# Marginal Analysis

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## Marginal analysis definition

What is Marginal Analysis? Simply put, it's the process of deciding if the benefit, or happiness, of consuming a bit more of something, is worth the cost of acquiring a bit more of that thing.

More technically put, Marginal Analysis is the process of determining the optimal level at which to pursue an activity by comparing its marginal benefits to its Marginal Cost, or the cost of purchasing one more unit of that activity (MC).

Marginal Analysis is the study of the trade-off between the costs and benefits of doing a little bit more of an activity.

Alternately stated, marginal analysis is the process of breaking decisions about consumption, or continued consumption, into 'yes' or 'no' answers, and the 'yes' or 'no' depends on how the happiness achieved from that continued consumption compares to the cost of acquiring the continued consumption.

Any consumption activity should continue until the happiness one gets from consuming one more unit of an item is equal to the cost associated with acquiring one more unit of that item.

For example, if you went to the store to buy freshly baked cookies, you'd have to mentally calculate at what point the cost of one more cookie, its marginal cost (MC) or Price (P), would be greater than the happiness you'd experience from that additional cookie.

When it comes to Consumer Choice, Economists call the happiness generated by consumption "utility" and the utility generated by consuming a bit more is called "Marginal Utility".

The marginal utility of a good or service is the change in total utility generated by consuming one additional unit of that good or service.

Implicit in this process is the idea that the more one consumes of something, the less happiness one gets from it.

This is what Economists call Diminishing Returns. In the case of Marginal Analysis with respect to Consumer Choice, Economists call this the Principle of Diminishing Marginal Utility.

The principle of diminishing marginal utility states that the additional utility a consumer gets from one more unit of a good or service decreases as the amount consumed of that good or service increases.

To put it in more ordinary terms, the more of a good or service you consume, the closer you get to being satisfied, or to the point where an additional unit of the good adds little or nothing to your satisfaction.

Can you think of examples where the marginal utility of consuming a bit more of something is actually negative?

In the cookie example, we recognized that the utility of the first bite of the first cookie is greater than the utility of the first bite of the tenth cookie. What if you ate so many cookies that you had stomachache afterwards? This would be an example of consumption that leads to negative utility!

Do you find the concepts of Marginal Analysis, Marginal Utility (MU), and Diminishing MU, intuitive, or self-evident? If so, Economists would consider you a rational person indeed!

## Marginal analysis formula

According to the principle of Marginal Analysis, every activity should continue until the marginal utility (MU) of consuming a bit more equals the marginal cost (MC) of consuming a bit more, or until MU = MC.

$OptimalConsumptionoccurswhenMarginalUtility=MarginalCost\phantom{\rule{0ex}{0ex}}or\phantom{\rule{0ex}{0ex}}MU=MC$

In fact, Marginal Analysis plays a central role in economics because the formula of doing things until the marginal benefit no longer exceeds the marginal cost is the key to deciding “how much” to do of any activity!

As you might have guessed, the purpose of Marginal Analysis is to help Economists determine, or model, how people make optimal decisions when it comes to consumption.

Another important idea in applying Marginal Analysis is to ask if a person is made better off by spending an additional dollar on a good, and if so, by how much.

To answer this question we must calculate the MU per dollar spent on an item.

The Marginal utility per dollar spent on a good equals the Marginal utility of one unit of the good divided by the Price of one unit of the good:

$M{U}_{dollar}=\frac{M{U}_{good}}{{P}_{good}}$

Economists measure the utility of consuming a particular good in a unit called 'util'.

## Marginal analysis example

Let's look at a numerical example to help us understand the idea of marginal utility (MU), diminishing marginal utility, marginal cost (MC), and Marginal Analysis.

Assume that each freshly baked cookie costs $2.00. Let's also say you only had$20. At what point do you suspect you will have maximized your total utility while also staying within your budget constraint of $20? Table 1 below shows us, in numerical terms, how much each additional cookie, up to 10 cookies, contributes to total utility, and therefore the Marginal Utility that each additional cookie generates. We also look at the Marginal Utility per Dollar in the last column to see how that compares to the Marginal Utility relative to the Price of the cookies. This concept will be key when making optimal consumption decisions between more than one good. Cookies (Price of Cookies is$2.00 per Cookie)
00
2010.0
120
189.0
238
168.0
354
136.5
467
105.0
577
63.0
683
21.0
785
-3-1.5
882
-8-4.0
974
-14-7.0
1060

Table 1. Marginal Analysis - Marginal Utility per Dollar - StudySmarter

As you can see, column 2 shows "Utility from Cookies (utils)" and that, while total utility initially increases, it does so at a decreasing rate. Furthermore, at a certain point, the total utility actually starts decreasing. This can be seen in column 3 "Marginal Utility per Cookie (utils)." Column 3 numerically demonstrates the idea of diminishing MU, where the first cookie provides 20 utils, but the eighth cookie actually becomes negative 3 utils!

Why would the MU of one more cookie be negative? Well, as you can imagine, by the time you start eating the eighth cookie, not only does it not bring additional happiness but actually brings you more unhappiness. This may be because you've developed a stomach ache from all the cookies or a toothache from the sugar. It's not a strange concept after all that too much of a good thing could end up providing negative MU.

What else can we determine from Table 1?

Well, most importantly, we can determine the optimal number of cookies you should buy.

Recall that the formula for optimizing a consumer decision is to find the point where the MU is equal to the MC.

As we can see from Table 1, the consumption of a seventh cookie produces exactly 2 utils. Therefore, 7 cookies is the optimal consumer choice in this example, because the cost of one additional cookie is equal to 2$! You might have noticed that the point where MU equals MC is also the point where Total Utility is maximized. This is not a coincidence! Marginal analysis is used in many instances in Economics, but all with the intent of maximizing some value. You might have also noticed that the total expenditure is$14 (assuming the optimal choice of 7 cookies), which means the consumer has stayed within their budget with some money to spare.

## Marginal analysis importance

The importance of Marginal Analysis in Consumer Choice theory can't be overstated.

It underpins the key concept that it is possible for consumers to achieve an ideal state given the constraints they face in terms of a limited budget.

Marginal Analysis is also very important because of the assumptions underlying the theory which tell us quite a bit about human behaviour

• The first assumption is that consumers make buying choices based on calculated decisions about what will make them the happiest, or maximize their utility.
• The second key assumption is that consuming infinite amounts of something does not produce unlimited utility because of diminishing marginal utility. In other words, the amount of happiness you get from a good decreases the more you consume of that good such that the utility you receive from eating your first cookie is greater than the utility you receive from eating the tenth cookie.
• Note, that the optimal quantity that the consumer chooses does not depend on any fixed costs or benefits that were previously incurred by the consumer.
• Lastly, since Economists believe consumers are rational, they expect consumers to utilize marginal analysis to make optimal consumption decisions. Therefore, Economists believe that all consumers consume up to the point where the Marginal Utility of consumption equals the Marginal Cost of consumption thereby maximizing utility.

## Marginal analysis rule

If you're wondering why the concept of marginal utility (MU) per dollar is important, let's consider another more realistic example.

Let's say you only had $20, and you had a sweet tooth. Let's also assume that, for you, the most effective goods at satisfying your sweet tooth are either cookies or ice cream cones. Assuming you're a rational consumer, which you already showed to be true, how would you make the decision of how much ice cream to purchase versus how many cookies? If you answered Marginal Analysis, you are correct. More specifically, in this scenario, we will use the concept of MU per Dollar. At what point do you suspect you will have maximized your total utility when having to choose between cookies and ice cream cones and facing a budget constraint of$20?

When choosing between two goods, rational consumers will consume additional units of each until the MU per Dollar is equal between the two goods.

In order to find the optimal consumption bundle with marginal analysis, we have to ask the question of whether the consumer can increase their utility by spending a little bit more of his income on cookies and less on ice cream cones, or

by doing the opposite.

In other words, the marginal decision in this situation becomes a question of how to spend the marginal dollar when choosing between cookies and ice cream cones in a way that maximizes utility.

The first step in applying marginal analysis in this scenario is to ask if the consumer is made better off by spending an additional dollar on either good and if so, by how much?

Let's consider another numerical example as seen in Table 2. Table 2 below shows us, in numerical terms, how much each additional cookie contributes to total utility, and therefore Marginal Utility, as well as how much each additional ice cream cone contributes to total utility and MU.

Cookies (Price of Cookies is $2 per Cookie)Ice Cream Cones (Price of Ice Cream Cones is$3 per Cone)
Quantity of CookiesUtility From Cookies (utils)Marginal Utility per Cookie (utils)Marginal Utility per Dollar (utils)Quantity of Ice Cream ConesUtility From Ice Cream Cones (utils)Marginal Utility per Cone (utils)Marginal Utility pre Dollar (utils)
0000
2010.0258.3
120125
189.0206.7
238245
168.0155.0
354360
136.5103.3
467470
105.051.7
577575
63.000.0
683675
21.0
785
-3-1.5
882
-8-4.0
974
-14-7.0
1060

Table 1. Marginal Analysis - Marginal Utility per Dollar for Two Goods - StudySmarter

Let's use Table 1 to understand some concepts.

First, we know that if we were making the optimal choice for cookies and the optimal choice for ice cream cones separately, we would choose 7 cookies where MU equals 2 and MC equals 2, and we would choose 5 ice cream cones where MU equals 5 and MC equals 3. Note that if we choose one more ice cream cone, the MU is 0 which is less than MC so we would never make that choice.

In this case, notice that the total utility in the cookie case is 85, while the total utility in the ice cream case is 75.

But what if we wanted to see if we could increase that total utility by choosing a bundle of cookies and ice cream cones?

In the case of choosing the optimal bundle of goods, we would consume one more unit of each good to the point where the MU per Dollar was equal for both goods.

In Table 2 we can see that the optimal bundle occurs when the MU per Dollar for both goods is 5.0, with 5 cookies, and 3 ice cream cones.

Now let's stop here and notice something really interesting. When we optimize the bundle of cookies and ice cream cones using the rule of MU per Dollar (cookies) equals MU per Dollar (ice cream cones), the total utility of that combination is 77 from the cookies plus 60 from the ice cream cones. The total utility when we optimize the bundle is 137! Almost double the total utility of choosing cookies and ice cream cones independently.

Also note that, at 5 cookies and 3 ice cream cones, the consumer has spent $19, just under the$20 budget.

The optimal consumption bundle when choosing between two goods is achieved when the MU per Dollar of Good 1 is equal to the MU per Dollar of Good 2.

$M{{U}_{d1}}_{}=M{{U}_{d2}}_{}$

Try it for yourself!

See if you can find any other combination that generates a greater amount of total utility given the \$20 budget.

This is the power of Economics. It allows Economists to model and identify optimal behaviours and outcomes. Did you know Economics was going to be this cool?

## Key takeaways

• Marginal Analysis is the study of the trade-off between the costs and benefits of doing a little bit more of an activity.
• The Marginal Utility (MU) of a good or service is the change in total utility generated by consuming one additional unit of that good or service.
• The principle of diminishing MU states that the additional utility a consumer gets from one more unit of a good or service decreases as the amount consumed of that good or service increases.
• Optimal consumption occurs where marginal utility (MU) equals marginal cost (MC) or where total utility is maximized.
• The MU per dollar spent on a good can be calculated by dividing the MU generated by one unit of a good by the Price of that unit of the good.
• The optimal consumption bundle when choosing between two goods is achieved when the MU per Dollar of Good 1 is equal to the MU per Dollar of Good 2.

#### Flashcards inMarginal Analysis 35

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What is marginal analysis?

Marginal Analysis is the study of the trade-off between the costs and benefits of doing a little bit more of an activity.

What are the benefits of marginal analysis?

Marginal analysis allows Economists to model and identify optimal behaviours and outcomes in the face of limited resources.

What are the rules of marginal analysis?

The rules of marginal analysis are:

1. Optimal consumption of a good occurs when the marginal utility and the marginal cost of consuming a bit more of that good are equal.

2. When choosing between two goods, optimal consumption of the bundle of these two goods occurs when the MU per Dollar is equal between the two goods.

What are the main assumptions of marginal analysis?

The main assumptions of marginal analysis are:

1. Diminishing Marginal Returns - the additional utility a consumer gets from one more unit of a good or service decreases as the amount consumed of that good or service increases.

2. Optimal Consumption of a good occurs at the point where the marginal utility of consuming a bit more of that good is equal to the marginal cost of consuming a bit more of that good.

How do you determine marginal analysis?

You determine marginal analysis at the point where the benefits of consuming a bit more of something are equal to the costs of consuming a bit more of that thing.

## Test your knowledge with multiple choice flashcards

Optimal consumption occurs when marginal cost is equal to:

The Marginal utility per dollar of a good equals the Marginal utility of one unit of the good _______ by the price of one unit of the good

If I'm considering buying one more shirt, and the marginal utility of buying one more shirt is 20 utils, I would only buy one more shirt if:

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