Consumer Optimum Consumption: Marginal Utility per Dollar Spent

Consumer Choice and Behavioral Economics

Consumer Optimum Consumption: Marginal Utility per Dollar Spent - Video Tutorials & Practice Problems

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Consumer Optimum Consumption: Marginal Utility per Dollar Spent

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Alright. So now let's consider how we can optimize consumption. When we're thinking about utility and marginal utility. So we can say that a consumer's optimum consumption, it's gonna represent the maximum utility we want to get the most utility possible within our budget, right? We're gonna have our budget constraint, but we want to get as much utility as we can out of that. Uh that amount of income. Okay. So when we think of optimum consumption and we're dealing with utility and marginal utility, we're gonna see that the optimum consumption occurs where marginal utility per dollar. So we want to see how much marginal utility we get per dollar spent is equal for both goods. We want an equal marginal utility per dollar for both goods. So we're gonna think about marginal utility per dollar because different goods have different prices, Right? So if we're gonna spend more on something that brings more utility, we have to consider how much extra we spent for that, right? So we want to go buy a per dollar basis, how much utility we get. So let's go here and let's talk about breakfast bill spends all his income. $10 on eggs and coffee, eggs cost $2. Coffee costs $1 right? $10 of income eggs cost to coffee costs one and then he's got some marginal utilities. These numbers would have to be given to you. There's no way you would know what breakfast bills, marginal utility would be from eating eggs and drinking coffee. Okay. So these numbers have to be given to you what is the optimum consumption. So we've got different number of eggs and then different marginal utility. And notice what's happening as he eats more and more eggs. Right? The quantity of eggs is increasing that marginal utility decreases, Right? And that's what we would expect. The diminishing returns as you eat more and more. Those last units aren't providing as much satisfaction. So, let's go ahead and calculate our marginal utility per dollar for each of these products. Okay? So the eggs cost $2 right? The price for the eggs was $2. So let's find a marginal utility per dollar. That first egg cost us $2 but it brought 20 marginal utility. So per dollar. We got 20 divided by the $2. Right? We have to spend $2 on it to get 20 marginal utility. So per dollar. We got 10 marginal utility. All right. How about the next one when we have 16 marginal utility. Well, 16. And we spent an extra $2 to get that egg right to get that second egg cost us an extra $2. So, we're dealing with the situation with eight marginal utility per dollar. Right? And we're not combining. It's not four total dollars for two eggs. It's two extra dollars for the second egg when we already have one egg. Right? So marginal utility per dollar. Third one. Now we've got 10 utility and we're spending $2 to get that. Well, that's five per dollar. Moving right along. Six divided by the $2 is 32 divided by the $2 is one and one divided by the $2. Well, that is that's gonna be half. Okay, so that is our marginal utility per dollar for eggs. Let's do the same thing with coffee. But remember the price of coffee is $1 right? So we're just gonna be dividing by one in all these cases. So the marginal utility per dollar is just equal to the marginal utility because the price is one. Right? So it would be 20 divided by 1 15 divided by 1, 10 divided by one. We would just end up with the same numbers. Ok. So remember what I said, optimum consumption, it's gonna be where marginal utility per dollar is equal for both goods. So where do we see marginal utility per dollar equal for both goods? Well, here's one where this one is 10 and this one is 10. So an optimum consumption would be one egg and three coffees, right? But there's other ones. Look at this one right here, three eggs and four coffees is also another situation where we reach optimum consumption And another one here, right? four eggs and uh and five coffees also does that for us. Okay, so notice in all these situations we are going to be able to maximize our our utility, but it depends on our income. What can we afford which of these packages can we afford with our $10 income. Alright. So what I want to do first is I want to show you how this package, this best best scenario package is going to be our optimum consumption by showing you some other consumption bundles. Okay. So let's start here where we have five eggs and zero coffee. And this is something we can afford five eggs times the $2 cost, that's $10, right? We can afford that within our income budget. So how much utility would we get from those five eggs? Well, we would get 20 from the first one, right? The marginal utility right here, this would be what we would get the first one. We need one egg and have 20 utility. Then we get another 16 we get another 10, another six and another two. Alright. So how much is this is gonna be 36 46 54. Alright. So 50 for utility from that package and he spent all $10. How about if he gives up one of those eggs and he gets some coffee. So we're still gonna be in a situation where we are spending all our income. Four eggs, times $2 is eight plus right? Four eggs plus two coffees, times $1 is +28 plus two. We're still spending all of our money. So let's see how much utility we get from this package. So in this case we're gonna have four eggs and two coffees. Right? So let's see what we get. We're gonna get 20 plus 16 plus 10 plus six from the eggs. And then from the coffee we're gonna get 20 plus 15. Alright so that's gonna be our utility there. And let's see what we get. 36 46 50 to 72. Oh man. This is really pushing my mental math right now, 87. Okay, 87 from four eggs and two coffee. I'm just gonna pull out a calculator just in case stuff. It's handy dandy for next time. How about the next one here we've got three eggs and four coffee, noticed this was one of our optimum consumption situations. Right? That was where marginal utility per dollar was five for each of the cases. Right? So if we have three eggs and four coffees, we are at our optimum consumption for this level of income. And we just so happen to be at the right level of income here. Right? We're gonna have three eggs, times $2 plus four coffees, times $1. Well three times two is six plus four is 10. Alright, so we're still spending all of our income. Now let's see how much utility we get in this case. So three eggs, we're gonna have 20 plus 16 plus 10 and four coffees. So we're gonna get 20 plus 15 plus 10 plus five. Okay so how much utility is this? This one's going in the calculator. So 20 plus 16 plus 10 plus 20 plus 15 plus 10 plus 5 96. I hope I did that right? Because I used the calculator at that time. So notice 96. That is more utility than all these other packages. If you tried other combinations of eggs and coffee within the $10 limit, you would see that this is the maximum amount. And that's because the marginal utility utility per dollar is equal in this case. Alright. So just just to reiterate notice here, when we have one egg and three coffees, right? This would be a budget of one egg being one times $2 plus three times $1. Well, this would be a budget of $5 here. Two plus three Is $5. And when we had one egg notice that was this situation, one egg and three coffees. That is an optimum consumption when we have $5, that would be what we would want to consume. Okay, let's do the same thing with four eggs and five coffees. Right? This was where four eggs we had three marginal utility per dollar. Five coffees. Three marginal utility per dollar. Let's see how much this cost. Four times the $2 plus five times $1. Right? That's gonna be $8.13. So, if we had $13 in our budget, that would be our optimum consumption. But bundle right there with four eggs and five coffee. Okay, so that's gonna be the clear cut way you do the marginal utility per dollar and you find where they're equal for both goods. All right. And just see if it's purchase herbal within your budget. Alright, cool. Let's go ahead and move on to the next video.

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Problem

Problem

As Caffeinated Carl consumes additional cups of coffee, his

A

Marginal utility from coffee increases

B

Marginal utility from coffee decreases

C

Total utility from coffee decreases

D

Both (b) and (c) are correct

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Problem

Problem

Hollywood Slim consumes movies and popcorn. If his marginal utility per dollar from movies is 8 and his marginal utility from popcorn is 7,

A

Total utility is maximized

B

Marginal utility is maximized

C

Total income must increase in order to reach an optimum consumption

D

Total utility could increase by buying more popcorn and less movies

E

Total utility could increase by buying more movies and less popcorn