Latticework of Mental Models: Law of Diminishing Marginal Utility

“Chocolates!” replied Soham, my nephew, with a glint in his eyes. That was his response to my question “What is happiness?”

“So you think the secret of happiness lies in chocolates?” I quizzed him further.

“Yeah! It’s bliss,” he blurted while going around in circles in his tricycle.

“Bliss?” I thought to myself, “That’s quite a mouthful of adjective coming from a five year old.”

“Okay! Here is a chocolate. Tell me if it makes you happy?”

“Thanks Mamaji (that’s what he calls me),” he screamed as he literally snatched it from my hand and in no time the chocolate was gone. He was ecstatic. May be he was right. Chocolate is bliss.

“So if one chocolate makes your happy, more chocolates should make you more happy. Isn’t it?” I was attempting to play Socratic Solitaire (the tradition of asking question that helps somebody discover the wisdom) with an unsuspecting kid.

“Yes…more bliss!” he quipped, while making bigger circles with his tricycle and relishing the after taste of the first eclair. Where in the world did he learn this word ‘bliss’, I wondered.

“All right. So here is another chocolate and let me know if this one makes you more happy than the first one?”

With this move, I thought I was just a few steps away to make the kid realize the futility of materialism. However, what the smart alec inside me didn’t know that in next few minutes, that little boy was going to stump me with his raw intellect.

“Very happy!” he screamed again and gulped the second eclair too.

After two more chocolates, as I expected, Soham’s excitement for the chocolates dwindled and he didn’t look interested in the fifth chocolate.

I started telling him, “So you see, you don’t want the fifth one as much as you wanted the first chocolate. It means happiness is not in chocolates.”

I expected a blank stare from him followed by the expression where the truth dawns upon him. Instead what he said left me dumbfounded.

“No. It’s not in all chocolates. Happiness is in the first four chocolates,” and he took off in his super bike leaving me with my chocolates and the seed for a remarkable insight.

The insight, of course, was about an important mental model from the field of economics. It’s called the Law of Diminishing Marginal Utility.

For the rest of this post, we will use the acronym DMU because it saves screen space, computer memory, internet congestion, and my keyboard strokes. 😉

Let me define DMU now. As a person increases consumption of a product – while keeping consumption of other products constant – there is a decline in the marginal utility that the person derives from consuming each additional unit of that product.

In other words, for each additional unit of a good (in my nephew’s case, a piece of chocolate) the added satisfaction you receive from consuming the good decreases.

Let’s deconstruct it and look at each term in isolation first. What does the term “utility” mean?

In economics, scientists are concerned with examining issues of the supply and demand of goods and services. This theory assumes that people are perfectly rational and make choices about purchasing goods or services depending on what is in their best self-interest.

And how do you measure what is in someone’s best self-interest? This is where the concept of utility comes in. Think of utility as the benefit a person gets from consuming a good or service. For Soham, utility was the satisfaction he gained from eating chocolates.

Now imagine how utility changes (increases or decreases) as a person consumes more of the same good. In Soham’s case, the utility was the highest for the first piece of chocolate. Even the second and third chocolates delivered the same utility as the first one. However, the satisfaction he got from the fourth piece was definitely not as high as the first three. As a result, he refused the offer for the fifth chocolate.

It is important to understand that the concept of utility is a relative one. As a kid, I probably had a higher threshold than Soham and would have accepted half a dozen more eclairs. Different people gain different levels of satisfaction from eating chocolate depending on their preferences.

My friend, Jana has penned a useful post on this concept using the example of pizza consumption.

Let’s explore some areas where DMU surfaces in the world around us.

DMU and Buffet (not Warren!)
I am sure you must have been to one of those “all you can eat” food buffet restaurants offering wide array of food items. Have you wondered how do they manage to provide you so much quantity and variety for such reasonable prices?

Buffet restaurant owners would not make the promise of unlimited food if they weren’t going to make a profit. The simple truth is, they know a secret. And the secret is that we can’t eat all.

Why? DMU, buddy!

Restaurant owners know all too well that each additional plate of food provides less utility than the plate before. By the time we get to our second or third serving, we’re so full that eating anything extra will actually harm us (dis-utility). So, in reality, there is no such thing as all you can eat because we simply cannot eat it all.

By the way, did you know that Coca Cola’s (yes, that caffeinated, celebrity promoted, black coloured sugar syrup) flavour is designed in such a way that it leaves very little aftertaste in your mouth, which means your marginal utility of coke consumption doesn’t diminish as rapidly as it should with any other sugared drink. That is, unfortunately though, the beauty of Coca Cola’s product.

Let’s talk about something other than food.

DMU and Taxes
Benjamin Franklin once said –

In this world nothing can be said to be certain, except death and taxes.

I don’t know about death (haven’t experienced it yet) but there is an interesting rationale behind progressive tax rates. Progressive taxation results when the rate of taxation increases with an increase in income. The logic is based on the assumption that the rich have lower marginal utility of money as compared to the poor people. Hence the rich should be taxed higher.

Loss aversion and DMU
Once you get a hang of DMU, it’s easy to understand Daniel Kahneman’s loss aversion theory which states that losses hurt more than gains feel good. Simply put, the pain generated by a loss of Rs 100 would be more than the pleasure of gaining Rs 100.

This explains why people’s fear of loss is much greater than desire to gain.

Look at the graph above. It shows how the utility goes down with every incremental step. To summarize the graph, if Rs 100 is added to your wallet which already contains two hundred rupees, it gives you a pleasure worth of 15 units. Another hundred, and your pleasure increases by a relatively smaller amount, i.e., 10 units. And so on.

When somebody moves from point B to point A, the utility derived by getting Rs 100 is 15 units. Whereas when one moves from point A to point C, 10 units of utility is derived by gaining Rs 100.

In the same graph, if we start from point A and move towards point B, loss of Rs 100 sets us back by 15 units of utility. On the contrary, if we move from point A to point C, a gain of Rs 100 fetches us a utility of 10 units. So the loss of Rs 100 is heavier, in terms of utility, than a gain of Rs 100. That proves the loss aversion theory. (please see the update on this at end of this post)

DMU in Business and Investing
The concept of marginal utility is also useful in thinking about the idea of marginal cost in businesses. Marginal cost is the cost of producing one more unit of a good. In general terms, marginal cost at each level of production includes any additional costs required to produce the next unit.

For a business which sells software products, the marginal cost of an extra piece of end product is close to zero. However, for a typical brick and mortar business, selling tangible products like FMCG, the marginal cost of additional product is significant.

Consider social networks like Facebook, Twitter or Linkedin. The marginal cost of signing up one additional member is close to zero. But each new member brings non-zero, sometimes pretty substantial, value to the entire network. In general, marginal cost favors businesses that have differentiated products and brand names.

So, extending the above logic, if a manufacturer wants to make a decision about producing more, it should keep producing unless the per unit revenue is less than the marginal cost of production (assuming that all products can be sold). However, this strategy can be fatal for commodity type of business, where every competitor cuts prices so that the price hovers just above the marginal cost.

Airlines is a great example of being victim of marginal cost. So much so that, Charlie Munger calls them ‘marginal cost with wings’.

Many researches have proven that DMU is applicable in case of portfolio construction also. Having multiple stocks in your portfolio decreases the risk of permanent capital loss. However, every additional stock in your portfolio brings down the risk in diminishing order. So much so that, after certain point (many expert suggest that number to be 20), the risk doesn’t decrease at all by adding more stocks.

Increasing Marginal Utility
Your knowledge about an idea, or mental model, isn’t complete until you know where it fails to work. What’s more important, than an idea itself, is the knowledge about its limitations.

Charlie Munger said –

I never allow myself to have an opinion on anything that I don’t know the other side’s argument better than they do.

So let’s see where DMU doesn’t work. Many a times the marginal utility or the marginal cost remains constant with additional unit of consumption. Can you think of an example?

If you buy 1 kg of gold bar for x rupees, how much would you have to spend for 2 kg of gold? 2x. And the equation is linear. No DMU here!

Can you think of an example where the marginal utility not just stays constant but increases with each additional unit of consumption? Some of you might be tempted to say “alcohol”. Well, I like the way you think but I am calling it a dry day today. 😉

Diamond! The price of a 10 carat diamond is not twice the price of a 5 carat diamond. In fact, the price for every additional carat increases pretty rapidly and non-linearly.

“Anshul, can we please talk about something other than jewelry and Jack Daniels?” I hear your concerns. Okay, how about stock market?

In stock market, when somebody wants to buy a meaningful stake in a company, perhaps with an intention of acquiring control, the marginal utility of every additional share and its cost increases. That’s why most of the acquisitions happen at a large premium to the current market price.

We can call this phenomenon as the law of increasing marginal utility. I am not sure if this term is recognized by economists so lets just keep it between you and me.

Oh, I almost forgot to mention. The pleasure I derive out of writing this Latticework series – that follows the law of increasing marginal utility for me. How about you? I hope it’s not DMU for you.

Conclusion
What we learnt today is that people aggressively place a lower value to each additional unit of something that they get in increasing abundance.

I am sure you can spot many other use cases where this mental model applies. I would be glad to hear from you.

We’ve had some great insights shared by our tribe members in previous posts. Let’s not lose the momentum. I urge you to keep the ball rolling. Let it become a snowball. A snowball of learning and worldly wisdom.

Take care and keep learning.

Update: One of the tribe members pointed out an error in my attempt to explain DMU and Prospect Theory using the same graph. Please read the snippet of the email exchange here.