Utility maximization example

Here we have an actual free response question from a previous AP Economics exam, and it tells us utility and price elasticity of demand are important concepts in explaining consumer behavior. I buy that! Now, part A, they say define marginal utility. So before I do that, pause the video and at least think about it. How would you define it in your head? Or even better, try to write it down in words, because this is what you would actually have to do on an AP exam.

So, we've defined it in previous videos with more depth, but if I were taking the exam, I would write something like the incremental benefit or gain or satisfaction from one more unit of something. I think that is a good definition or shorthand for marginal utility. The marginal tells us that's what's for the next thing, not in total, but just for the next thing that you're going to get. How much gain or satisfaction are you going to have?

Now let’s try part B. The table below shows the quantities, prices, and marginal utilities of two goods, fudge and coffee, which Mandy purchases. So we see, I guess so far, she's bought ten pounds of fudge and seven pounds of coffee. Fudge is two dollars a pound, coffee is four dollars a pound, and then the marginal utility of the last pound of fudge is 12 and it’s 20 for coffee.

This is interesting because you notice marginal utility doesn't have units; it tends to be unitless. It kind of has your marginal utility units, and what matters more is how it might compare from the first pound to the second pound as opposed to the absolute value here. But we're going to, I'm suspecting, before even reading this, that we're going to make use of this in some way in this next part of this question.

Mandy spends all her money and buys only these two goods. In order to maximize her utility, should Mandy purchase more fudge and less coffee, purchase more coffee and less fudge, or maintain her current consumption?

Okay, so some of you might immediately say, "All right, I'm just going to look at how much gain satisfaction she gets for the next pound of coffee versus the next pound of fudge." It looks pretty clear that 20 is higher than 12, and so you'd say, "All right, she should just buy more coffee." But that would be a mistake, and to realize it let me give you another example.

If your marginal utility of a Rolls Royce is going to be higher than the marginal utility of a strawberry, so if you use a lot that logic that you just directly compare marginal utilities, you would always buy more Rolls Royces and less strawberries. The key idea here is what matters is marginal utility per dollar or marginal utility divided by price. Then all of a sudden a strawberry might be able to compete a little bit more with the Rolls Royce.

So, we want to do the exact same thing here, and on a test like the AP exam, you definitely want to show your work. So let's say for fudge, we could calculate the marginal utility per price. It’s going to be equal to, here they give the utility of the last pound. I guess this could be indicative of also the next pound, so this is going to be 12 divided by two dollars, which is equal to six.

Then for coffee, the marginal utility divided by price is going to be equal to 20 divided by four, which is equal to five. And so I would say that Mandy—so I would circle that—and I would say Mandy should buy or purchase more fudge by more fudge to maximize her utility, because the marginal utility per dollar is higher than coffee, and we'd be done.