
We see the equivalent here. To get the turning point/ maximum point in the total benefits curve, we simply set the marginal benefits equals to zero and calculate the units of food (or the x-value) from there.
This mathematical approach to marginal benefit is NOT in your syllabus, but I included it because I think some of you will be able to relate to this better. It uses concepts from secondary math that most of you should still have some memory of. But please don’t let it faze or worry you if you can’t grasp this!
In summary, the marginal benefit is defined as the change in the total benefit from adding additional unit of something. It can also be defined derivative of total benefits with respect to the quantity.
Question of the Day
In the buffet example given, when should you stop eating and why?
The answer to yesterday’s question is d — We do not have enough information to decide. All three decisions can potentially be consistent with rationality. We have deliberately left out the key part of the question — what is the next best alternative? Imagine the alternative available was to spend $10 on a meal and get $30 worth of benefits. Choosing a or b would thus be irrational.
- What if instead of a buffet you are now at an Ala Carte restaurant? How does that change the problem?
Google “Diminishing marginal utility”. How does it relate to the above?
Not In Syllabus & Advanced: When does a derivative not exist? What assumptions have we made here implicitly?
We look forward to seeing your responses in the comments section below!
And if you have yet to subscribe to the daily 5 Minutes Only Lah!, you can read more about it here or simply subscribe below.
Till next time, dream economics.
Anyone remotely interesting is mad, in some way or another.