Utility Maximization

Consumer choice is based on the idea that people make decisions to maximize their happiness, or utility. The utility maximizing quantity of a good or service can be found when the marginal utility of that product is 0.

This cornerstone of economics can be framed in any form of financial decision, whether it be deciding between spending on movie tickets and going out to eat, or deciding how much to invest in capital, like factories and machinery.

Example:

Those three tennis courts, the four swimming pools, and the porcelain fountain imported from Milan? You own them all. Not to mention a G6 with a hot tub and your own basketball team. So...think of your resources as being, well, infinite. More or less. Utility maximization wouldn't come up much in your life. That is, you’re not too worried about using your pencil after you’ve sharpened it so that it’s only 2 inches long. You just toss it, rather than use another inch.

Utility maximization has to do with decisions consumers make as they spend their limited resources. You get a modest paycheck; you have to figure out how to divide it up. You’ve got rent, food, utilities, entertainment, and all the other stuff you need to live.

So the basic question with regard to utility maximization: how do consumers budget their spending in order to get the most out of it? In other words: how do they maximize utility? Utility maximization has to do with value, or rather, how you allocate precious resources so they produce the most value to you, the consumer. Or, said another way, how consumers get the most satisfaction from the spending of their hard-earned dollars.

Another question: how many gold-plated toilets is Jeff Bezos, founder of Amazon, limited to buy? Answer: he isn’t. The guy has a couple hundred billion dollars in Amazon wealth, so he doesn’t spend a nanosecond worrying about resource allocation. He just buys what he wants. “No, no, no, Mr. Yacht Broker, I’ll take two of ‘em.” But a normal person would probably not take both the pink and the green Buffy and Muffy yachts. In fact, they wouldn’t even be able to afford one. Normal people have constrained budgets and, before they spend their dough, they predict a given level of satisfaction they'll “achieve” from hitting that “Buy now!” button. What they have to spend is essentially a kind of mathematical constraint on their happiness, or utility, or ability to make their life better. So everything in their mindset begins from their financial foundation, i.e. a “budget.”

You're an Average Joe liberal arts major. Your big tradeoff choices might be more about buying ramen noodles in bulk or getting the soft toilet paper. (Hint: buy the Ramen. You can always borrow toilet paper from the Burger King bathroom.) This dynamic is called a budget constraint.

Utility maximization is all about budget choices. The goal of utility maximization is get the most total value from the money you have available to spend. Going back to the bulk ramen...you have $50. It's your last $50 and it has to last you nine days until your next paycheck comes. Costco, the discount retailer, has super-bulk boxes of ramen on sale. The cost for one year’s worth of noodles? $50. Which is great...but for the fact that you will be evicted in an hour, and the cost to remain in your hovel under the freeway for 9 more days happens to be exactly $50.

So you have a tradeoff here. You can either eat, or you can be sheltered, but you can’t do both. So in theory, there should be a tradeoff you could make, where maybe you share a cardboard box for $25 for 9 days with someone, and spend the remaining $25 on noodles that will get you through until you can collect your next paycheck, as you rue the day you committed to being a liberal arts major. Because economists are economists, they have a bunch of mathematical formulas to optimize the budget allocation of your precious dollars. The basic notion behind this math revolves around the idea that consumers will allocate their money so that they get the most marginal utility for each dollar they spend.

Okay, last concept for understanding utility maximization: marginal utility. Marginal utility is the amount of extra use you get out of buying more of something. Like…you need some ramen to keep you alive. But you don’t need 40 pounds of it to keep you alive for 9 days. A storage locker full of ramen won't do you much good; it would just sit around, doing nothing. One pair of pants is good for keeping your legs warm and making sure you don't get arrested. But 1,000 pairs of pants is just wasteful. There's not much marginal utility being gained from that thousandth pair of Dockers.

So utility maximization involves trying to get the most value out of limited resources, such that the n+1th unit then begins to decline dramatically in value. Like…if you need 2,000 calories a day to basically maintain your current weight, and one packet of ramen is 500 calories, then if you need to survive 9 days, you’ll want 4 packets a day for 9 days, or 36 packets to just keep you alive until your next payday. At that point, you hope you can afford to make a change in your life and lifestyle. But for now, you realize that you would probably die, or at least suffer greatly, if you went with no ramen for all 9 days, and just tried to survive on water. You would gain great utility from having at least one packet a day for 9 days, but you’d realize that you’d have lost so much weight in living on 500 calories a day that the storage locker of 1,000 Dockers would have almost no pants that fit you anymore. You would continue to gain meaningful marginal value from the 2nd and 3rd packets of ramen per day, getting you to 1,500 calories a day, such that you might only lose a few pounds over the course of 9 days, until you get to that golden paycheck. After 4 packets a day, the value of those ramen noodles begins to decline massively. Or, said another way, their marginal utility approaches zero.

This set of calculations mirrors the marginal utility value model, with the goal of getting the most marginal utility out of each dollar. Or the most ramen out of each dollar, which is…actually quite a bit of ramen.