Marginal Analysis

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.

$$\begin{gathered} OptimalConsumptionoccurswhenMarginalUtility=MarginalCost \\ or \\ MU=MC \end{gathered}$$

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.

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.

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?

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.

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.

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?