Consumer Optimum Consumption: Marginal Utility per Dollar Spent - Online Tutor, Practice Problems & Exam Prep

To achieve maximum utility within a budget, consumers must equalize marginal utility per dollar spent across goods. For example, if eggs cost $2 and coffee $1, calculating marginal utility per dollar helps identify optimum consumption bundles. This involves diminishing returns, where additional units yield less satisfaction. By comparing combinations, such as 3 eggs and 4 coffees, consumers can maximize utility while adhering to budget constraints. Understanding these principles aids in making informed consumption choices, reflecting concepts like consumer surplus and opportunity cost in economic decision-making.

Consumer Optimum Consumption: Marginal Utility per Dollar Spent

Alright, so now let's consider how we can optimize consumption when we're thinking about utility and marginal utility. We can say that a consumer's optimum consumption represents the maximum utility. We want to get the most utility possible within our budget, right? We're going to have our budget constraint, but we want to get as much utility as we can out of that amount of income, okay? So when we think of optimum consumption and we're dealing with utility and marginal utility, we're going to see that the optimum per dollar spent is equal for both goods. We want equal marginal utility per dollar for both goods. So we're going to think about marginal utility per dollar because different goods have different prices, right? If we're going to 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 by a per dollar basis, how much utility we get. So let's talk about Breakfast Bill. He spends all his income, $10, on eggs and coffee. Eggs cost $2, coffee costs $1, right? $10 of income, eggs cost 2, coffee costs 1, 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 Bill's 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 a different number of eggs and then different marginal utility and notice what's happening. As he eats more and more eggs, 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. 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∕12 marginal utility. How about the next one? When we have 16 marginal utility, well, 16∕12 and we spent an extra $2 to get that egg. We're calculating it as 8∕12 marginal utility per dollar, right? And we're not combining. It's not 4 total dollars for 2 eggs, it's 2 extra dollars for the second egg when we already have 1 egg. Let's continue for each subsequent egg: 10∕12, 6∕12, 2∕12, and 1∕12 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 going to be dividing by 1 in all these cases, so the marginal utility per dollar is just equal to the marginal utility because the price is $1, right? It would be 20, 15, 10, etc.

Now, remember what I said, optimum consumption, it's going to be where marginal utility per dollar is equal for both goods. So where do we see marginal utility per dollar equal for both goods? Here's one where this one is 10 and this one is 10. So an optimum consumption would be 1 egg and 3 coffees, right? But there are other ones. Look at this one right here, 3 eggs and 4 coffees is also another situation where we reach optimum consumption and another one here, right? 4 eggs and 5 coffees also does that for us. So notice in all these situations, we are going to be able to maximize our utility, but it depends on our income. What can we afford? Which of these packages can we afford with our $10 income? So what I want to do first is show you how this package, this best scenario package, is going to be our optimum consumption by showing you some other consumption bundles.

Let's start here where we have 5 eggs and 0 coffee and this is something we can afford. 5 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 5 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'd eat 1 egg and have 20 utility, then we'd get another 16, we'd get another 10, another 6, and another 2. Alright. So how much is this? This is going to be 36, 46, 54. How about if he gives up one of those eggs and he gets some coffee? So we're still going to be in a situation where we are spending all our income. 4 eggs times $2 is 8, plus 2 coffees times $1 is 2, 8 +2, we're still spending all our money. So let's see how much utility we get from this package. So in this case, we're going to have 4 eggs and 2 coffees. So let's see what we get. We're going to get 20 plus 16 plus 10 plus 6 from the eggs and then from the coffee, we're going to get 20 plus 15. Alright. So that's going to be our utility there, and let's see what we get. 36, 46, 52, 72 oh man, this is really pushing my mental math right now. 87. If we have 3 eggs and 4 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 going to have 3 eggs times $2 plus 4 coffees times $1. Well, 3 times 2 is 6 plus 4 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 3 eggs, we're going to have 20 plus 16 plus 10, and 4 coffees. So we're going to get 20, plus 15, plus 10, plus 5. 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 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 per dollar is equal in this case. Alright, so just to reiterate, notice here when we have one egg and 3 coffees, this would be a budget of 1 egg being 1 times $2 plus 3 times $1, well this would be a budget of $5 here. 2 plus 3 is $5 and when we had 1 egg notice that was this situation, 1 egg and 3 coffees. That is an optimum consumption. When we have $5 that would be what we would want to consume. Let's do the same thing with 4 eggs and 5 coffees, Right, this was where at 4 eggs, we had 3 marginal utility per dollar, 5 coffees, 3 marginal utility per dollar. Let's see how much this costs. 4 times the $2 plus 5 times $1. Right? That's going to be 8 plus 5, $13. So if we had $13 in our budget, that would be our optimum consumption bundle right there with 4 eggs and 5 coffee. So that's going to be the clear-cut way, you do the marginal utility per dollar and you find where they're equal for both goods. Alright? And just see if it's purchasable within your budget. Alright, cool. Let's go ahead and move on to the next video.

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

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

Here’s what students ask on this topic:

What is marginal utility per dollar spent and why is it important in consumer choice?

Marginal utility per dollar spent is the additional satisfaction (utility) a consumer gains from spending one more dollar on a good or service. It is calculated by dividing the marginal utility of a good by its price. This concept is crucial in consumer choice because it helps consumers allocate their budget in a way that maximizes their total utility. By equalizing the marginal utility per dollar spent across all goods, consumers can ensure they are getting the most satisfaction possible from their limited income. This principle guides decisions on how much of each good to purchase, reflecting the idea of diminishing returns and budget constraints.

How do you calculate the marginal utility per dollar spent for different goods?

To calculate the marginal utility per dollar spent for different goods, you need to know the marginal utility of each good and its price. The formula is:

$\frac{\mathrm{MU}}{P}$

where $\mathrm{MU}$ is the marginal utility of the good and $P$ is the price of the good. For example, if the marginal utility of eggs is 20 and the price is $2, the marginal utility per dollar spent on eggs is:

$\frac{20}{2}=\; 10$

This calculation helps consumers compare the utility they get from spending money on different goods, guiding them to the optimal consumption bundle.

What is the principle of diminishing marginal utility and how does it affect consumer choices?

The principle of diminishing marginal utility states that as a consumer consumes more units of a good, the additional satisfaction (marginal utility) gained from each additional unit decreases. This affects consumer choices by influencing how they allocate their budget. As the marginal utility of a good decreases with each additional unit consumed, consumers will shift their spending to other goods that provide higher marginal utility per dollar spent. This behavior helps consumers maximize their total utility within their budget constraints, ensuring they get the most satisfaction from their limited income.

How do budget constraints impact the optimum consumption bundle?

Budget constraints limit the amount of money a consumer can spend, affecting their ability to purchase goods and services. The optimum consumption bundle is the combination of goods that maximizes a consumer's total utility within their budget. To find this bundle, consumers compare the marginal utility per dollar spent on different goods and allocate their budget to equalize this value across all goods. By doing so, they ensure they are getting the most satisfaction possible from their limited income. Budget constraints force consumers to make trade-offs and prioritize spending on goods that provide the highest marginal utility per dollar.

Can you provide an example of calculating the optimum consumption bundle?

Sure! Let's say a consumer has $10 to spend on eggs and coffee. Eggs cost $2 each, and coffee costs $1 each. The marginal utilities for eggs are 20, 16, 10, 6, and 2, while for coffee, they are 20, 15, 10, 5, and 1. To find the optimum consumption bundle, we calculate the marginal utility per dollar for each good:

For eggs: 20/2 = 10, 16/2 = 8, 10/2 = 5, 6/2 = 3, 2/2 = 1

For coffee: 20/1 = 20, 15/1 = 15, 10/1 = 10, 5/1 = 5, 1/1 = 1

We look for combinations where the marginal utility per dollar is equal. One such combination is 3 eggs (10, 8, 5) and 4 coffees (10, 5, 5, 5), which costs $10 and provides maximum utility.