Marginal utllity free response example | APⓇ Microeconomics | Khan Academy

We are told that Teresa consumes both bagels and toy cars, and they tell us that the table above shows Teresa's marginal utility from bagels and toy cars. The first question is, what is her total utility from purchasing three toy cars? So pause this video and see if you can answer that.

All right, now let's work through this together. So let's just make sure we understand this table here. This says that the first bagel that Teresa consumes, she gets eight units of marginal utility from that. Then the second bagel, she gets a little bit less marginal utility; some of her big bagel craving has already been satisfied by that first one. The marginal utility goes down a little bit for the third bagel, and then that keeps happening for each incremental bagel.

On the toy side, we see that for the first toy, she gets a lot of marginal utility: 10. Then the next toy gets a little bit less, and you see that the marginal utility for each incremental toy gets lower and lower. Now, let's answer the first question: what is her total utility from purchasing three toy cars? Well, that first toy car, she gets utility of 10. Then that second toy car, she gets a utility of 8. For that third toy car, her marginal utility for that incremental car is 6.

So the total utility is going to be 10 plus 8 plus 6, which is what? 10 plus 14, this is going to be equal to 24 units of marginal utility. All right, now let's do part two. Teresa's weekly income is 11. The price of a bagel is two dollars, and the price of a toy car is one dollar. What quantity of bagels and toy cars will maximize Teresa's utility if she spends her entire weekly income on bagels and toy cars? Explain your answer using marginal analysis.

So once again, pause this video and see if you can figure that out. All right, now let's do this together, and I'll scroll down a little bit so I have some space. The key thing is that once we know the price of a bagel and the price of a toy, and we know the marginal utility for every incremental bagel or toy, we can figure out our bang for our buck. We can figure out what is going to be the marginal utility per dollar from that incremental bagel and that incremental toy car.

So we can, let's just explain first. Teresa will maximize her marginal utility per incremental dollar when making purchases on the margin. We can write over here: bagel marginal utility per dollar, and that will be one row here. Then we could write car or toy marginal utility per dollar. Let me set up these rows right over here. We could think about it: if she, for the first one, for the second one, for the third one, for the fourth one, let's see, if we go up to the sixth, the fifth one, and then we go to our sixth one.

So let's start with bagels. Bagels cost two dollars. The first bagel gives her eight marginal utility units; that’s going to be four marginal utility units per dollar (8 divided by 2). For the second bagel, she gets seven units, but it costs two dollars, so it's seven divided by two units per dollar, which is 3.5. Then, 6 divided by 2 is 3. 5 divided by 2 is 2.5, and for 4 divided by 2, it is 2. So that fifth bagel has two marginal utility units per dollar, and that sixth bagel at three divided by two is 1.5 marginal utility units per dollar.

Now we can think about toys: each toy is one dollar. She gets 10 marginal utility units from that first toy; it only costs her a dollar, so it’s 10 utility units per dollar. So, it is 10 there. It would be 8 here; we’re just dividing each of these by 1. Then, for 6, it’s the same: 4, 3, and 2.

Now that we've set this up, let me scroll down a little bit so I have a little bit more space. I have all the data I need. We can think about what would be rational for how she's going to spend that eleven dollars per week. Her first purchase, she's like, “Wow, from the get-go, if I'm picking between bagels and toys, that first toy has a much higher marginal utility per dollar than that first bagel.” So, she's going to start here.

Then she says, "Okay, next do I want to buy a bagel or a toy?" But even that second toy, the marginal utility per dollar is still higher than that first bagel. So then she'll buy a second toy. Then she'll think about it, and so far she's only spent two dollars, so we have a lot of money still left.

Then she'll think about, "Okay, do I want to spend that next incremental amount on a toy or a bagel?" Well, still, she gets more marginal utility per dollar from the toy, so she'll spend that. She's spent three dollars so far: one dollar, two dollars, and three dollars. Now, when she thinks about how to spend her next few dollars, she says, “Well now, I'm indifferent between bagels and toys; the marginal utility per dollar is the same."

So she might spend the next one on a toy and then right after that, she'll go to bagels finally and buy a bagel. Let's think about how much she has spent so far. She spent four dollars on toys and two dollars on bagels, so the order might look something like this. Then she goes and maybe buys her bagel, and now the marginal utility per dollar for that incremental bagel is higher than for her next toy.

So then she’ll probably buy another bagel right here. Let's see how much money she has spent. Two bagels are four dollars, plus she spent four dollars on toys, so that’s a total of eight dollars. She still has three dollars to spend. Now, her marginal utility per dollar is neutral between bagels and toys; between the incremental third bagel and that fifth toy, she's indifferent between the two.

So she could probably get both of them. She might do something like that; she could buy that or she could do that in the other order. Let's see how much money she spent: she has spent five dollars on toys and six dollars on bagels. So, she has spent her eleven dollars.

To answer the first question, she would buy five toys and three bagels based on this strategy of maximizing marginal utility per dollar for each incremental purchase. Did I answer all the questions? So we said the quantity of bagels and toys that will maximize her marginal utility if she spends her weekly income, and then we have explained using marginal analysis. Yup, we're looking good.