Marginal utility free response example

- [Instructor] We are told that Theresa consumes both bagels and toy cars and they tell us that the table above shows Theresa's marginal utility from bagels and toy cars. And 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 lets work through this together. So let's just make sure we understand this table here. So this says that the first bagel that Theresa consumes, she gets eight units of marginal utility from that. Then the second bagel, she gets a little bit less marginal utility. Some or her bagel craving has already been satisfied by that first one. And then the third bagel, the marginal utility goes down a little bit and then that keeps happening for each incremental bagel. And on the toy side, we see that that first toy, she gets a lotta marginal utility, 10, and then the next toy gets a little bit less, and then you see that the marginal utility for each incremental toy gets a little bit lower and lower. So 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 eight. And then that third toy car, her marginal utility for that incremental car is six. So the total utility is going to be 10 plus eight plus six, 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. Theresa's weekly income is $11, the price of a bagel is $2, and the price of a toy car is $1. What quantity of bagels and toy cars will maximize Theresa'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. I'll scroll down a little bit so I have some space. So the key thing is, is when 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? And so we can, let's just explain first. So Theresa, Theresa will maximize, maximize her marginal utility per incremental dollar, per dollar, or let me put it this way, per dollar, when making purchases on the margin, making maybe, making purchases on the margin. So her next incremental purchase, her next incremental, incremental purchase. So we can write over here bagel marginal utility per dollar. That'll be one row here. And then we could write car or toy marginal utility per dollar. And then we set up these rows right over here. And then 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 we go up to six, fifth one, and then we go to our sixth one. So let's start with bagels. Bagels cost $2. So that first bagel, if she gets eight marginal utility units, well that's going to be four marginal utility units per dollar, eight divided by two. So that's four units per dollar, and then that second bagel, she gets seven units but it costs $2, so it's seven divided by two units per dollar. So that's going to be 3.5. And then six divided by two is three, five divided by two is 2.5, four divided by two is two. So that fifth bagel, two marginal utility units per dollar, and then that sixth bagel, three divided by two is 1.5 marginal utility units per dollar. And now we can think about toys. Each toy is $1. So if she gets 10 marginal utility units from that first toy, it only cost her $1, so it's 10 utility units per dollar. So it's 10 there. It would be eight here. We're just dividing each of these by one. So six here, so this is gonna be the same number again. Four, three, and two. So now that we set this up, and 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 her if we're thinking about how she's gonna spend that $11 per week. Her first purchase, she's like wow, from the get go, that 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, and then she says, okay next do I wanna 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 $2, so we have a lot of money still left. Then she'll think about okay, do I wanna spend that next incremental amount on a toy or bagel? Well still, she gets more marginal utility per dollar from the toy, so she'll spend that. She's spent $3 so far, $1, $2, $3. And now, when she thinks about how to spend her next few dollars, she says, well know I'm indifferent between bagels and toys. The marginal utility per dollar is the same. So she might maybe spend the next one on a toy and then right after that, she'll go to bagels finally and buy a bagel. Well let's think about how much she has spent so far. She's spent $4 on toys and $2 on bagels. So the order might look something like this, and 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, and so then she'll probably buy, she would buy another bagel right here, and let's see how much money she has spent. Two bagels are $4 plus she's spent $4 on toys because they're $1 each, so it's $8. So she still has $3 to spend. Now, her marginal utility per dollar is neutral between bagels and toys, between the incremental, the third bagel and that fifth toy, so she's indifferent between the two. So she could probably get both of them. So she might do something like that, buy that, and then she could buy that or she could do that in the other order. And let's see how much money she's spent. She has spent $5 on toys and she has spent $6 on bagels, and so she has spent her $11. And so to answer the first question, so she would buy, she would buy five toys, five toys, and three bagels, and three bagels based on this strategy of maximizing marginal utility per dollar for each incremental, incremental purchase. Did I answer all of the questions? 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. Yep, we're looking good.