Heresy: Disbelieving Demand Theory Part 2

To briefly recap where we stood yesterday:

I like drinking coffee
My first cup is a lot more valuable to me that my seventh.
I’m measuring my satisfaction/value/derived-joy in “utils”.
I have this graph to show how much extra satisfaction I get from each additional cup of coffee:

Just to reiterate: what we’re doing is trying to find is an explanation of how we ascribe value. And it may surprise you (it surprised me) to hear that marginal utility theory has its roots in Aristotle. Which must mean, obviously, that Aristotle was first and foremost the father of economics. On that bombshell…

The Next Step

So when I drink coffee, I can ascribe some arbitrary measure of value (measured in utils) to every cup that I drink.

And at this point, I would make this observation: everything is arbitrary without context.

That, and value is always relative.

The classic example: “How long is a piece of string?”

The answer would begin by asking for context (Are you talking about this piece of string or that piece of string?), and it would measure it by referencing something else (It’s as long as the room, or it’s 5 metres*, etc).
*Interestingly (I learned this from a podcast), if you measured the piece of string in metres, then you would be referencing light. Specifically, a metre is “the length of the path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second”. And a second is defined as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”. I feel like I should be repeating the word “arbitrary”.

The point is: talking about 3 utils for my first cup of coffee is utterly meaningless until I reference something else.

So let’s do it. By pretending that someone wakes me in bed and says:

“Because you’re my favourite person in the Universe, I left the house early and have returned bearing gifts. Specifically: a triple-shot latte, and chocolate and pistachio slice from Starbucks. You can have one, and I’ll have the other. Which would you like?”

I sit in torturous consternation, because I really want both. Eventually, unable to pick between them, I say this to the gift-bearer:

“You choose.”

What can we say here? We can say that, for me, the utility I derive from the coffee is the same as the utility that I derive from the slice. And presto: a triple shot latte is worth roughly a chocolate pistachio slice, and vice versa.

1 × triple shot latte = 1 × chocolate pistachio slice

It even works in Canada

If I can define the value of a cup of coffee in terms of chocolate pistachio slices; by extension, it means that I can define anything in terms of almost anything else.

And it has fun implications. Aero conducted a survey in Canada (here’s the article) which found that 40% of Canadian women would give up sex and alcohol before they gave up chocolate. We may joke about everyone having a price… But on the assumption that sex happens once a week, and chocolate bars happen once a day: 40% of Canadian women are ready to party for a literal box of chocolates.

And seeing as Canadian men valued sex as five times more important than chocolate, it sounds to me like everyone is getting a good deal!

Taking It One Step Further

Economists are never happy to leave a relative value proposition on the table without extrapolating it. And if I’m to return to the cup of coffee and chocolate pistachio slice example, they would tell me that I’m aiming too low with the cake.

Idea: replace the cake with everything else that you would use.

That is: how does my cup of coffee stack up against everything else that I derive utility from?

That’s easy. If I was only allowed to have a single cup per day, then it would represent at least 5% of my general happiness quota.

1 × triple shot latte = 0.05 × everything else

Okay – it wasn’t that easy to get that number. But here’s my justification:

My main pleasure is food. So that’s worth at least half of my daily happiness.
Then shelter, clothing, and other necessities – probably also close to half, but a little less than food.
Leaving my cup of coffee at +/- 5% of my daily allocation of awesome.

And let’s assume that I’m a minimum wage worker in America (earning about $7.50 per hour) that works 8 hours per day. My daily wage is therefore $60, meaning that all my daily achievable utils (ie. utility maximisation) are collectively equal to $60.

So if I’m to attach a price that I’m willing to pay for my first cup of the day, it’d be 5% of $60 – or $3*.
*Yes, it’s conveniently equal to my number of utils. I cheated!

Given that, if I redraft the graph up top to reflect a monetary value for cups of coffee (always remembering that “money” is just a convenient unit of transaction – being society’s way of measuring the value of something relative to everything else), then I get this:

Ta-dah!

My demand curve for coffee:

If a coffee costs $3, then I’ll only buy one cup.
If a coffee costs $2, then I’ll buy two cups (And I’ll be very happy – because my first cup is worth 3 utils, my second is worth 2 utils, in total that’s 5 utils – and I only paid $4 for that*).
*in case you’re wondering, that extra util and/or relative $1 saving? It’s called my “consumer surplus”.
And so on.

Getting to Market Demand

When you take everyone’s individual marginal utilities curves, translate them into individual demand curves, and aggregate those together: you get: